A new similarity measure for generalized fuzzy numbers

Allahviranloo, Tofigh; Abbasbandy, Saeid; Hajighasemi, S.

doi:10.1007/s00521-012-0836-2

Cited by 9 publications

(5 citation statements)

References 10 publications

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“…4 are used to compare the new similarity measure with the eight exiting methods proposed by Hsu and Chen [12], Chen [4], Hsieh and Chen [11], Lee [14], Chen and Chen [5], Deng et al [8], Chou [6] and Allahviranloo et al [1]. A comparison of the results for the proposed similarity measure and the existing methods are shown in Table 1.…”

Section: Comparing the Proposed Methods With The Existing Methodsmentioning

confidence: 99%

“…The degree of similarity between fuzzy numbersÃ 2 andB is also S(Ã 2 ,B) =8 9 . (h) A similarity measure based on the distance measurement combining with generalized Hausdorff distance is defined by Allahviranloo et al[1]. Assume there are two generalized trapezoidal fuzzy numbers,Ã = (a 1 , a 2 , a 3 , a 4 ; w A ) andB = (b1 , b 2 , b 3 , b 4 ; w B ), where 0 ≤ a 1 ≤ a 2 ≤ a 3 ≤ a 4 , and 0 ≤ b 1 ≤ b 2 ≤ b 3 ≤ b4 .…”

mentioning

confidence: 99%

“…(h) A similarity measure based on the distance measurement combining with generalized Hausdorff distance is defined by Allahviranloo et al[1]. Assume there are two generalized trapezoidal fuzzy numbers,Ã = (a 1 , a 2 , a 3 , a 4 ; w A ) andB = (b1 , b 2 , b 3 , b 4 ; w B ), where 0 ≤ a 1 ≤ a 2 ≤ a 3 ≤ a 4 , and 0 ≤ b 1 ≤ b 2 ≤ b 3 ≤ b4 . Then the degree of similarity S(Ã,B) between fuzzy numbersÃ andB can be calculated as Equation(19) m = max{a 2 + a 4 , b 2 + b 4 }.…”

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confidence: 99%

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A new similarity measure of fuzzy numbers

Chou

2014

Journal of Intelligent &Amp; Fuzzy Systems

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A new method for measuring the degree of similarity between fuzzy numbers is proposed in this paper. The advantage of the proposed method is to take account of the membership functions of fuzzy numbers while measuring the degree of similarity of fuzzy numbers. Finally, six sets of fuzzy numbers are used to compare the proposed method with the existing methods for similarity measure of fuzzy numbers. The results show that the proposed method for similarity measure seems to be more reasonable.

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Section: Comparing the Proposed Methods With The Existing Methodsmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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A new similarity measure of fuzzy numbers

Chou

2014

Journal of Intelligent &Amp; Fuzzy Systems

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“…To solve this problem, Guha and Chakraborty [68] introduced a new distance for general fuzzy numbers through using the cut concept. Allahviranloo et al [69] proposed a method based on cut for calculating fuzzy distance between two trapezoidal fuzzy numbers.…”

Section: Fuzzy Distancementioning

confidence: 99%

An extended fuzzy VIKOR for group decision making based on fuzzy distance to supplier selection

2016

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Supplier Selection Problem (SSP) has become a critical objective of purchasing departments because of its signi cant e ect on successful logistic and Supply Chain Management (SCM). In real-life situations, SSP parameters are often imprecise, vague, uncertain, or incomplete. In this respect, fuzzy sets theory is the best developed approach to formulate these uncertainties. In this paper, we have extended fuzzy VIKOR using an e cient fuzzy distance measure to solve applicable SSP under group decision-making process. In our study, an e cient fuzzy VIKOR for solving SSP under group decisionmaking process is presented in which decision makers have di erent weights in decisionmaking process and their opinions are collected in the form of linguistic variables. In our methodology, preference ratio method is applied to rank the alternatives. Ultimately, several numerical illustrations and sensitivity analyses are performed to demonstrate the applicability of the proposed method.

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“…In approaches [21][22][23][24], ␣-cut set and decision-maker's preference are used to construct ranking function. On the other hand, another commonly used technique is the distance measurement [17][18][19][20][21][22][23][24][25][26]. Asady and Zendehnam [20] proposed ranking and defuzzication method based on "Distance Minimization".…”

Section: Introductionmentioning

confidence: 99%

The new weighted magnitude mean value and variance of fuzzy numbers

Guo

2014

Journal of Intelligent &Amp; Fuzzy Systems

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Fullér and Majlender (Fuzzy Sets and Systems 136 (2003) 363-374) introduced the notation of weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-valued probabilistic mean. In this paper, we introduce the new notation of lower and upper weighted magnitude mean values of a fuzzy number. The new interval-valued weighted magnitude mean and variance are defined, which differs from the one given by Fullér and Majlender. We will show the relationship of interval-valued weighted magnitude mean and interval-valued weighted possibilistic mean. Furthermore, we shall also introduce the notations of crisp weighted magnitude mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. Finally, some comparative examples are used to illustrate the advantage of the proposed weighted magnitude mean value and variance method to order fuzzy numbers.

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A new similarity measure for generalized fuzzy numbers

Cited by 9 publications

References 10 publications

A new similarity measure of fuzzy numbers

A new similarity measure of fuzzy numbers

An extended fuzzy VIKOR for group decision making based on fuzzy distance to supplier selection

The new weighted magnitude mean value and variance of fuzzy numbers

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