Abstract
TODIM is a well-known multiple-criteria decision-making (MCDM) which considers the bounded rationality of decision makers (DMs) based on prospect theory (PT). However, in the classical TODIM, the perceived probability weighting function and the difference of the risk attitudes for gains and losses are not consistent with the original idea of PT. Moreover, probabilistic hesitant fuzzy information shows its superiority in handling the situation that the DMs hesitate among several possible values with different possibilities. Hence, a novel TODIM with probabilistic hesitant fuzzy information is proposed in this paper to simulate the perceptions of the DMs in PT. To show the advantages of the proposed method, a novel TODIM is combined with hesitant fuzzy information. Finally, a case study is carried out to demonstrate the feasibility of the proposed method, and a series of comparative analyses and the sensitivity analyses are used to show the stability of the proposed method.
Highlights
Decision makers (DMs) are considered to be completely rational among the existing multiple-criteria decision-making (MCDM) methods based on expected utility theory
Based on the above analysis, this section presents a new procedure of the novel TODIM with probabilistic hesitant fuzzy information, which is based on the idea of the original prospect theory (PT). e procedure is given as follows: Step 1: obtain the original evaluation information matrix Y (hij(pij))n×m according to equation (4) and the weight of the corresponding criterion
Based on equation (6) of the classical TODIM, the relative weight is calculated by the one-dimensional probability weight; according to equation (3), the original PT considers that the DMs adopt the nonlinear transformed probability weight function in the decision-making process
Summary
Decision makers (DMs) are considered to be completely rational among the existing multiple-criteria decision-making (MCDM) methods based on expected utility theory. Erefore, TODIM (TOmada deDecisão Iterativa Multicriterio), a well-known MCDM method considering the bounded rational behaviors based on prospect theory (PT) [1], was proposed by Gomes and Lima [2]. The TODIM has demonstrated its unparalleled advantages in solving the MCDM problems by considering the psychological factors of the DMs. according to our review, we find that most of the existing TODIMs ignore the importance of the transformed probability weight in the original PT. E contributions of this paper are as follows: (i) a novel TODIM with probabilistic hesitant fuzzy information is proposed, which is fully aligned with the original idea of PT compared with the classical TODIM. The novel TODIM is combined with probabilistic hesitant fuzzy information and hesitant fuzzy information according to the original PT from the perspective of dominance function.
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