Multiple-criteria decision analysis

205:: These problems consist of a finite number of alternatives, explicitly known in the beginning of the solution process. Each alternative is represented by its performance in multiple criteria. The problem may be defined as finding the best alternative for a decision-maker (DM), or finding a set of good alternatives. One may also be interested in "sorting" or "classifying" alternatives. Sorting refers to placing alternatives in a set of preference-ordered classes (such as assigning credit-ratings to countries), and classifying refers to assigning alternatives to non-ordered sets (such as diagnosing patients based on their symptoms). Some of the MCDM methods in this category have been studied in a comparative manner in the book by Triantaphyllou on this subject, 2000. 154:

solutions. A solution is called nondominated if it is not possible to improve it in any criterion without sacrificing it in another. Therefore, it makes sense for the decision-maker to choose a solution from the nondominated set. Otherwise, they could do better in terms of some or all of the criteria, and not do worse in any of them. Generally, however, the set of nondominated solutions is too large to be presented to the decision-maker for the final choice. Hence we need tools that help the decision-maker focus on the preferred solutions (or alternatives). Normally one has to "tradeoff" certain criteria for others.

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concept of "outranking relations", analytical hierarchy process, and some rule-based decision methods try to solve multiple criteria evaluation problems utilizing prior articulation of preferences. Similarly, there are methods developed to solve multiple-criteria design problems using prior articulation of preferences by constructing a value function. Perhaps the most well-known of these methods is goal programming. Once the value function is constructed, the resulting single objective mathematical program is solved to obtain a preferred solution.

42: 146:"Solving" can be interpreted in different ways. It could correspond to choosing the "best" alternative from a set of available alternatives (where "best" can be interpreted as "the most preferred alternative" of a decision-maker). Another interpretation of "solving" could be choosing a small set of good alternatives, or grouping alternatives into different preference sets. An extreme interpretation could be to find all "efficient" or " 1163: 1544: 1190: 804: 111:. On the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria. In making the decision of whether to build a nuclear power plant or not, and where to build it, there are not only very complex issues involving multiple criteria, but there are also multiple parties who are deeply affected by the consequences. 814: 104:, managers are interested in getting high returns while simultaneously reducing risks; however, the stocks that have the potential of bringing high returns typically carry high risk of losing money. In a service industry, customer satisfaction and the cost of providing service are fundamental conflicting criteria. 211:: In these problems, the alternatives are not explicitly known. An alternative (solution) can be found by solving a mathematical model. The number of alternatives is either finite or infinite (countable or not countable), but typically exponentially large (in the number of variables ranging over finite domains.) 539: 1854:

The AHP first decomposes the decision problem into a hierarchy of subproblems. Then the decision-maker evaluates the relative importance of its various elements by pairwise comparisons. The AHP converts these evaluations to numerical values (weights or priorities), which are used to calculate a score

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EMO algorithms start with an initial population, and update it by using processes designed to mimic natural survival-of-the-fittest principles and genetic variation operators to improve the average population from one generation to the next. The goal is to converge to a population of solutions which

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The achievement scalarizing function can be used to project any point (feasible or infeasible) on the efficient frontier. Any point (supported or not) can be reached. The second term in the objective function is required to avoid generating inefficient solutions. Figure 3 demonstrates how a feasible

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In Figure 1, the extreme points "e" and "b" maximize the first and second objectives, respectively. The red boundary between those two extreme points represents the efficient set. It can be seen from the figure that, for any feasible solution outside the efficient set, it is possible to improve both

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Some methods require preference information from the DM throughout the solution process. These are referred to as interactive methods or methods that require "progressive articulation of preferences". These methods have been well-developed for both the multiple criteria evaluation (see for example,

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Garnett, H. M., Roos, G., & Pike, S. (2008, September). Reliable, Repeatable Assessment for Determining Value and Enhancing Efficiency and Effectiveness in Higher Education. OECD, Directorate for Education, Programme on Institutional Management in Higher Education [IMHE) Conference, Outcomes of

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The decision space corresponds to the set of possible decisions that are available to us. The criteria values will be consequences of the decisions we make. Hence, we can define a corresponding problem in the decision space. For example, in designing a product, we decide on the design parameters

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Let us assume that we evaluate solutions in a specific problem situation using several criteria. Let us further assume that more is better in each criterion. Then, among all possible solutions, we are ideally interested in those solutions that perform well in all considered criteria. However, it

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MCDM has been an active area of research since the 1970s. There are several MCDM-related organizations including the International Society on Multi-criteria Decision Making, Euro Working Group on MCDA, and INFORMS Section on MCDM. For a history see: Köksalan, Wallenius and Zionts (2011). MCDM draws

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Weakly nondominated points include all nondominated points and some special dominated points. The importance of these special dominated points comes from the fact that they commonly appear in practice and special care is necessary to distinguish them from nondominated points. If, for example, we

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Multiple-criteria design problems typically require the solution of a series of mathematical programming models in order to reveal implicitly defined solutions. For these problems, a representation or approximation of "efficient solutions" may also be of interest. This category is referred to as

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Several papers reviewed the application of MCDM techniques in various disciplines such as fuzzy MCDM, classic MCDM, sustainable and renewable energy, VIKOR technique, transportation systems, service quality, TOPSIS method, energy management problems, e-learning, tourism and hospitality, SWARA and

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or value functions are elicited and used to identify the most preferred alternative or to rank order the alternatives. Elaborate interview techniques, which exist for eliciting linear additive utility functions and multiplicative nonlinear utility functions, may be used (Keeney and Raiffa, 1976).

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The MCDM problem can be represented in the criterion space or the decision space. Alternatively, if different criteria are combined by a weighted linear function, it is also possible to represent the problem in the weight space. Below are the demonstrations of the criterion and weight spaces as

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The difficulty of the problem originates from the presence of more than one criterion. There is no longer a unique optimal solution to an MCDM problem that can be obtained without incorporating preference information. The concept of an optimal solution is often replaced by the set of nondominated

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Achievement scalarizing functions also combine multiple criteria into a single criterion by weighting them in a very special way. They create rectangular contours going away from a reference point towards the available efficient solutions. This special structure empower achievement scalarizing

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Structuring complex problems well and considering multiple criteria explicitly leads to more informed and better decisions. There have been important advances in this field since the start of the modern multiple-criteria decision-making discipline in the early 1960s. A variety of approaches and

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If we combine the multiple criteria into a single criterion by multiplying each criterion with a positive weight and summing up the weighted criteria, then the solution to the resulting single criterion problem is a special efficient solution. These special efficient solutions appear at corner

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There are methods that require the DM's preference information at the start of the process, transforming the problem into essentially a single criterion problem. These methods are said to operate by "prior articulation of preferences". Methods based on estimating a value function or using the

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or price is usually one of the main criteria, and some measure of quality is typically another criterion, easily in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider – it is unusual that the cheapest car is the most

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When the mathematical programming models contain integer variables, the design problems become harder to solve. Multiobjective Combinatorial Optimization (MOCO) constitutes a special category of such problems posing substantial computational difficulty (see Ehrgott and Gandibleux, 2002, for a

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We present the criterion space graphically in Figure 2. It is easier to detect the nondominated points (corresponding to efficient solutions in the decision space) in the criterion space. The north-east region of the feasible space constitutes the set of nondominated points (for maximization

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objectives by some points on the efficient set. Conversely, for any point on the efficient set, it is not possible to improve both objectives by moving to any other feasible solution. At these solutions, one has to sacrifice from one of the objectives in order to improve the other objective.

