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    188宝金博页面版: An index for ordering fuzzy numbers

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    内容提示： Fuzzy Sets and Systems 54 (1993) 287-294 287 North-Holland An index for ordering fuzzy numbers F. Choobineh and Huishen Li Industrial and Management Systems Engineering Department, University of Nebraska-Lincoln, NE, USA Received January 1991 Revised May 1992 Abstract: A new index that is useful for ordering (ranking) of fuzzy numbers is proposed. To use this index the membership functions of fuzzy numbers need not be normal or convex. Properties of this index and its relationship to the 1981 Yager's index...

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    Fuzzy Sets and Systems 54 (1993) 287-294 287 North-Holland An index for ordering fuzzy numbers F. Choobineh and Huishen Li Industrial and Management Systems Engineering Department, University of Nebraska-Lincoln, NE, USA Received January 1991 Revised May 1992 Abstract: A new index that is useful for ordering (ranking) of fuzzy numbers is proposed. To use this index the membership functions of fuzzy numbers need not be normal or convex. Properties of this index and its relationship to the 1981 Yager's index are explained. A numerical comparison between the proposed and four other ordering procedures is presented. Keywords: Ordering fuzzy numbers; maximizing barrier; minimizing barrier. 1. Introduction Often in fuzzy decision analysis the merit of each alternative under consideration is represented by a fuzzy number, and ordering (ranking) of these fuzzy numbers is needed for making a choice among the alternatives. Several indices have been proposed for ordering fuzzy numbers (for examples see [1, 3, 4, 5, 7]). However, a few surveys of these indices (for examples see [2, 6]) indicate that no single index is superior to all other indices. In this paper, first, a new index is proposed that is closely related to Yager's index [7] but is easier to use and possesses additional properties that are useful in decision making. Second, the properties and the relation of the proposed index to Yager's index are explained. Third, a numerical comparison between an ordering procedure using the proposed index and four other procedures is made. Finally, the use of the proposed index for discrete fuzzy numbers is stated and some concluding remarks are made. 2. The proposed index Let/~a(x) be the membership function of the fuzzy set A defined on R. The height of A is defined as h a = max I~m(X), and its a-cut is defined as A(t~) = {x [x e R, gA(X) >I re}. NO assumptions about the normality nor convexity of/~A(x) are made. The loci of left and right ends of the t~-cuts of the fuzzy set A are defined as fa(a~) and gA(x), 0 <~ OC <~ ha, respectively, where (i) If A(tr) is denumerable or connected, then fa(oO=min{x [x eA(tr)}, 0 << - o¢~hA, and gA(O{) =max{x I x ea(a0}, 0 < - Ol<~ha. Correspondence to: Prof. F. Choobineh, Industrial and Management Systems Engineering Department, University of Nebraska-Lincoln, 175 Nebraska Hall, Lincoln, NE 68588-0518, USA. Tel. 402-4721388. 0165-0114/93/$06.00 © 1993----Elsevier Science Publishers B.V. All rights reserved

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