Several Intuitionistic Fuzzy Multi-Attribute Decision Making Methods and Their Applications by Zhinan Hao & Zeshui Xu & Hua Zhao

Author:Zhinan Hao & Zeshui Xu & Hua Zhao
Language: eng
Format: epub
ISBN: 9789811538919
Publisher: Springer Singapore

The loss-aversion coefficient λ determines to what extent the expectation of losses will prevail over the gains. λ < 1 indicates that the loss is acceptable and can be attenuated while λ ≥ 1 implies that the loss is unbearable and will be amplified. Setting large values of λ indicates that we are to find the alternatives possessing the small losses on all the attributes, that is, the larger λ produces the safer alternative(s) for the DMs. This reflects the loss aversion phenomenon of risk decision. The existing researches have shown that the losses raise more attention than the gains for the DMs under risk situations, and the experimental value for this coefficient is 2.25 (Tversky and Kahneman 1992). This is consistent with the finding that the final results are accepted if the gains are at least twice as high as the losses (Kontek 2011). The parameters and determine the concave for the gains and the convex for the losses. Tversky also gave the experimental value 0.88 for these two parameters (Tversky and Kahneman 1992). From Fig. 3.6, we find that the different scenarios produce the same optimal one, i.e., Scheme 3. As a result, we should choose Scheme 3 as the final decision result. For Group 1, the values of λ affect the ranking orders of the alternative set. As λ increases, the DM hopes to find the one with fewer losses, which results in the position changes of Scheme 1. The worst alternative Scheme 2 still remains the same. When we change the values of and , the ranking sequence also changes subtly. The order of the optimal alternative is not affected but the inferior ones are rearranged. This change also happens in Scheme 1, which implies that the prospect values of Scheme 1 are sensitive to the parameters. From the perspective of practical situations, it corresponds to a plan that much depends on the evolution of exterior environment and the risk preferences of the DMs. The changes of the DMs’ attitudes or the events will influence the evaluation of this plan. As has been analyzed before, the parameters and will influence the risk attitudes of the DMs. Such influences are implemented by altering the prospect values on each criterion, which are then accumulated to affect the final results. On the contrary, the loss-aversion coefficient λ, as the name suggests, will directly amplify or diminish the prospect values of alternatives. From this perspective, the parameters and exert the subtle changes to the decision results while the parameter λ performs overall influences on the decision results. The ranking results also reflect this mechanism. The changes of λ arrange Scheme 1 from the second place to the last second place. The changes of and subtly insert Scheme 1 to the middle of Scheme 4 and Scheme 5 while the other orders remain the same. Hence, it is expected that the changes of λ will rapidly produce the safest results. If we wish to analyze the detailed differences of alternatives for the final results, it

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