A New Approach of Ranking of Generalized Trapezoidal Fuzzy Numbers and Application in Fuzzy Risk Analysis

Patra, Kartik

doi:10.1080/01969722.2022.2134162

Cited by 1 publication

(7 citation statements)

References 29 publications

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“…The other three methods Wang and Lee [19], Nasseri et al [11], and Patra [14] demonstrated the same ranking result, whereas, Abbasbandy and Asady [1], Asady and Zendehnam [3] and Abbasbandy et al [2] have failed to discriminate any order and yields A 1 ∼ A 2 . Also, from Table 2, the ranking outcome for the trapezoidal fuzzy numbers by the proposed method is the same as the intuitive results.…”

Section: Authormentioning

confidence: 73%

“…However, the approaches of Abbasbandy and Asady [1], Asady and Zendehnam [3], Nasseri et al [11], and Patra [14] failed to demonstrate any order. Hence the proposed approach is capable of ranking the fuzzy numbers and their respective images in a difficult situation for intuition.…”

Section: Comparative Reviewsmentioning

confidence: 94%

“…Asady [1], Asady and Zendehnam [3], Abbasbandy et al [2], and Nasseri [11] are congruent with the proposed method. Patra's method [14] is inconsistent and yields B 1 ≻ B 2 ≻ B 3 . 3 shows the result of the proposed method and some convenient methods for ordering the above fuzzy numbers.…”

Section: Authormentioning

confidence: 99%

“…Nguyen [13] defined a unified index that multiplies the weighted mean and the weighted area of the fuzzy number as two different discriminatory components and obtained very good comparative results. Patra [14] presented a fuzzy risk analysis technique based on ranking generalized fuzzy numbers using the mean, area, and perimeter of the fuzzy number. Prasad and Sinha [18] suggested a unified integral that multiplies the core value and the left-right area integrals.…”

Section: Introductionmentioning

confidence: 99%

“…Contrary to a large number of ranking indices based on the centroid point and other parameters of the fuzzy numbers, there is a wide scope for further studies and comparative reviews because none of them is superior to all others. For instance, Patra [14] incorporated the mean, area, and perimeter of the fuzzy number leading to counterintuitive ranking results for the fuzzy numbers having different degrees of representative locations on the horizontal axis. Numerical illustrations are shown in Example 4.2.…”

Section: Introductionmentioning

confidence: 99%

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A New Approach of Centroid based Ranking Fuzzy Numbers and its Comparative Reviews

Prasad,

Sinha,

Sen

2024

Comm. Math. Appl.

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The numeric values represented by fuzzy numbers are vague and ranking them according to their location on the real axis is not adequate and logical. Ranking of fuzzy numbers plays a vital role in measuring the degree of importance of different alternatives in decision-making under the fuzzy environment and the comparison of fuzzy numbers reflects that of alternatives. Although a lot of methods for ranking fuzzy numbers exist in the literature, even then none of them is superior to all others. This paper proposes a new method for ranking fuzzy numbers using the coordinates of the centroid point of the fuzzy numbers. It suggests a ranking score for the fuzzy number that multiplies the ordinate and the exponential value of the ratio of the ordinate to the abscissa of the centroid point. The proposed ranking score method can rank two or more fuzzy numbers simultaneously irrespective of their linear or non-linear membership functions. Furthermore, it consistently ranks symmetric fuzzy numbers of the same or different altitudes, images of fuzzy numbers, and the fuzzy numbers that describe the compensation of areas. Comparative reviews show an edge of the proposed method over several representative approaches.

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