Credibility Measure for Intuitionistic Fuzzy Variables

Rahimi, Mohamadtaghi; Kumar, Pranesh; Yari, Gholamhossein

doi:10.3390/math6040050

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…Since then, a handful of theoretical research on entropy under the credibility theory is carried out (see, e.g., [ 20 , 21 ]). Recently, Rahimi et al [ 22 ] provided novel definitions of entropy of intuitionistic fuzzy variables based on the notion of credibility under intuitionistic fuzzy environment. According to credibility measure, Zhou et al [ 23 ] studied the entropy of LR fuzzy numbers, and the calculation formulas together with related concepts were proposed in great detail.…”

Section: Introductionmentioning

confidence: 99%

Calculation Formulas and Simulation Algorithms for Entropy of Function of LR Fuzzy Intervals

Shen¹,

Zhou²

2019

Entropy

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Entropy has continuously arisen as one of the pivotal issues in optimization, mainly in portfolios, as an indicator of risk measurement. Aiming to simplify operations and extending applications of entropy in the field of LR fuzzy interval theory, this paper first proposes calculation formulas for the entropy of function via the inverse credibility distribution to directly calculate the entropy of linear function or simple nonlinear function of LR fuzzy intervals. Subsequently, to deal with the entropy of complicated nonlinear function, two novel simulation algorithms are separately designed by combining the uniform discretization process and the numerical integration process with the proposed calculation formulas. Compared to the existing simulation algorithms, the numerical results show that the advantage of the algorithms is well displayed in terms of stability, accuracy, and speed. On the whole, the simplified calculation formulas and the effective simulation algorithms proposed in this paper provide a powerful tool for the LR fuzzy interval theory, especially in entropy optimization.

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Section: Introductionmentioning

confidence: 99%

Calculation Formulas and Simulation Algorithms for Entropy of Function of LR Fuzzy Intervals

Shen¹,

Zhou²

2019

Entropy

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“…In this paper, relative entropy and also some properties of the credibility based fuzzy entropy measure are defined. Then, Rahimi et al [12] defined the credibility for intuitionistic fuzzy variables. They axiomatized that credibility measure and based on the notion of the concepts, expected values, entropy and a general formula for central moments had been defined.…”

Section: Introductionmentioning

confidence: 99%

Portfolio optimization based on fuzzy entropy

Rahimi

Kumar

2018

Int J Interact Des Manuf

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In this paper, a general solution is presented for portfolio optimization in a situation where the expressed prices are estimated as fuzzy numbers. To reach the solution, the expected returns, semi-variance, skewness, semi-kurtosis and semi-entropy are considered with this assumption that the portfolio returns are asymmetric. In this method, all the data about the expected returns are considered and no expected return value is ignored just because of a little growth of risk. We have the conclusion by discussing an illustrative example to verify the developed approach.

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Parabolic fuzzy variables and their some properties: A comparative SWOT up

Dutta

Das²

2021

International Conference on Recent Trends in Applied Mathematical Sciences (Icrtams-2020)

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Credibility Measure for Intuitionistic Fuzzy Variables

Cited by 4 publications

References 18 publications

Calculation Formulas and Simulation Algorithms for Entropy of Function of LR Fuzzy Intervals

Calculation Formulas and Simulation Algorithms for Entropy of Function of LR Fuzzy Intervals

Portfolio optimization based on fuzzy entropy

Parabolic fuzzy variables and their some properties: A comparative SWOT up

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