1158:{\displaystyle {\begin{aligned}\max f_{1}(\mathbf {x} )&=-x_{1}+2x_{2}\\\max f_{2}(\mathbf {x} )&=2x_{1}-x_{2}\\{\text{subject to}}\\x_{1}&\leq 4\\x_{2}&\leq 4\\x_{1}+x_{2}&\leq 7\\-x_{1}+x_{2}&\leq 3\\x_{1}-x_{2}&\leq 3\\x_{1},x_{2}&\geq 0\end{aligned}}} 3544:

Mardani, Abbas; Zavadskas, Edmundas Kazimieras; Khalifah, Zainab; Zakuan, Norhayati; Jusoh, Ahmad; Nor, Khalil Md; Khoshnoudi, Masoumeh (1 May 2017). "A review of multi-criteria decision-making applications to solve energy management problems: Two decades from 1995 to 2015".

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Whether it is an evaluation problem or a design problem, preference information of DMs is required in order to differentiate between solutions. The solution methods for MCDM problems are commonly classified based on the timing of preference information obtained from the DM.

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is unlikely to have a single solution that performs well in all considered criteria. Typically, some solutions perform well in some criteria and some perform well in others. Finding a way of trading off between criteria is one of the main endeavors in the MCDM literature.

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for each alternative (Saaty, 1980). A consistency index measures the extent to which the decision-maker has been consistent in her responses. AHP is one of the more controversial techniques listed here, with some researchers in the MCDA community believing it to be flawed.

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An Interactive Approach for Multi-Criterion Optimization, with an Application to the Operation of an Academic Department, A. M. Geoffrion, J. S. Dyer and A. Feinberg, Management Science, Vol. 19, No. 4, Application Series, Part 1 (Dec., 1972), pp. 357–368 Published by:

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If an MCDM problem represents a decision situation well, then the most preferred solution of a DM has to be an efficient solution in the decision space, and its image is a nondominated point in the criterion space. Following definitions are also important.

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is a polyhedron defined by linear inequalities and equalities. If all the objective functions are linear in terms of the decision variables, this variation leads to multiple objective linear programming (MOLP), an important subclass of MCDM problems.

1734:: Phases of computation alternate with phases of decision-making (Benayoun et al., 1971; Geoffrion, Dyer and Feinberg, 1972; Zionts and Wallenius, 1976; Korhonen and Wallenius, 1988). No explicit knowledge of the DM's value function is assumed. 575:

There are several definitions that are central in MCDM. Two closely related definitions are those of nondominance (defined based on the criterion space representation) and efficiency (defined based on the decision variable representation).

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maximize a single objective, we may end up with a weakly nondominated point that is dominated. The dominated points of the weakly nondominated set are located either on vertical or horizontal planes (hyperplanes) in the criterion space.

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Zavadskas, Edmundas Kazimieras; Mardani, Abbas; Turskis, Zenonas; Jusoh, Ahmad; Nor, Khalil MD (1 May 2016). "Development of TOPSIS Method to Solve Complicated Decision-Making Problems — An Overview on Developments from 2000 to 2015".

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There are several ways to generate nondominated solutions. We will discuss two of these. The first approach can generate a special class of nondominated solutions whereas the second approach can generate any nondominated solution.

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Zare, Mojtaba; Pahl, Christina; Rahnama, Hamed; Nilashi, Mehrbakhsh; Mardani, Abbas; Ibrahim, Othman; Ahmadi, Hossein (1 August 2016). "Multi-criteria decision making approach in E-learning: A systematic review and classification".

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Millar, L. A., McCallum, J., & Burston, L. M. (2010). Use of the conjoint value hierarchy approach to measure the value of the national continence management strategy. Australian and New Zealand Continence Journal, The, 16(3),

788:: (in criterion space) represents the worst (the minimum for maximization problems and the maximum for minimization problems) of each objective function among the points in the nondominated set and is typically a dominated point. 1461:

points of the set of available solutions. Efficient solutions that are not at corner points have special characteristics and this method is not capable of finding such points. Mathematically, we can represent this situation as

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Different schools of thought have developed for solving MCDM problems (both of the design and evaluation type). For a bibliometric study showing their development over time, see Bragge, Korhonen, H. Wallenius and J. Wallenius .

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The purpose is to set apriori target values for goals, and to minimize weighted deviations from these goals. Both importance weights as well as lexicographic pre-emptive weights have been used (Charnes and Cooper, 1961).

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represent the nondominated set (Schaffer, 1984; Srinivas and Deb, 1994). More recently, there are efforts to incorporate preference information into the solution process of EMO algorithms (see Deb and Köksalan, 2010).

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The ideal point and the nadir point are useful to the DM to get the "feel" of the range of solutions (although it is not straightforward to find the nadir point for design problems having more than two criteria).

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MCDM is concerned with structuring and solving decision and planning problems involving multiple criteria. The purpose is to support decision-makers facing such problems. Typically, there does not exist a unique

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Sałabun, W., Piegat, A. (2016). Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome. Artificial Intelligence Review. First Online: 3 September 2016.

782:: (in criterion space) represents the best (the maximum for maximization problems and the minimum for minimization problems) of each objective function and typically corresponds to an infeasible solution. 349:

The quotation marks are used to indicate that the maximization of a vector is not a well-defined mathematical operation. This corresponds to the argument that we will have to find a way to resolve the

4047: 1727:: The purpose of vector maximization is to approximate the nondominated set; originally developed for Multiple Objective Linear Programming problems (Evans and Steuer, 1973; Yu and Zeleny, 1975). 228:"posterior articulation of preferences", implying that the DM's involvement starts posterior to the explicit revelation of "interesting" solutions (see for example Karasakal and Köksalan, 2009). 1704:

using an achievement scalarizing function. The dashed and solid contours correspond to the objective function contours with and without the second term of the objective function, respectively.

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Kylili, Angeliki; Christoforou, Elias; Fokaides, Paris A.; Polycarpou, Polycarpos (2016). "Multicriteria analysis for the selection of the most appropriate energy crops: The case of Cyprus".

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Sałabun, W. (2015). The Characteristic Objects Method: A New Distance-based Approach to Multicriteria Decision-making Problems. Journal of Multi-Criteria Decision Analysis, 22(1-2), 37-50.

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By varying the weights, weighted sums can be used for generating efficient extreme point solutions for design problems, and supported (convex nondominated) points for evaluation problems.

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Mardani, Abbas; Jusoh, Ahmad; Zavadskas, Edmundas Kazimieras (15 May 2015). "Fuzzy multiple criteria decision-making techniques and applications – Two decades review from 1994 to 2014".

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Köksalan, M.M. and Sagala, P.N.S., M. M.; Sagala, P. N. S. (1995). "Interactive Approaches for Discrete Alternative Multiple Criteria Decision Making with Monotone Utility Functions".

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There are different classifications of MCDM problems and methods. A major distinction between MCDM problems is based on whether the solutions are explicitly or implicitly defined.

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Ehrgott, Matthias; Gandibleux, Xavier (2003). "Multiobjective Combinatorial Optimization – Theory, Methodology, and Applications". In Ehrgott, Matthias; Gandibleux, Xavier (eds.).

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Another approach is to elicit value functions indirectly by asking the decision-maker a series of pairwise ranking questions involving choosing between hypothetical alternatives (

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Fuzzy sets were introduced by Zadeh (1965) as an extension of the classical notion of sets. This idea is used in many MCDM algorithms to model and solve fuzzy problems.

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Geoffrion, A.; Dyer, J.; Feinberg, A. (1972). "An Interactive Approach for Multicriterion Optimization with an Application to the Operation of an Academic Department".

