New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle

Parkash, Om; Sharma, Praveen Kumar; Mahajan, Renuka

doi:10.1016/j.ins.2007.12.003

Cited by 98 publications

(61 citation statements)

References 17 publications

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“…The satisfability of (9) and (10) indicates that the implicit function theorem [13] can be applied to solvability of (6) with respect to 0 , 1 , … , . The obtained results for solvability of (6) …”

Section: Minimum Cross Fuzzy Entropy Problem the Existence Of Its Somentioning

confidence: 99%

“…After these developments, a large number of measures of fuzzy entropy were discussed, characterized and generalized by various authors. Some other interesting findings related with theoretical measures of fuzzy entropy and their applications have been provided by Kapur [5], Parkash and Sharma [13], Yager [14], Bhandari and Pal [8] etc. The starting point for the cross entropy approach is information theory developed by Shannon [6].…”

Section: Introductionmentioning

confidence: 99%

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Minimum Cross Fuzzy Entropy Problem, The Existence of Its Solution and Generalized Minimum Cross Fuzzy Entropy Problems

Shamilov¹,

Ince²

2016

JMSS

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Abstract:In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem (Minx(F)EntP) and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the set of membership functions satisfying the given moment constraints generated by given moment functions it is required to choose the membership function that is closest to a priori membership function in the sense of cross fuzzy entropy measure. The existence of solution of formulated problem is proved by virtue of concavity property of cross fuzzy entropy measure, the implicit function theorem and Lagrange multipliers method.

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Section: Minimum Cross Fuzzy Entropy Problem the Existence Of Its Somentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimum Cross Fuzzy Entropy Problem, The Existence of Its Solution and Generalized Minimum Cross Fuzzy Entropy Problems

Shamilov¹,

Ince²

2016

JMSS

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“…Some other interesting findings are related with theoretical measures of fuzzy entropy and their applications have been provided by Kapur [7], Parkash and Sharma [8], Yager [9], Bhandari and Pal [10], Parkash, Sharma and Kumar [11] etc. In [12], Parkash, Sharma and Mahajan introduced new measures of weigted fuzzy entropy including two moment conditions.…”

Section: Introductionmentioning

confidence: 99%

Bulanık Üyelik Fonksiyonunun Yaklaşımı İçin Bir Yeni Metot ve Uygulama

Ince¹,

Shamilov²

2017

Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler

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In the present study we have formulated a new Maximum Fuzzy Entropy Problem (Max(F)EntP) for fuzzy membership function and proposed sufficient conditions for existence of its solution. Mentioned problem consists of approximation fuzzy membership function by maximizing Maximum Fuzzy Entropy (Max(F)Ent) measure with respect to membership functions with finite number of the fuzzy values subject to constraints generated by given moment functions. The existence of solution of mentioned problem is proved by virtue of convexity property of Max(F)Ent measure, the implicit function theorem and Lagrange multipliers method. Moreover, by using MATLAB programme one application of suggested method on fuzzy data analysis is given.

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“…In order to boost the significance of entropy weight in IFS-MCDM and to mine the importance of hesitation degree, a similar function with maximum value of 1 could be proposed. Parkash et al, [12] provide some clues over this matter by introducing weighted measures of fuzzy entropy based on the maximum entropy principle. However, the multiplication of weights to cyclic or trigonometric function in Parkash et al, [12] would exaggerate the contribution of weight to entropy.…”

Section: Introductionmentioning

confidence: 99%

“…Parkash et al, [12] provide some clues over this matter by introducing weighted measures of fuzzy entropy based on the maximum entropy principle. However, the multiplication of weights to cyclic or trigonometric function in Parkash et al, [12] would exaggerate the contribution of weight to entropy. On the other hand, entropy is basically a measure of weight in perception based on theory of probability.…”

Section: Introductionmentioning

confidence: 99%

Weighted Correlation Coefficient with a Trigonometric Function Entropy of Intuitionistic Fuzzy Set in Decision Making

Ismail¹,

Abdullah²

2015

IJAPM

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Abstract:Weighted correlation coefficient is one of the methods for intuitionistic fuzzy sets based multi-criteria decision making (IFS-MCDM). It uses a method of entropy to find criteria weights for alternatives. Entropy weight that employed the arithmetic operations of addition and subtraction in IFS memberships is used for establishing the weighted correlation coefficient. However, the entropy obtained from the use of the arithmetic operations may deprive the significance of membership degree, non-membership degree and hesitation degree of IFS. This paper proposes a sine function entropy weight for measuring weighted correlation coefficients of IFS-MCDM. An example is given to illustrate the proposed method. The comparison results are also presented to show the feasibility and effectiveness of the proposed sine function entropy weight.

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New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle

Cited by 98 publications

References 17 publications

Minimum Cross Fuzzy Entropy Problem, The Existence of Its Solution and Generalized Minimum Cross Fuzzy Entropy Problems

Minimum Cross Fuzzy Entropy Problem, The Existence of Its Solution and Generalized Minimum Cross Fuzzy Entropy Problems

Bulanık Üyelik Fonksiyonunun Yaklaşımı İçin Bir Yeni Metot ve Uygulama

Weighted Correlation Coefficient with a Trigonometric Function Entropy of Intuitionistic Fuzzy Set in Decision Making

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