Entropy Of Intuitionistic Fuzzy Sets Research Articles

Risk Priority Evaluation for Power Transformer Parts Based on Intuitionistic Fuzzy Preference Selection Index Method

The risk assessment of power transformer equipment can not only improve the safety and management level of transformer operation, but also reduce the operation and maintenance costs of the equipment on the basis of ensuring the overall reliable operation of the power system. As a result, it can enhance the rewards of assets investment. The quantitative analysis of power equipment risk often contains qualitative indicators that are difficult to quantify. These indicators have the characteristics of fuzziness. In order to improve the accuracy and reliability of risk assessment results, this paper proposed a new risk evaluation method based on intuitionistic fuzzy set. Firstly, language variables are transformed into corresponding intuitionistic fuzzy numbers. Secondly, a novel entropy of intuitionistic fuzzy set is established. Thirdly, a weighting method for determining each expert’s importance is proposed based on the new propose entropy. Furthermore, an extended preference selection index is put forward under intuitionistic fuzzy environment. Finally, an example of the risk assessment of power transformer components is discussed to illustrate the effectiveness of the new risk evaluation method.

A novel entropy of intuitionistic fuzzy sets based on similarity and its application in finance

In this paper, we propose a new formula for the entropy based on similarity measures of intuitionistic fuzzy sets (IFS). The contribution of this work is the proof that the new formula satisfies all the conditions of entropy. The experimentation on some examples shows that the new entropy is useful. Besides, we use the new entropy and similarity measures to design an algorithm for ranking assets in stock markets. The numerical results on 5 benchmark data sets were reported. It points out that the entropy and the similarity measures of IFS may provide an alternative tool for solving portfolio selection problems.

Application of a new entropy measure for Pythagorean intuitionistic fuzzy sets

The Pythagorean fuzzy set (PFS) is an effective tool for depicting uncertainty in multi-criteria decision-making problems. In this paper, we explained the concept of probability for characterising the fuzzy entropy of PFSs as an extension of the fuzzy entropy of intuitionistic fuzzy sets (IFSs). When contrasted with some past measures, the new proposed measure is simple, closer to the factual significance and it reflects better fuzzy properties. New generalised parametric measures of exponential entropy on IFSs are characterised. Further, fundamental properties are demonstrated. Through dissecting the consequences of the model, it has been demonstrated that this technique is progressively dependable and increasingly effective in handy applications for introducing the level of fuzziness of an IFS. A numerical example is given to validate the method and compare its performance with the existing IFS entropy measures.

Novel similarity measures, entropy of intuitionistic fuzzy sets and their application in software quality evaluation

Intuitionistic fuzzy sets (IFSs), including member and nonmember functions, have many applications in managing uncertain information. The similarity measures of IFSs proposed to represent the similarity between different types of sensitive fuzzy information. However, some existing similarity measures do not meet the axioms of similarity. Moreover, in some cases, they could not be applied appropriately. In this study, we proposed some novel similarity measures of IFSs constructed by combining the exponential function of membership functions and the negative function of non-membership functions. In this paper, we also proposed a new entropy measure as a stepping-stone to calculate the weights of the criteria in the proposed multi-criteria decision-making (MCDM) model. The similarity measures used to rank alternatives in the model. Finally, we used this MCDM model to evaluate the quality of software projects.

A Minimum Trust Discount Coefficient Model for Incomplete Information in Group Decision Making with Intuitionistic Fuzzy Soft Set

This article proposes a framework to deal with incomplete information in multiple criteria group decision making with intuitionistic fuzzy soft set. To do that, the weighted sum method for choice values and simple mathematical expectation method are extended to the case of obtained fuzzy soft set, and they are proved to have the same result in estimating the incomplete information. In order to reduce the system error in the estimating process cause by multiple decision information, a minimum trust discount coefficient model is established according to the relevant methods of evidence theory. Then, a new definition of entropy for intuitionistic fuzzy sets is introduced to determine the weights of group experts. Therefore, individual decision-making matrices are integrated into a comprehensive decision-making matrix by the integration operation formula of intuitionistic fuzzy soft matrix. The decision making is realized according to the difference of the score values of objects. Finally, the steps of this method are concluded, and one example is given to explain the application of this method.

The Novel Generalized Exponential Entropy for Intuitionistic Fuzzy Sets and Interval Valued Intuitionistic Fuzzy Sets

The purpose of this paper is to propose the novel generalized exponential intuitionistic fuzzy entropy (GIFE) and generalized exponential interval valued intuitionistic fuzzy entropy (GIVIFE) with interval area. First, we propose a novel GIFE. Then we compare the new GIFE with the existing intuitionistic fuzzy entropy (IFE) measures. Second, we define the interval area and the new axioms for the interval valued intuitionistic fuzzy entropy (IVIFE). Third, according to the newly defined axioms for the IVIFE, we use the interval area to construct the new GIVIFE. Finally, the advantages of the new generalized entropy measures are compared with the existing IVIFE measures by some examples. The two novel generalized exponential entropy measures can distinguish the special cases well. We have the conclusion that the two novel generalized entropy measures are reasonable and more flexible than the existing entropy.