534:{\displaystyle {\begin{aligned}\max q&=f(x)=f(x_{1},\ldots ,x_{n})\\{\text{subject to}}\\q\in Q&=\{f(x):x\in X,\,X\subseteq \mathbb {R} ^{n}\}\end{aligned}}} 107:

In their daily lives, people usually weigh multiple criteria implicitly and may be comfortable with the consequences of such decisions that are made based on only

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Mardani, Abbas; Nilashi, Mehrbakhsh; Zakuan, Norhayati; Loganathan, Nanthakumar; Soheilirad, Somayeh; Saman, Muhamad Zameri Mat; Ibrahim, Othman (1 August 2017).

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Karasakal, E. K. and Köksalan, M., E.; Koksalan, M. (2009). "Generating a Representative Subset of the Efficient Frontier in Multiple Criteria Decision Making".

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Amoyal, Justin (2018). "Decision analysis : Biennial survey demonstrates continuous advancement of vital tools for decision-makers, managers and analysts".

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Mahmoudi, Amin; Deng, Xiaopeng; Javed, Saad Ahmed; Zhang, Na (January 2021). "Sustainable Supplier Selection in Megaprojects: Grey Ordinal Priority Approach".

135:. Stanley Zionts helped popularizing the acronym with his 1979 article "MCDM – If not a Roman Numeral, then What?", intended for an entrepreneurial audience. 4054: 2674:

Bragge, J.; Korhonen, P.; Wallenius, H.; Wallenius, J. (2010). "Bibliometric Analysis of Multiple Criteria Decision Making/Multiattribute Utility Theory".

3467:"Application of multiple-criteria decision-making techniques and approaches to evaluating of service quality: a systematic review of the literature" 1770:

has a wide application in real-world situations. In this regard, some MCDM methods were designed to handle ordinal data as input data. For example,

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Hansen, Paul; Ombler, Franz (2008). "A new method for scoring additive multi-attribute value models using pairwise rankings of alternatives".

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Benayoun, R.; deMontgolfier, J.; Tergny, J.; Larichev, O. (1971). "Linear Programming with Multiple Objective Functions: Step-method (STEM)".

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between criteria (typically based on the preferences of a decision maker) when a solution that performs well in all criteria does not exist.

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Roughly speaking, a solution is nondominated so long as it is not inferior to any other available solution in all the considered criteria.

119:, have been developed for their application in an array of disciplines, ranging from politics and business to the environment and energy. 4671: 4443: 1981: 2460: 2211:

Weistroffer, HR, and Li, Y (2016). "Multiple criteria decision analysis software". Ch 29 in: Greco, S, Ehrgott, M and Figueira, J, eds,

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family of outranking methods that originated in France during the mid-1960s. The method was first proposed by Bernard Roy (Roy, 1968).

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Javed, S. A. (2020). "Grey Absolute Decision Analysis (GADA) Method for Multiple Criteria Group Decision-Making Under Uncertainty".

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The following two-variable MOLP problem in the decision variable space will help demonstrate some of the key concepts graphically.

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functions to reach any efficient solution. This is a powerful property that makes these functions very useful for MCDM problems.

3360:"Sustainable and Renewable Energy: An Overview of the Application of Multiple Criteria Decision Making Techniques and Approaches" 1875: 3426:"Multiple criteria decision-making techniques in transportation systems: a systematic review of the state of the art literature" 3266: 3137: 2691: 2658: 2454: 2087: 4040: 3633:"A systematic review and meta-Analysis of SWARA and WASPAS methods: Theory and applications with recent fuzzy developments" 27: 3099:

Deb, K.; Köksalan, M. (2010). "Guest Editorial Special Issue on Preference-Based Multiobjective Evolutionary Algorithms".

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is defined explicitly (by a set of alternatives), the resulting problem is called a multiple-criteria evaluation problem.

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Multi-Criteria Inventory Classification Using a New Method of Evaluation Based on Distance from Average Solution (EDAS)

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Mardani, Abbas; Jusoh, Ahmad; Nor, Khalil MD; Khalifah, Zainab; Zakwan, Norhayati; Valipour, Alireza (1 January 2015).

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solution for such problems and it is necessary to use decision-makers' preferences to differentiate between solutions.

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Mardani, Abbas; Jusoh, Ahmad; Zavadskas, Edmundas Kazimieras; Cavallaro, Fausto; Khalifah, Zainab (19 October 2015).

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is defined implicitly (by a set of constraints), the resulting problem is called a multiple-criteria design problem.

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Mardani, Abbas; Zavadskas, Edmundas Kazimieras; Govindan, Kannan; Amat Senin, Aslan; Jusoh, Ahmad (4 January 2016).

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Mardani, Abbas; Jusoh, Ahmad; Zavadskas, Edmundas Kazimieras; Khalifah, Zainab; Nor, Khalil MD (3 September 2015).

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Zionts, S.; Wallenius, J. (1976). "An Interactive Programming Method for Solving the Multiple Criteria Problem".

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In this example a company should prefer product B's risk and payoffs under realistic risk preference coefficients

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Franco, L.A.; Montibeller, G. (2010). "Problem structuring for multicriteria decision analysis interventions".

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Serafim, Opricovic; Gwo-Hshiung, Tzeng (2007). "Extended VIKOR Method in Comparison with Outranking Methods".

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Rezaei, Jafar (2016). "Best-worst multi-criteria decision-making method: Some properties and a linear model".

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Mardani, Abbas; Zavadskas, Edmundas Kazimieras; Khalifah, Zainab; Jusoh, Ahmad; Nor, Khalil MD (2 July 2016).

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Srinivas, N.; Deb, K. (1994). "Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms".

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Geoffrion, Dyer and Feinberg, 1972, and Köksalan and Sagala, 1995 ) and design problems (see Steuer, 1986).

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Malakooti, B. (2013). Operations and Production Systems with Multiple Objectives. John Wiley & Sons.

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proposed Grey System Theory (GST) and its first multiple-attribute decision-making model, called Deng's

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Mathematically, a multiple-criteria design problem can be represented in the decision space as follows:

4898: 4427: 1881: 1847: 1842:'s Absolute GRA model, Grey Target Decision Making (GTDM) and Grey Absolute Decision Analysis (GADA). 4727: 4540: 4534: 4271: 3983:"An assessment of sustainable housing affordability using a multiple criteria decision making method" 2008: 1999: 1916: 1771: 76:(both in daily life and in settings such as business, government and medicine). It is also known as 4693: 4509: 4254: 4124: 3850:

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Due to its simplicity, the above problem can be represented in criterion space by replacing the

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Figure 3. Projecting points onto the nondominated set with an Achievement Scalarizing Function

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Mathematically, the MCDM problem corresponding to the above arguments can be represented as

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Some Experiments in Machine Learning Using Vector Evaluated Genetic Algorithms, PhD thesis

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Multiple-criteria design problems (multiple objective mathematical programming problems)

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The following MCDM methods are available, many of which are implemented by specialized

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Uses and limitations of the AHP method : a non-mathematical and rational analysis

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Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems

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Operations research that evaluates multiple conflicting criteria in decision making

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Technique for the Order of Prioritisation by Similarity to Ideal Solution (TOPSIS)

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Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys

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Wiley Encyclopedia of Operations Research and Management Science

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The French school focuses on decision aiding, in particular the

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Figure 2. Demonstration of the solutions in the criterion space

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Potentially All Pairwise RanKings of all possible Alternatives

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Mathematically, we can represent the corresponding problem as

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Disaggregation – Aggregation Approaches (UTA*, UTAII, UTADIS)

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Multiple Criteria Decision Analysis: An Integrated Approach

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Revue d'Informatique et de Recherche Opérationelle (RIRO)

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Evaluation Based on Distance from Average Solution (EDAS)

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Multiple Criteria Decision Making Theory and Application

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Conflicting criteria are typical in evaluating options:

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is weakly nondominated if there does not exist another

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Grey Data Analysis - Methods, Models and Applications

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Korhonen, P.; Wallenius, J. (1988). "A Pareto Race".

