TY - JOUR

T1 - The preference order of fuzzy numbers

AU - Chen, L. H.

AU - Lu, H. W.

PY - 2002

Y1 - 2002

N2 - Many fuzzy number ranking approaches are developed in the literature for multiattribute decision-making problems. Almost all of the existing approaches focus on quantity measurement of fuzzy numbers for ranking purpose. In this paper, we consider the ranking process to determine a decision-maker's preference order of fuzzy numbers. A new ranking index is proposed to not only take quantity measurement, but incorporate quality factor into consideration for the need of general decision-making problems. For measuring quantity, several α-cuts of fuzzy numbers are used. A signal/noise ratio is defined to evaluate quality of a fuzzy number. This ratio considers the middle-point and spread of each α-cut of fuzzy numbers as the signal and noise, respectively. A fuzzy number with the stronger signal and the weaker noise is considered better. Moreover, the associated α levels are treated as the degree of belief about the α-cut and used as weights in the index for strengthening the influence of α-cut with higher α levels. The membership functions of fuzzy numbers are not necessarily to be known beforehand while applying this index. Only a few left and right boundary values of α-cuts of fuzzy numbers are required. We have proved the feature of the proposed index in a particular case. Several examples are also used to illustrate the feature and applicability in ranking fuzzy numbers.

AB - Many fuzzy number ranking approaches are developed in the literature for multiattribute decision-making problems. Almost all of the existing approaches focus on quantity measurement of fuzzy numbers for ranking purpose. In this paper, we consider the ranking process to determine a decision-maker's preference order of fuzzy numbers. A new ranking index is proposed to not only take quantity measurement, but incorporate quality factor into consideration for the need of general decision-making problems. For measuring quantity, several α-cuts of fuzzy numbers are used. A signal/noise ratio is defined to evaluate quality of a fuzzy number. This ratio considers the middle-point and spread of each α-cut of fuzzy numbers as the signal and noise, respectively. A fuzzy number with the stronger signal and the weaker noise is considered better. Moreover, the associated α levels are treated as the degree of belief about the α-cut and used as weights in the index for strengthening the influence of α-cut with higher α levels. The membership functions of fuzzy numbers are not necessarily to be known beforehand while applying this index. Only a few left and right boundary values of α-cuts of fuzzy numbers are required. We have proved the feature of the proposed index in a particular case. Several examples are also used to illustrate the feature and applicability in ranking fuzzy numbers.

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U2 - 10.1016/S0898-1221(02)00270-5

DO - 10.1016/S0898-1221(02)00270-5

M3 - Article

AN - SCOPUS:0036859743

VL - 44

SP - 1455

EP - 1465

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 10-11

ER -