Multiple criteria decision making with interval stochastic variables: A method based on interval stochastic dominance

Abstract A novel method based on interval stochastic dominance to solve the stochastic multiple criteria decision making (SMCDM) problem with interval stochastic variables is proposed. By analyzing the uncertainty of interval stochastic variables, we propose the method of determining cumulative distribution function of interval stochastic variables. Then, three types of interval stochastic dominance (ISD) rules are investigated, the definition of interval stochastic dominance degree (ISDD) is presented and some interesting properties of ISD and ISDD are proved. With respect to the SMCDM problem with interval stochastic variables, to begin with, interval cumulative distribution functions of alternative criterion values are determined. Then, the ISD relations matrix associated with pairwise comparison of alternatives on each criterion is obtained based on ISD rules and the ISDD matrix on each criterion is calculated. Further, based on PROMETHEE-Ⅱ method, the net flows of each alternative are derived so as to obtain the ranking result. Consequently, examples are presented to illustrate the effectiveness of the proposed method.

[1]  Reza Tavakkoli-Moghaddam,et al.  A Fuzzy Stochastic Multi-Attribute Group Decision-Making Approach for Selection Problems , 2011, Group Decision and Negotiation.

[2]  Maciej Nowak,et al.  Preference and veto thresholds in multicriteria analysis based on stochastic dominance , 2004, Eur. J. Oper. Res..

[3]  Susana Montes,et al.  Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance , 2014, Eur. J. Oper. Res..

[4]  Yao Zhang,et al.  A method based on stochastic dominance degrees for stochastic multiple criteria decision making , 2010, Comput. Ind. Eng..

[5]  J. Kyburg Higher order probability and intervals , 1988 .

[6]  Francesco Cesarone,et al.  Innovative Applications of O.R. On exact and approximate stochastic dominance strategies for portfolio selection , 2018 .

[7]  Kazimierz Zaras,et al.  Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems , 2004, Eur. J. Oper. Res..

[8]  G. Whitmore,et al.  Third-Degree Stochastic Dominance , 1970 .

[9]  R. Yager,et al.  Decision Making Under Various Types of Uncertainties , 1995, J. Intell. Fuzzy Syst..

[10]  Yao Zhang,et al.  A method for stochastic multiple attribute decision making based on concepts of ideal and anti-ideal points , 2013, Appl. Math. Comput..

[11]  Xiaohong Chen,et al.  Stochastic multiple criteria decision making with aspiration level based on prospect stochastic dominance , 2014, Knowl. Based Syst..

[12]  Maciej Nowak,et al.  Aspiration level approach in stochastic MCDM problems , 2007, Eur. J. Oper. Res..

[13]  Ting-Yu Chen,et al.  A PROMETHEE-based outranking method for multiple criteria decision analysis with interval type-2 fuzzy sets , 2013, Soft Computing.

[14]  Kaisa Miettinen,et al.  Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA) , 2003, Eur. J. Oper. Res..

[15]  Risto Lahdelma,et al.  SMAA - Stochastic multiobjective acceptability analysis , 1998, Eur. J. Oper. Res..

[16]  Feng Yang,et al.  SMAA-AD Model in Multicriteria Decision-Making Problems with Stochastic Values and Uncertain Weights , 2014 .

[17]  Minghe Sun,et al.  A method for discrete stochastic MADM problems based on the ideal and nadir solutions , 2015, Comput. Ind. Eng..

[18]  P. Salminen,et al.  Prospect theory and stochastic multicriteria acceptability analysis (SMAA) , 2009 .

[19]  Peide Liu,et al.  Stochastic multiple-criteria decision making with 2-tuple aspirations: a method based on disappointment stochastic dominance , 2018, Int. Trans. Oper. Res..

[20]  Cornel Resteanu,et al.  ON SOLVING STOCHASTIC MADM PROBLEMS , 2009 .

[21]  Xin Zhang,et al.  Research on the multi-attribute decision-making under risk with interval probability based on prospect theory and the uncertain linguistic variables , 2011, Knowl. Based Syst..

[22]  P. Vincke,et al.  Note-A Preference Ranking Organisation Method: The PROMETHEE Method for Multiple Criteria Decision-Making , 1985 .

[23]  Kazimierz Zaras,et al.  Rough approximation of a preference relation by a multi-attribute stochastic dominance for determinist and stochastic evaluation problems , 2001, Eur. J. Oper. Res..

[24]  Philippe Vincke,et al.  An outranking method under uncertainty , 1988 .

[25]  Bo Feng,et al.  A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations , 2010, Eur. J. Oper. Res..

[26]  Ronald R. Yager,et al.  Stochastic Dominance for Measure Based Uncertain Decision Making , 2014, Int. J. Intell. Syst..

[27]  Risto Lahdelma,et al.  SMAA-2: Stochastic Multicriteria Acceptability Analysis for Group Decision Making , 2001, Oper. Res..

[28]  M. K. Sheikh-El-Eslami,et al.  A Stochastic-Based Decision-Making Framework for an Electricity Retailer: Time-of-Use Pricing and Electricity Portfolio Optimization , 2011, IEEE Transactions on Power Systems.

[29]  Susana Montes,et al.  Stochastic dominance with imprecise information , 2014, Comput. Stat. Data Anal..

[30]  K. Zaras,et al.  Stochastic dominance in multicriterion analysis under risk , 1995 .

[31]  Yao Zhang,et al.  A method for stochastic multiple criteria decision making based on dominance degrees , 2011, Inf. Sci..