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Evolutionary multiobjective optimization school (EMO)

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Organizational Behavior and Human Decision Processes

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Köksalan, M., Wallenius, J., and Zionts, S. (2011).

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Nonstructural Fuzzy Decision Support System (NSFDSS)

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is weakly efficient if there does not exist another

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Multi-Criteria Decision Making: A Comparative Study

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System Redesigning to Creating Shared Value (SYRCS)

3923: 1718:Multiple objective mathematical programming school 1157: 796:Illustrations of the decision and criterion spaces 533: 235: 2994: 2748:Journal of Mathematical Analysis and Applications 2580: 2207: 2205: 2175: 2028:Stratified Multi Criteria Decision Making (SMCDM) 244: 4885: 3235: 2141:Rew, L. (1988). "Intuition in Decision-making". 2025:Simple Multi-Attribute Rating Technique (SMART) 886: 822: 591:is nondominated if there does not exist another 380: 357: 4062: 3734:Higher Education–Quality, Relevance and Impact. 3098: 3063: 2706: 2032:Stochastic Multicriteria Acceptability Analysis 563:A well-developed special case is obtained when 150:" alternatives (which we will define shortly). 68:that explicitly evaluates multiple conflicting 2442: 2202: 1672:, are projected onto the nondominated points, 807:Figure 1. Demonstration of the decision space 312:criterion functions (objective functions) and 4132: 4048: 4025:A Brief History prepared by Steuer and Zionts 3883:Information Systems and E-Business Management 3101:IEEE Transactions on Evolutionary Computation 2613: 639:is efficient if there does not exist another 3849: 3471:Journal of Business Economics and Management 3000: 2909:: CS1 maint: multiple names: authors list ( 2741: 2566:: CS1 maint: multiple names: authors list ( 2524: 2510:: CS1 maint: multiple names: authors list ( 2428:: CS1 maint: multiple names: authors list ( 2223: 2221: 524: 475: 4672:Hazard analysis and critical control points 4008: 3981:Mulliner E, Smallbone K, Maliene V (2013). 3953: 3165:(1). Research Information Ltd. (UK): 1–11. 3003:Journal of Multi-Criteria Decision Analysis 2261:International Journal of Sustainable Energy 1982:Multi-Attribute Global Inference of Quality 560:is the decision variable vector of size n. 4139: 4125: 4055: 4041: 2640: 2123:Superiority and inferiority ranking method 2038:Superiority and inferiority ranking method 3971: 3826: 3482: 3441: 3408: 3375: 3334: 2946: 2759: 2218: 514: 505: 158:upon knowledge in many fields including: 115:methods, many implemented by specialized 4645:Structured or semi-structured interviews 3960:Journal of Retail & Leisure Property 3926:European Journal of Operational Research 3547:Renewable and Sustainable Energy Reviews 3323:Economic Research-Ekonomska Istraživanja 3132:. Singapore: Springer. pp. 67–104. 3053:(phd). Nashville: Vanderbilt University. 2436: 1996:Markovian Multi Criteria Decision Making 1707: 1542: 1188: 802: 40: 3753:Keshavarz Ghorabaee, M. et al. (2015) " 3046: 2140: 1876:Aggregated Indices Randomization Method 4886: 3688: 3661: 3254: 3194:International Journal of Fuzzy Systems 3028:Roy, B. (1968). "La méthode ELECTRE". 2387:: CS1 maint: archived copy as title ( 2227: 4120: 4036: 3843: 3776:Business Strategy and the Environment 3226: 3191: 2923: 2113:Multicriteria classification problems 2088:Architecture tradeoff analysis method 1907:Characteristic Objects METhod (COMET) 203:Multiple-criteria evaluation problems 3599: 2986:Keeney, R. & Raiffa, H. (1976). 1696:, respectively, along the direction 86:multiple attribute preference theory 28:Micro Channel Developers Association 4894:Multiple-criteria decision analysis 4146: 3612:from the original on 29 August 2017 3241:Belton, V, and Stewart, TJ (2002). 3152: 3125: 3027: 2343:from the original on 7 October 2017 2313:from the original on 3 October 2017 1993:Multi-attribute value theory (MAVT) 133:multiple-criteria decision analysis 100:comfortable and the safest one. In 58:multiple-criteria decision analysis 13: 4775:Bayesian statistics and Bayes nets 3947: 3248: 2463:from the original on 24 June 2010. 2155:10.1111/j.1547-5069.1988.tb00056.x 1937:Dominance-based rough set approach 123:Foundations, concepts, definitions 14: 4925: 4704:Failure mode and effects analysis 4009:Maliene, V.; et al. (2002). 3261:. Eloy Hontoria. Cham: Springer. 2118:Rank reversals in decision-making 1779:Multi-attribute utility theorists 1444:Generating nondominated solutions 241:well as some formal definitions. 129:multiple-criteria decision-making 90:multi-objective decision analysis 78:multiple attribute utility theory 50:Multiple-criteria decision-making 4807:Multi-criteria decision analysis 4755:Reliability centered maintenance 4091:Computer supported brainstorming 3292:Expert Systems with Applications 1848:Analytic hierarchy process (AHP) 1537:Achievement scalarizing function 903: 839: 4018:FIG XXII International Congress 3917: 3870: 3802: 3767: 3764:", Informatica, 26(3), 435-451. 3747: 3737: 3727: 3718: 3709: 3682: 3655: 3624: 3593: 3565: 3537: 3499: 3458: 3417: 3384: 3351: 3310: 3283: 3220: 3185: 3146: 3119: 3092: 3057: 3040: 3021: 2979: 2917: 2884: 2857: 2830: 2803: 2768: 2735: 2700: 2667: 2634: 2607: 2574: 2533: 2518: 2477: 2467: 2408:. Singapore: World Scientific. 