Ranking generalized fuzzy numbers in fuzzy decision making based on the left and right transfer coefficients and areas

Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews

“…First, this finding is consistent with that of Wang and Luo [39] and Yu et al [65]. In fact, with respect to the unified index, these results are reasonable because the chosen value manifests the decision-maker's optimism towards revelation of left-and right-area data.…”

“…Actually, majority of the existing ranking measures in category one (evaluating the fuzzy number itself) rank̃1 ≃̃2, and their image ranking is not available. Therefore, this example is to compare the proposed unified index with the category two ranking measures (not only evaluating the fuzzy number itself, but also gauging decision-maker's attitude in regard to specific purposes such as confidence and risk), initiated by Wang and Luo [39], Yu and Dat [48], Yu et al [65], and Liou and Wang [67], in terms of ranking indices' reliability and consistency.…”

“…Centroid value of a fuzzy number = ( , , , ; ) for = 1, , symbolized by CV , is defined as [3,4,38,63,65,71] …”

“…Based on the area between the centroid point and the original point, Chu and Tsao [63] succeeded in establishing an areadriven ranking index; unfortunately, because of its inherent computation flaw, the area index was questioned by Wang and Lee [64] who illustrated some numerical examples to show its counterintuitive results and further provided a compelling revised index to resolve the problem. Nonetheless, Wang and Lee's area index does have its own deficiency of ordering correctness when encountering fuzzy numbers with identical centroid points [65]. By defining fuzzy-number maximal and minimal reference sets, Wang et al [66] first introduced a deviation-driven ordering index by combining right-and-left deviation degree with the coefficient of relative variation; not surprisingly, this index was argued (1) bearing mathematical incapability with zero value in the denominator [53] and pointed out (2) leaving substantial room for improvement under some special occasions such as fuzzy numbers with the same left, right, and total utilities [39] as well as ranking fuzzy numbers' images [46].…”

An improved ranking method for generalized fuzzy numbers based on Euclidian distance concept

“…Yu et al [13] improved the ranking method for fuzzy numbers with integral values and also introduce the ranking based on epsilon-deviation degree in [14]. Moreover, in [15] Yu et al ranking generalized fuzzy numbers with application in fuzzy decision making was represented. Each method has its own shortcomings.…”