Comparing methods for multiattribute decision making with ordinal weights
Computers and Operations Research
Information Sciences: an International Journal
Multiattribute choice with ordinal information: a comparison of different decision rules
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
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Computers and Operations Research
An integrated model-based interactive approach to FMAGDM with incomplete preference information
Fuzzy Optimization and Decision Making
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Approaches to hesitant fuzzy multiple attribute decision making with incomplete weight information
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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This paper is concerned with the use of incomplete information on both multicriteria alternative value scores and importance weights in evaluating decision alternatives under certainty. Two decision concepts-dominance and potential optimality (PO)-are employed to determine outperforming alternatives or acts. Given incomplete weights and exact value scores, it is known that the set of nondominated acts implies the set of potentially optimal acts. We here rediscover this set inclusive relation in a different and computationally efficient manner that develops a mixed-integer programming approach to dominance. When both value scores and weights are incomplete, we show that the set inclusive relation between dominance and PO may or may not hold. This is a result of how we define PO. Two different definitions of PO-weak PO and strong PO-are made in the sense that an act is weak potentially optimal when there exists at least one exact vector of value scores in the given incomplete value scores which render this act potentially optimal. An act is strong potentially optimal when this act is potentially optimal for all possible value scores. Less formally, this means that under the given incomplete information, weak PO stands for sometimes good while strong PO stands for always good, so we can thus say that the latter outperforms than the former. As a result, we show that the set of nondominated acts implies the set of strong potentially optimal acts. No certain set inclusive relationship exists between nondominated acts and weak potentially optimal acts. We also present computational aspects of establishing dominance, weak and strong PO, which include transformations of nonlinear problems into linear programming problems.