2186:10.1002/9780470400531.eorms0683 2009:Ordinal Priority Approach (OPA) 1862: 236:Representations and definitions 82:multiple attribute value theory 4723:Cause and consequence analysis 4597:Occupational safety and health 4505:Identity and access management 3815:Operations Management Research 2355: 2325: 2295: 2252: 2143:Journal of Nursing Scholarship 2134: 1988:Multi-attribute utility theory 1913:Conjoint Value Hierarchy (CVA) 907: 899: 843: 835: 487: 481: 443: 411: 402: 396: 245:Criterion space representation 127:MCDM or MCDA are acronyms for 1: 3606:www.transformations.knf.vu.lt 3484:10.3846/16111699.2015.1095233 3443:10.3846/16484142.2015.1121517 3336:10.1080/1331677X.2015.1075139 2948:10.1016/S0019-9958(65)90241-X 2742:Yu, P.L.; Zeleny, M. (1975). 2333:"Welcome to EWG-MCDA website" 2128: 1952:Evidential reasoning approach 358:Decision space representation 193: 4683:Structured What If Technique 4666:Hazard and operability study 4522:Business continuity planning 2761:10.1016/0022-247X(75)90189-4 2684:10.1007/978-3-642-04045-0_22 2651:10.1007/978-3-642-48782-8_32 2281:10.1080/14786451.2014.898640 1910:Choosing By Advantages (CBA) 1792:; Hansen and Ombler, 2008). 35:Multi-objective optimization 7: 4660:Preliminary hazard analysis 4479:Operational risk management 4002:10.1016/j.omega.2012.05.002 3703:10.1016/j.omega.2015.12.001 3676:10.1016/j.omega.2014.11.009 2443:Triantaphyllou, E. (2000). 2081: 1661:, and an infeasible point, 10: 4930: 4744:Human reliability analysis 4428:Enterprise risk management 3938:10.1016/j.ejor.2006.01.020 3895:10.1007/s10257-021-00525-4 3828:10.1007/s12063-021-00178-z 3649:10.1016/j.asoc.2017.03.045 3587:10.1016/j.asoc.2016.04.020 3559:10.1016/j.rser.2016.12.053 3304:10.1016/j.eswa.2015.01.003 3206:10.1007/s40815-020-00827-8 3200:(4). Springer: 1073–1090. 3171:10.1007/s40815-020-00827-8 3159:The Journal of Grey System 1882:Analytic hierarchy process 1762:Ordinal data based methods 32: 25: 18: 4909:Mathematical optimization 4816: 4733:Layer protection analysis 4728:Cause-and-effect analysis 4610: 4535:Financial risk management 4417: 4382: 4272:Vulnerability (computing) 4161: 4154: 4071: 3523:10.1142/S0219622016300019 3255:Munier, Nolberto (2021). 3113:10.1109/TEVC.2010.2070371 3078:10.1162/evco.1994.2.3.221 2941:(3). San Diego: 338–353. 2000:New Approach to Appraisal 1917:Data envelopment analysis 1772:Ordinal Priority Approach 64:) is a sub-discipline of 4694:Business impact analysis 4510:Vulnerability management 4456:Personal risk management 4255:Global catastrophic risk 3760:2 September 2016 at the 3231:. New York: McGraw-Hill. 3066:Evolutionary Computation 2866:Naval Research Logistics 2777:Mathematical Programming 2709:Mathematical Programming 2108:Decisional balance sheet 2098:Decision-making software 1970:Inner product of vectors 1964:Grey relational analysis 1888:Analytic network process 1869:decision-making software 1836:Grey relational analysis 1456:(Gass & Saaty, 1955) 552:is the feasible set and 117:decision-making software 4575:Precautionary principle 4527:Disaster risk reduction 4106:Nominal group technique 2934:Information and Control 2591:10.1007/0-306-48107-3_8 2529:. New York: John Wiley. 2238:10.1287/orms.2018.05.13 2103:Decision-making paradox 1785:Multi-attribute utility 1740:Goal programming school 1732:Interactive programming 4770:Monte Carlo simulation 4760:Sneak circuit analysis 4155:Risk type & source 3864:10.1006/obhd.1994.1087 3637:Applied Soft Computing 3575:Applied Soft Computing 3047:Shaffer, J.D. (1984). 2554:10.1287/opre.1080.0581 2498:10.1287/mnsc.41.7.1158 2069:Weighted product model 1774:and Qualiflex method. 1548: 1194: 1159: 808: 535: 46: 4795:Cost/benefit analysis 4439:Regulatory compliance 4065:creativity techniques 2851:10.1287/mnsc.22.6.652 2824:10.1287/mnsc.19.4.357 2818:(4–Part–1): 357–368. 2525:Steuer, R.E. (1986). 2215:, Springer: New York. 1708:Solving MCDM problems 1546: 1192: 1160: 806: 536: 318:is the feasible set, 44: 21:Meta-cold dark matter 4558:Strategic management 4434:Corporate governance 4212:Anthropogenic hazard 3954:Maliene, V. (2011). 3227:Saaty, T.L. (1980). 3153:Liu, Sifeng (2013). 3126:Liu, Sifeng (2017). 2628:10.1287/opre.2.3.316 2337:www.cs.put.poznan.pl 1933:(Rough set approach) 1893:Balance Beam process 815: 373: 183:Software engineering 102:portfolio management 4718:Event tree analysis 4713:Fault tree analysis 4699:Root cause analysis 4678:Toxicity assessment 4620:Exposure assessment 4590:Disaster management 4517:Incident management 4500:Security management 4193:Psychosocial hazard 4176:Reputational damage 3600:Diedonis, Antanas. 3370:(10): 13947–13984. 2616:Operations Research 2542:Operations Research 2307:www.mcdmsociety.org 2273:2016IJSE...35...47K 1752:Fuzzy-set theorists 1725:Vector maximization 188:Information systems 178:Computer technology 66:operations research 4904:Management systems 4800:Risk–benefit ratio 4602:Swiss cheese model 4563:Risk communication 4471:Disease management 4345:Exchange rate risk 4340:Interest rate risk 4076:6-3-5 Brainwriting 3973:10.1057/rlp.2011.7 3377:10.3390/su71013947 2990:. 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New York: Wiley. 