Experimental comparison of ranking functions in fuzzy decision
making
Hui-Chin Tang
∗Kuang-Hang Hsieh
Hwapeng Chang
Department of Industrial Engineering and Management
National Kaohsiung University of Applied Sciences
Kaohsiung 80778
Taiwan, R.O.C.
Abstract
The comparison of fuzzy numbers is a very important topic in decision making problem. This paper considers some selected methods which are based on ranking functions: Yager (1978, 1980, 1981), Adamo (1980), Chang (1981), Campos and Munoz (1989), Liou and Wang (1992), Choobineh and Li (1993), Fortemps and Roubens (1996) and Lee and Li (1988). We present the computational algorithms for these ranking functions. Five representative sets of examples, adopted from Bortolan and Degani (1985), Cheng (1998), and Liou and Wang (1992), are considered in this paper. We empirically analyze the influence of the different ranking functions on the ordering of fuzzy numbers for the five representative sets of examples.
Keywords :Fuzzy ranking, ranking function, trapezoidal fuzzy number, triangular fuzzy number.
1.
Introduction
Ranking fuzzy numbers (FNs) has been a problem of long
stand-ing interest for practitioners and researchers. In the literature, various
approaches have been proposed for the ranking FNs problem. These
approaches can be classified into three categories: ranking functions,
reference sets and preference relations (see references [2, 10, 11] for more
details). Here we consider eight selected methods which are based on
ranking functions: Yager [12-14], Adamo [1], Chang [4], Campos and
∗E-mail: tang@cc.kuas.edu.tw
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Journal of Information & Optimization Sciences
Vol. 31 (2010), No. 5, pp. 1127–1136
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