Uncertain Fuzzy Preference Relations and Their Applications by Zaiwu Gong

By Zaiwu Gong

On the root of fuzzy units and a few in their correct generalizations, this booklet systematically provides the elemental rules and purposes of crew determination making less than diverse eventualities of choice kin. through the use of intuitionistic wisdom because the box of discourse, this paintings investigates by using cutting edge examine skill the elemental ideas and techniques of staff selection making with a number of varied intuitionistic personal tastes: Mathematical reasoning is hired to check the consistency of crew determination making; tools of fusing details are utilized to examine the aggregation of a number of personal tastes; recommendations of sentimental computing and optimization are applied to go looking for passable choice choices.

each one bankruptcy follows the next structurally transparent structure of presentation: literature overview, improvement of uncomplicated concept, verification and reasoning of ideas , building of types and computational schemes, and numerical examples, which disguise such components as expertise, company competitiveness, number of airways, specialists determination making in weather-sensitive organizations, and so forth.

when it comes to theoretical ideas, this booklet can be utilized as a reference for researchers within the components of administration technological know-how, info technology, structures engineering, operations study, and different appropriate fields. it might even be hired as textbook for top point undergraduate scholars and graduate scholars. when it comes to purposes, this publication may be an exceptional better half for all these determination makers in govt, enterprise, and expertise parts.

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For simplicity, let N = {1, 2, , n} and M = {1, 2, , m} . Consider the following complementary judgment matrix of interval fuzzy numbers: R s= ⎛ ⎜ 11s ⎜ ⎜ ⎜ 21s ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ n1s ⎞ ⎟ ⎟ ⎟ 21ns ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ nns ⎠ r r12 s r1ns r r22 s r r rn 2 s r ,s∈M where the (i,j) entry rijs denotes the degree of pairwise preference between the decision alternative X i over X j as estimated by the s th decision maker, and takes the form of interval fuzzy numbers, for all i, j ∈ N , s ∈ M . In many practical cases, the decision makers may possibly provide incomplete information.

Each multiplicatively consistent IFNCPR has the general consistency. Proof. Let R = (rij ) n× n be a multiplicatively consistent IFNP. For any i, j, k ∈ N, satisfying i ≠ j ≠ k . 7 then implies that riku ≥ λ . 5 , if rij ≤ [λ , λ ], rjk ≤ [λ , λ ] , it follows rji ≥ [1 − λ ,1 − λ ], rkj ≥ [1 − λ ,1 − λ ] . In the following, we verify rikl ≤ λ . that Suppose for the purpose of producing a contradiction that there exist i0 , j0 , k0 ∈ N , i0 ≠ j0 ≠ k0 , such that when ri0 k0l > λ , ri0 k0u > λ . That is, ri0 k0 > [λ , λ ] , and rk0i0 < [1 − λ ,1 − λ ] .

5 , the following inequality λ3 λ 3 + (1 − λ )3 ≤λ holds true. That is, we have rikl < λ3 λ + (1 − λ )3 3 ≤ λ < rikl which is a contradiction. Thus we have rikl ≤ λ . QED. 5 ≤ λ ≤ 1 , if rij ≥ [λ , λ ], rjk ≥ [λ , λ ] , then riku ≥ λ . 5 , if rij ≤ [λ , λ ], rjk ≤ [λ , λ ] , then the lower limit rikl of the interval rik is smaller than λ . 14. Let R = (rij ) n× n be an INFNPR. For all i, j, k ∈ N, satisfying i ≠ j ≠ k , if 1 1 1 1 1 rij ≥ [ , ], rjk ≥ [ , ] ⇒ rik+ ≥ ; 2 2 2 2 2 or 1 1 1 1 1 rij ≤ [ , ], rjk ≤ [ , ] ⇒ rik− ≤ 2 2 2 2 2 then R is said to have the weak consistency.

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