Intuitionistic Preference Modeling and Interactive Decision by Zeshui Xu

By Zeshui Xu

This booklet deals an in-depth and accomplished creation to the concern tools of intuitionistic choice relatives, the consistency and consensus enhancing techniques for intuitionistic choice family members, the techniques to team selection making in line with intuitionistic choice family, the techniques and types for interactive determination making with intuitionistic fuzzy info, and the prolonged leads to interval-valued intuitionistic fuzzy environments.

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58) j=1 to fuse all the interval-valued intuitionistic fuzzy preference values r˜i j = (μ˜ i j , v˜ i j ) ( j = 1, 2, . . , n) corresponding to the alternative yi into the overall interval-valued intuitionistic fuzzy preference value r˜i = (μ˜ i , v˜ i ) of the alternative yi . To rank the interval-valued intuitionistic fuzzy preference values r˜i = (μ˜ i , v˜ i ) (i = 1, 2, . . , n), Xu and Chen (2007c) defined the scores and the accuracy degrees of r˜i (i = 1, 2, . . , n) as follows: 1 − (μ − vi− + μi+ − vi+ ), i = 1, 2, .

6]) Similarly, we use Eq. 1790 y2 and then, r˜1 > r˜2 > r˜4 > r˜3 . Therefore, the ranking of the factors is y1 y4 y3 , which is slightly different from the ranking result derived by the approach of Sect. 3. 65) is a nonlinear function; and (2) it could clearly produce the loss of preference information in the aggregation process when the lower or upper limit of the membership degree or nonmembership degree takes the value of 0 or 1. Xu and Cai (2012b)’s approach can overcome all these issues and thus has a broader range of application potentials.

4]), respectively. 3]), respectively. 5]) (1) We know from the data above that there is one missing element r˜14 in R˜ (1) , it (1) (1) can be derived indirectly from the two pairs of adjoining known elements, (˜r12 , r˜24 ) (1) (1) and (˜r13 , r˜34 ). To do so, we use Eqs. 6]) In a similar way, we can use Eqs. 3 Group Decision Making 41 By Eqs. 573]) In order to compare r˜i (i = 1, 2, 3, 4), we calculate their scores by Eq. 1865 2 S(˜r1 ) = by which we have r˜1 > r˜2 > r˜3 > r˜4 , and thus, the ranking of the factors is y1 y2 y3 y4 .

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