Intuitionistic Fuzzy Calculus by Qian Lei & Zeshui Xu

Author:Qian Lei & Zeshui Xu
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

and

Based on the calculating formula of the definite integral of the IFF, we can get

In addition, the following inequalities hold:(1)

(2)

Moreover, for , , , and , we get the inequality below:

which is equivalent to . ■

Theorem 3.16

(Monotonicity) (Lei and Xu 2015c) If we let and be two IFFs, which meet and , then

whose proof of Theorem 3.16 is omitted here.

These basic proprieties (idempotency, boundedness and monotonicity) of show that it is feasible and reasonable to be considered as an aggregation method. Based on which, we introduce the process to aggregate the IFNs by in detail (Lei and Xu 2015c): Step 1. According to the assessments provided by the DMs, we obtain the minimum value of the non-membership degree, , and the maximal value of the membership degree, , and let be .

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