2839:Management Science 2812:Management Science 2789:10.1007/bf01584098 2721:10.1007/BF01580111 2486:Management Science 2075:Weighted sum model 1903:Brown–Gibson model 1823:Grey system theory 1549: 1539:(Wierzbicki, 1980) 1195: 1155: 1153: 809: 531: 529: 47: 4899:Decision analysis 4881: 4880: 4873:Crisis management 4689:Scenario analysis 4630:Scenario planning 4585:Crisis management 4466:Stress management 4413: 4412: 4306:Reputational risk 4114: 4113: 3410:10.3390/su8010037 3268:978-3-030-60392-2 3245:, Kluwer: Boston. 3139:978-981-10-1841-1 2693:978-3-642-04044-3 2660:978-3-540-09963-5 2456:978-0-7923-6607-2 2369:on 11 August 2011 2058:Value engineering 1897:Best worst method 950: 453: 308:is the vector of 168:Decision analysis 4921: 4868:Opportunity cost 4817:Related concepts 4750:Bow tie analysis 4635:Contingency plan 4461:Health insurance 4449:Internal control 4290:Operational risk 4205:Natural disaster 4159: 4158: 4141: 4134: 4127: 4118: 4117: 4081:Affinity diagram 4057: 4050: 4043: 4034: 4033: 4021: 4015: 4005: 3987: 3977: 3975: 3942: 3941: 3921: 3915: 3914: 3874: 3868: 3867: 3847: 3841: 3840: 3830: 3821:(1–2): 208–232. 3806: 3800: 3799: 3788:10.1002/bse.2623 3771: 3765: 3751: 3745: 3741: 3735: 3731: 3725: 3722: 3716: 3713: 3707: 3706: 3686: 3680: 3679: 3659: 3653: 3652: 3628: 3622: 3621: 3619: 3617: 3597: 3591: 3590: 3569: 3563: 3562: 3541: 3535: 3534: 3503: 3497: 3496: 3486: 3477:(5): 1034–1068. 3462: 3456: 3455: 3445: 3421: 3415: 3414: 3412: 3388: 3382: 3381: 3379: 3355: 3349: 3348: 3338: 3314: 3308: 3307: 3298:(8): 4126–4148. 3287: 3281: 3280: 3252: 3246: 3239: 3233: 3232: 3224: 3218: 3217: 3189: 3183: 3182: 3150: 3144: 3143: 3123: 3117: 3116: 3096: 3090: 3089: 3061: 3055: 3054: 3044: 3038: 3037: 3025: 3019: 3018: 3015:10.1002/mcda.428 2998: 2992: 2991: 2983: 2977: 2976: 2950: 2921: 2915: 2914: 2908: 2900: 2891:Charnes, A. and 2888: 2882: 2881: 2861: 2855: 2854: 2834: 2828: 2827: 2807: 2801: 2800: 2772: 2766: 2765: 2763: 2739: 2733: 2732: 2704: 2698: 2697: 2671: 2665: 2664: 2638: 2632: 2631: 2611: 2605: 2604: 2578: 2572: 2571: 2565: 2557: 2537: 2531: 2530: 2522: 2516: 2515: 2509: 2501: 2492:(7): 1158–1171. 2481: 2475: 2471: 2465: 2464: 2440: 2434: 2433: 2427: 2419: 2399: 2393: 2392: 2386: 2378: 2376: 2374: 2365:. 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652–663. 2829: 2802: 2767: 2754:(2): 430–468. 2734: 2699: 2692: 2666: 2659: 2633: 2622:(3): 316–319. 2606: 2599: 2573: 2532: 2517: 2476: 2466: 2455: 2435: 2414: 2394: 2354: 2324: 2294: 2251: 2217: 2201: 2194: 2168: 2149:(3): 150–154. 2132: 2130: 2127: 2126: 2125: 2120: 2115: 2110: 2105: 2100: 2095: 2090: 2083: 2080: 2079: 2078: 2072: 2066: 2061: 2055: 2052:Value analysis 2049: 2044: 2041: 2035: 2029: 2026: 2023: 2017: 2011: 2006: 2003: 1997: 1994: 1991: 1985: 1979: 1973: 1967: 1961: 1955: 1949: 1946: 1940: 1934: 1928: 1925: 1919: 1914: 1911: 1908: 1905: 1900: 1894: 1891: 1885: 1879: 1864: 1861: 1830:In the 1980s, 1790:PAPRIKA method 1709: 1706: 1698: 1689: 1685: 1677: 1666: 1655: 1647: 1646: 1645: 1644: 1643: 1642: 1626: 1625: 1624: 1623: 1617: 1616: 1615: 1614: 1606: 1597: 1588: 1578: 1541: 1540: 1530: 1529: 1528: 1527: 1526: 1525: 1509: 1508: 1507: 1506: 1500: 1499: 1498: 1497: 1481: 1469: 1458: 1457: 1445: 1442: 1437: 1436: 1435: 1434: 1433: 1432: 1427: 1420: 1408: 1407: 1406: 1405: 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495: 492: 489: 486: 483: 480: 477: 474: 471: 469: 467: 464: 461: 458: 457: 449: 448: 445: 440: 436: 432: 429: 426: 421: 417: 413: 410: 407: 404: 401: 398: 395: 392: 389: 387: 385: 382: 379: 378: 359: 356: 300: 299: 298: 297: 296: 295: 279: 278: 277: 276: 270: 269: 268: 267: 261: 246: 243: 237: 234: 213: 212: 206: 195: 192: 191: 190: 185: 180: 175: 170: 165: 124: 121: 15: 9: 6: 4: 3: 2: 4926: 4915: 4912: 4910: 4907: 4905: 4902: 4900: 4897: 4895: 4892: 4891: 4889: 4874: 4871: 4869: 4866: 4862: 4859: 4858: 4857: 4854: 4852: 4849: 4847: 4844: 4842: 4841:Risk appetite 4839: 4837: 4834: 4830: 4829:ISO/IEC 31010 4827: 4826: 4825: 4822: 4821: 4819: 4815: 4808: 4805: 4801: 4798: 4797: 4796: 4793: 4791: 4788: 4786: 4783: 4781: 4778: 4776: 4773: 4771: 4768: 4766: 4763: 4761: 4758: 4756: 4753: 4751: 4748: 4745: 4742: 4740: 4739:Decision tree 4737: 4734: 4731: 4729: 4726: 4724: 4721: 4719: 4716: 4714: 4711: 4709: 4705: 4702: 4700: 4697: 4695: 4692: 4690: 4687: 4684: 4681: 4679: 4676: 4673: 4670: 4667: 4664: 4661: 4658: 4656: 4653: 4651: 4650:Delphi method 4648: 4646: 4643: 4641: 4640:Brainstorming 4638: 4636: 4633: 4631: 4628: 4626: 4623: 4621: 4618: 4617: 4615: 4613: 4609: 4603: 4600: 4598: 4595: 4591: 4588: 4587: 4586: 4583: 4581: 4578: 4576: 4573: 4569: 4566: 4565: 4564: 4561: 4559: 4556: 4552: 4549: 4547: 4544: 4542: 4539: 4538: 4537: 4536: 4532: 4528: 4525: 4523: 4520: 4518: 4515: 4511: 4508: 4506: 4503: 4502: 4501: 4498: 4496: 4493: 4491: 4488: 4486: 4483: 4482: 4481: 4480: 4476: 4472: 4469: 4467: 4464: 4462: 4459: 4458: 4457: 4454: 4450: 4447: 4445: 4442: 4440: 4437: 4435: 4432: 4431: 4430: 4429: 4425: 4424: 4422: 4420: 4416: 4406: 4405:Vulnerability 4403: 4401: 4398: 4396: 4393: 4391: 4388: 4387: 4385: 4381: 4375: 4374:Residual risk 4372: 4370: 4369: 4365: 4361: 4360:Systemic risk 4358: 4356: 4353: 4351: 4348: 4346: 4343: 4341: 4338: 4336: 4333: 4331: 4328: 4327: 4326: 4325: 4321: 4317: 4314: 4312: 4309: 4307: 4304: 4302: 4299: 4297: 4294: 4293: 4292: 4291: 4287: 4283: 4280: 4278: 4275: 4273: 4270: 4269: 4268: 4267:Security risk 4265: 4263: 4262:Safety hazard 4260: 4256: 4253: 4251: 4248: 4247: 4246: 4245:External risk 4242: 4239: 4235: 4232: 4230: 4227: 4226: 4225: 4222: 4218: 4215: 4214: 4213: 4210: 4206: 4203: 4202: 4201: 4198: 4194: 4191: 4189: 4186: 4185: 4184: 4183:Personal risk 4181: 4177: 4174: 4173: 4172: 4171: 4167: 4166: 4164: 4160: 4157: 4153: 4149: 4142: 4137: 4135: 4130: 4128: 4123: 4122: 4119: 4107: 4104: 4102: 4099: 4097: 4096:Disney method 4094: 4092: 4089: 4087: 4086:Brainstorming 4084: 4082: 4079: 4077: 4074: 4073: 4070: 4066: 4058: 4053: 4051: 4046: 4044: 4039: 4038: 4035: 4028: 4026: 4023: 4019: 4012: 4007: 4003: 3999: 3996:(2): 270–79. 3995: 3991: 3984: 3979: 3974: 3969: 3966:(5): 443–50. 3965: 3961: 3957: 3952: 3951: 3939: 3935: 3931: 3927: 3920: 3912: 3908: 3904: 3900: 3896: 3892: 3888: 3884: 3880: 3873: 3865: 3861: 3857: 3853: 3846: 3838: 3834: 3829: 3824: 3820: 3816: 3812: 3805: 3797: 3793: 3789: 3785: 3781: 3777: 3770: 3763: 3759: 3756: 3750: 3740: 3730: 3721: 3712: 3704: 3700: 3696: 3692: 3685: 3677: 3673: 3669: 3665: 3658: 3650: 3646: 3642: 3638: 3634: 3627: 3611: 3607: 3603: 3596: 3588: 3584: 3580: 3576: 3568: 3560: 3556: 3552: 3548: 3540: 3532: 3528: 3524: 3520: 3516: 3512: 3511: 3502: 3494: 3490: 3485: 3480: 3476: 3472: 3468: 3461: 3453: 3449: 3444: 3439: 3435: 3431: 3427: 3420: 3411: 3406: 3402: 3398: 3394: 3387: 3378: 3373: 3369: 3365: 3361: 3354: 3346: 3342: 3337: 3332: 3328: 3324: 3320: 3313: 3305: 3301: 3297: 3293: 3286: 3278: 3274: 3270: 3264: 3260: 3259: 3251: 3244: 3238: 3230: 3223: 3215: 3211: 3207: 3203: 3199: 3195: 3188: 3180: 3176: 3172: 3168: 3164: 3160: 3156: 3149: 3141: 3135: 3131: 3130: 3122: 3114: 3110: 3106: 3102: 3095: 3087: 3083: 3079: 3075: 3071: 3067: 3060: 3052: 3051: 3043: 3035: 3031: 3024: 3016: 3012: 3008: 3004: 2997: 2989: 2982: 2974: 2970: 2966: 2962: 2958: 2954: 2949: 2944: 2940: 2936: 2935: 2930: 2927:(June 1965). 2926: 2920: 2912: 2906: 2898: 2894: 2887: 2879: 2875: 2871: 2867: 2860: 2852: 2848: 2844: 2840: 2833: 2825: 2821: 2817: 2813: 2806: 2798: 2794: 2790: 2786: 2782: 2778: 2771: 2762: 2757: 2753: 2749: 2745: 2738: 2730: 2726: 2722: 2718: 2714: 2710: 2703: 2695: 2689: 2685: 2681: 2677: 2670: 2662: 2656: 2652: 2648: 2644: 2637: 2629: 2625: 2621: 2617: 2610: 2602: 2600:9780306481079 2596: 2592: 2588: 2584: 2577: 2569: 2563: 2555: 2551: 2547: 2543: 2536: 2528: 2521: 2513: 2507: 2499: 2495: 2491: 2487: 2480: 2470: 2462: 2458: 2452: 2448: 2447: 2439: 2431: 2425: 2417: 2415:9789814335591 2411: 2407: 2406: 2398: 2390: 2384: 2368: 2364: 2358: 2342: 2338: 2334: 2328: 2312: 2308: 2304: 2298: 2290: 2286: 2282: 2278: 2274: 2270: 2266: 2262: 2255: 2247: 2243: 2239: 2235: 2231: 2224: 2222: 2214: 2208: 2206: 2197: 2195:9780470400531 2191: 2187: 2183: 2179: 2172: 2164: 2160: 2156: 2152: 2148: 2144: 2137: 2133: 2124: 2121: 2119: 2116: 2114: 2111: 2109: 2106: 2104: 2101: 2099: 2096: 2094: 2091: 2089: 2086: 2085: 2076: 2073: 2070: 2067: 2065: 2062: 2059: 2056: 2053: 2050: 2048: 2045: 2042: 2039: 2036: 2033: 2030: 2027: 2024: 2021: 2018: 2015: 2012: 2010: 2007: 2004: 2001: 1998: 1995: 1992: 1989: 1986: 1983: 1980: 1977: 1974: 1971: 1968: 1965: 1962: 1959: 1956: 1953: 1950: 1947: 1944: 1941: 1938: 1935: 1932: 1929: 1926: 1923: 1920: 1918: 1915: 1912: 1909: 1906: 1904: 1901: 1898: 1895: 1892: 1889: 1886: 1883: 1880: 1877: 1874: 1873: 1872: 1870: 1860: 1856: 1852: 1851: 1850: 1849: 1843: 1841: 1837: 1833: 1828: 1827: 1826: 1825:based methods 1824: 1818: 1814: 1813: 1812: 1807: 1805: 1800: 1799: 1798: 1797:French school 1793: 1791: 1786: 1782: 1781: 1780: 1775: 1773: 1769: 1765: 1764: 1763: 1758: 1755: 1754: 1753: 1748: 1744: 1743: 1742: 1741: 1735: 1733: 1728: 1726: 1721: 1720: 1719: 1714: 1705: 1701: 1692: 1688: 1680: 1676: 1669: 1665: 1658: 1654: 1640: 1636: 1632: 1631: 1630: 1629: 1628: 1627: 1621: 1620: 1619: 1618: 1609: 1605: 1600: 1596: 1591: 1586: 1581: 1572: 1569: 1565: 1560: 1559: 1558: 1557: 1556: 1553: 1545: 1538: 1535: 1534: 1533: 1523: 1519: 1515: 1514: 1513: 1512: 1511: 1510: 1504: 1503: 1502: 1501: 1492: 1488: 1484: 1476: 1472: 1466: 1465: 1464: 1463: 1462: 1455: 1454:Weighted sums 1452: 1451: 1450: 1441: 1426: 1419: 1414: 1413: 1412: 1411: 1410: 1409: 1397: 1390: 1386: 1385: 1384: 1383: 1382: 1381: 1369: 1362: 1357: 1356: 1355: 1354: 1353: 1352: 1340: 1333: 1329: 1328: 1327: 1326: 1325: 1324: 1312: 1305: 1301: 1300: 1299: 1298: 1297: 1296: 1284: 1277: 1272: 1271: 1270: 1269: 1268: 1267: 1255: 1248: 1244: 1243: 1242: 1241: 1240: 1239: 1233: 1232: 1231: 1230: 1216: 1215: 1214: 1213: 1199: 1198: 1197: 1196: 1191: 1187: 1170: 1148: 1145: 1143: 1136: 1132: 1128: 1123: 1119: 1111: 1108: 1106: 1099: 1095: 1091: 1086: 1082: 1074: 1071: 1069: 1062: 1058: 1054: 1049: 1045: 1041: 1034: 1031: 1029: 1022: 1018: 1014: 1009: 1005: 997: 994: 992: 985: 981: 973: 970: 968: 961: 957: 938: 934: 930: 925: 921: 917: 914: 912: 894: 890: 877: 873: 869: 866: 861: 857: 853: 850: 848: 830: 826: 811: 810: 805: 801: 793: 789: 787: 783: 781: 777: 773: 768: 764: 760: 756: 749: 745: 739: 735: 731: 730:Definition 4. 727: 724: 720: 714: 710: 704: 700: 696: 695:Definition 3. 692: 688: 684: 680: 676: 672: 665: 661: 657: 653: 647: 643: 637: 633: 629: 628:Definition 2. 625: 622: 619: 615: 609: 605: 599: 595: 589: 585: 581: 580:Definition 1. 577: 573: 568: 561: 557: 549: 519: 509: 506: 502: 499: 496: 493: 490: 484: 478: 472: 470: 465: 462: 459: 438: 434: 430: 427: 424: 419: 415: 408: 405: 399: 393: 390: 388: 383: 369: 368: 367: 364: 355: 353: 347: 344: 338: 335: 329: 326: 322: 316: 311: 306: 293: 289: 285: 284: 283: 282: 281: 280: 274: 273: 272: 271: 264: 258: 257: 256: 255: 254: 251: 242: 233: 229: 225: 221: 217: 210: 207: 204: 201: 200: 199: 189: 186: 184: 181: 179: 176: 174: 171: 169: 166: 164: 161: 160: 159: 155: 151: 149: 144: 142: 136: 134: 130: 120: 118: 112: 110: 105: 103: 98: 93: 91: 87: 83: 79: 75: 71: 67: 63: 59: 55: 51: 43: 39: 36: 29: 22: 4533: 4485:Supply chain 4477: 4455: 4426: 4366: 4322: 4311:Country risk 4288: 4266: 4250:Extreme risk 4200:Natural risk 4182: 4168: 4017: 3993: 3989: 3963: 3959: 3929: 3925: 3919: 3886: 3882: 3872: 3855: 3851: 3845: 3818: 3814: 3804: 3779: 3775: 3769: 3749: 3739: 3729: 3720: 3711: 3694: 3690: 3684: 3667: 3663: 3657: 3640: 3636: 3626: 3614:. Retrieved 3605: 3595: 3578: 3574: 3567: 3550: 3546: 3539: 3514: 3508: 3501: 3474: 3470: 3460: 3433: 3429: 3419: 3400: 3396: 3386: 3367: 3363: 3353: 3326: 3322: 3312: 3295: 3291: 3285: 3257: 3250: 3242: 3237: 3228: 3222: 3197: 3193: 3187: 3162: 3158: 3148: 3128: 3121: 3104: 3100: 3094: 3069: 3065: 3059: 3049: 3042: 3033: 3029: 3023: 3006: 3002: 2996: 2987: 2981: 2938: 2932: 2929:"Fuzzy sets" 2919: 2896: 2893:Cooper, W.W. 2886: 2869: 2865: 2859: 2842: 2838: 2832: 2815: 2811: 2805: 2780: 2776: 2770: 2751: 2747: 2737: 2712: 2708: 2702: 2675: 2669: 2642: 2636: 2619: 2615: 2609: 2582: 2576: 2562:cite journal 2545: 2541: 2535: 2526: 2520: 2506:cite journal 2489: 2485: 2479: 2469: 2445: 2438: 2404: 2397: 2371:. Retrieved 2367:the original 2357: 2345:. Retrieved 2336: 2327: 2315:. Retrieved 2306: 2297: 2267:(1): 47–58. 2264: 2260: 2254: 2229: 2212: 2177: 2171: 2146: 2142: 2136: 2064:VIKOR method 2040:(SIR method) 2022:(Outranking) 1945:(Outranking) 1866: 1863:MCDM methods 1857: 1853: 1846: 1845: 1844: 1829: 1821: 1820: 1819: 1815: 1810: 1809: 1808: 1801: 1796: 1795: 1794: 1783: 1778: 1777: 1776: 1768:Ordinal data 1766: 1761: 1760: 1759: 1756: 1751: 1750: 1749: 1745: 1738: 1737: 1736: 1731: 1729: 1724: 1722: 1717: 1716: 1715: 1711: 1699: 1690: 1686: 1678: 1674: 1667: 1663: 1656: 1652: 1648: 1638: 1634: 1607: 1603: 1598: 1594: 1589: 1584: 1579: 1570: 1567: 1563: 1554: 1550: 1536: 1531: 1521: 1517: 1490: 1486: 1482: 1474: 1470: 1459: 1453: 1447: 1438: 1424: 1417: 1395: 1388: 1367: 1360: 1338: 1331: 1310: 1303: 1282: 1275: 1253: 1246: 1186:as follows: 1171: 1167: 799: 790: 785: 784: 779: 778: 774: 766: 762: 758: 754: 747: 743: 737: 733: 729: 728: 722: 718: 712: 708: 702: 698: 694: 693: 689: 682: 678: 674: 670: 663: 659: 655: 651: 645: 641: 635: 631: 627: 626: 623: 617: 613: 607: 603: 597: 593: 587: 583: 579: 578: 574: 566: 562: 555: 547: 543: 365: 361: 348: 342: 339: 333: 330: 324: 320: 314: 309: 304: 301: 291: 287: 262: 252: 248: 239: 230: 226: 222: 218: 214: 208: 202: 197: 156: 152: 148:nondominated 145: 137: 132: 128: 126: 113: 106: 94: 89: 85: 81: 77: 61: 57: 53: 49: 48: 38: 4851:Rare events 4790:Risk Matrix 4400:Uncertainty 4383:Risk source 4355:Profit risk 4350:Market risk 4330:Credit risk 4188:Health risk 3858:: 306–325. 3697:: 126–130. 3643:: 265–292. 3581:: 108–128. 3553:: 216–256. 2925:Zadeh, L.A. 2783:: 366–375. 2548:: 187–199. 2230:OR/MS Today 1832:Deng Julong 1440:problems). 786:Nadir point 780:Ideal point 163:Mathematics 4888:Categories 4846:Hazard map 4785:Risk index 4316:Legal risk 4301:Model risk 4241:Macro risk 3277:1237399430 2965:0139.24606 2129:References 1840:Liu Sifeng 1622:subject to 1505:subject to 1234:subject to 949:subject to 751:such that 716:such that 649:such that 601:such that 452:subject to 275:subject to 194:A typology 33:See also: 4824:ISO 31000 4706:(FMEA) / 4655:Checklist 4580:Insurance 4551:Risk pool 4162:Risk type 3911:236544531 3903:1617-9846 3837:232240914 3796:224917346 3670:: 49–57. 3616:29 August 3531:0219-6220 3493:1611-1699 3452:1648-4142 3430:Transport 3403:(1): 37. 3345:1331-677X 3214:219090787 3179:219090787 2973:Q25938993 2957:0019-9958 2905:cite book 2715:: 54–72. 2424:cite book 2289:108512639 2020:PROMETHEE 2016:(PAPRIKA) 1978:(MACBETH) 1931:Rough set 1577:Min {max 1179:with the 1146:≥ 1109:≤ 1092:− 1072:≤ 1042:− 1032:≤ 995:≤ 971:≤ 931:− 854:− 510:⊆ 497:∈ 463:∈ 428:… 352:trade-off 232:review). 173:Economics 109:intuition 4861:Security 4780:FN curve 4395:Conflict 4282:Accident 4101:Mind map 4020:: 19–26. 3758:Archived 3610:Archived 3086:13997318 3036:: 57–75. 2969:Wikidata 2895:(1961). 2797:29348836 2729:32037123 2461:Archived 2383:cite web 2373:7 August 2347:26 April 2341:Archived 2317:26 April 2311:Archived 2082:See also 1568:g, q, w, 70:criteria 4914:Utility 4685:(SWIFT) 4674:(HACCP) 4668:(HAZOP) 4495:Quality 4490:Project 4229:IT risk 2474:INFORMS 2269:Bibcode 2163:3169833 1984:(MAGIQ) 1943:ELECTRE 1804:ELECTRE 1650:point, 761:) > 141:optimal 4809:(MCDA) 4735:(LOPA) 4390:Hazard 4277:Threat 4063:Group 3909: 3901: 3835: 3794: 3529: 3491: 3450: 3343: 3275: 3265: 3212: 3177: 3136: 3084: 2971: 2963: 2955: 2795: 2727: 2690: 2657: 2597: 2453: 2412: 2287: 2246:642562 2244: 2192: 2161: 2034:(SMAA) 2002:(NATA) 1990:(MAUT) 1939:(DRSA) 1878:(AIRM) 544:where 302:where 260:"max" 88:, and 4746:(HRA) 4708:FMECA 4662:(PHA) 4546:Hedge 4014:(PDF) 3990:Omega 3986:(PDF) 3907:S2CID 3833:S2CID 3792:S2CID 3691:Omega 3664:Omega 3210:S2CID 3175:S2CID 3082:S2CID 2793:S2CID 2725:S2CID 2285:S2CID 2242:S2CID 2077:(WSM) 2071:(WPM) 1972:(IPV) 1966:(GRA) 1924:(DEX) 1899:(BWM) 1890:(ANP) 1884:(AHP) 1493:> 721:> 56:) or 4836:COSO 3899:ISSN 3618:2017 3527:ISSN 3489:ISSN 3448:ISSN 3341:ISSN 3273:OCLC 3263:ISBN 3134:ISBN 2953:ISSN 2911:link 2688:ISBN 2655:ISBN 2595:ISBN 2568:link 2512:link 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Multiple-criteria decision analysis

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