A Novel VIKOR-TODIM Approach Based on Havrda–Charvat–Tsallis Entropy of Intuitionistic Fuzzy Sets to Evaluate Management Information System

The utilisation of Management information system has grabbed the attention since last decades. The selection of management sources is a difficult assignment for decision-experts. Thus, the present article develops a new technique using entropy measures and a novel extended VIKOR-TODIM model of Intuitionistic Fuzzy Sets. A new parametric entropy measure based on Havrda–Charvat–Tsallis entropy for a probability distribution is proposed and discussed their particular cases. Some properties of this measure has been proved mathematically. A comparison of proposed entropy measure with several existing entropy measures is shown to demonstrate the consistency of the proposed approach. In this paper, we proposed an integrated approach based on VIKOR and TODIM and entropy-weighted method for solving multi-criteria decision-making problems under intuitionistic fuzzy environment and the criteria weights are partial known. Firstly, the problem with multi-criteria decision-making is designed and the steps, principles of the proposed VIKOR-TODIM method are presented. Finally, to verify the applicability and feasibility of the proposed approach, a problem of management information system in a teaching hospital is presented and compared the results with other existing methods. The present work demonstrated, that the proposed VIKOR-TODIM is effective to select and evaluate management information system in any organisation.

New hesitation-based distance and similarity measures on intuitionistic fuzzy sets and their applications

ABSTRACTIn this paper, we present new definitions on distance and similarity measures between intuitionistic fuzzy sets (IFSs) by combining with hesitation degree. First, we discuss the limitations in traditional distance and similarity measures, which are caused by the neglect of hesitation degree's influence. Even though a vector-valued similarity measure was proposed, which has two components indicating similarity and hesitation aspects, it still cannot perform well in practical applications because hesitation works only when the values of similarity measures are equal. In order to overcome the limitations, we propose new definitions on hesitation, distance and similarity measures, and research some theorems which satisfy the requirements of the proposed definitions. Meanwhile, we investigate the relationships among hesitation, distance, similarity and entropy of IFSs to verify the consistency of our work and previous research. Finally, we analyse and discuss the advantages and disadvantages of the proposed similarity measure in detail, and then we apply the proposed measures (dH and SH) to deal with pattern recognition problems, and demonstrate that they outperform state-of-the-art distance and similarity measures.

A new definition and formula of entropy for intuitionistic fuzzy sets

The entropy of an intuitionistic fuzzy set (IFS) is a measure of uncertainty related to the IFS. The purpose of this paper is to develop a new axiomatical entropy for an IFS. The axioms for a new entropy of an IFS are defined and a mathematical expression/formula of the new entropy of the IFS is given. The newly defined entropy concerns both the amount of information and reliability of the IFS. It is proven that the new entropy has some remarkable and useful properties. The examples and comparison analysis show the validity and applicability of the new entropy proposed in this paper.

Some notes on characters of intuitionistic fuzzy sets

The paper recalls the definition of intuitionistic fuzzy sets and the principle of information diffusion and analyzes several existent point operators. Giving an axiomatic definition for transforming intuitionistic fuzzy sets into fuzzy sets, we deduce a new conversion operator which seeks to obtai n one and only one fuzzy set for each intuitionistic set. A new distance measure is defined for intuitionistic fuzzy sets, and then the corresponding measure formula for the fuzzy entropy of intuitionistic fuzzy sets is proposed. Finally, some examples are illustrated for comparison with some existing formulae.

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

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

A Family of Entropies on Interval-valued Intuitionistic Fuzzy Sets and Their Applications in Multiple Attribute Decision Making

The entropy of intuitionistic fuzzy sets is used to indicate the degree of fuzziness of an interval-valued intuitionistic fuzzy set(IvIFS). In this paper, we deal with the entropies of IvIFS. Firstlt, we propose a family of entropies on IvIFS with a parameter λ ∈ [0, 1], which generalize two entropy measures defined independently by Zhang and Wei, for IvIFS, and then we prove that the new entropy is an increasing function with respect to the parameter λ. Furthermore, a new multiple attribute decision making(MADM) method using entropy-based attribute weights is proposed to deal with the decision making situations where the alternatives on attributes are expressed by IvIFS and the attribute weights information is unknown. Finally, a numerical example is given to illustrate the applications of the proposed method. Keywords—Interval-valued intuitionistic fuzzy sets, intervalvalued intuitionistic fuzzy entropy, multiple attribute decision making

The relationship between similarity measure and entropy of intuitionistic fuzzy sets

In this paper, we introduce an axiomatic definition of the similarity measure of intuitionistic fuzzy sets (IFS) that differs from the definition of Li [15]. The relationship between the similarity measure and the entropy of IFS is investigated in detail. Six theorems on how the similarity measure could be transformed into the entropy for IFS and vice versa are proposed based on their axiomatic definitions. Some formulas have been proposed to calculate the similarity measure and the entropy of IFS. Finally, sufficient conditions to transform the similarity measures to the entropy for IFS and vice versa are given.

Multicriteria decision making method based on intuitionistic fuzzy weighted entropy

This paper proposes the concept of intuitionistic fuzzy weighted entropy, and presents a new method for intuitionistic fuzzy multicriteria decision making problems. We first introduce some classical intuitionistic fuzzy entropy measures and verify the entropy of the intuitionistic fuzzy set is the average value of the entropies of its intuitionistic fuzzy values. Then, we present the concept of the intuitionistic fuzzy weighted entropy, which is a natural extension of the entropy for intuitionistic fuzzy sets. Some important weight entropy measures, such as the weighted Szmidt and Kacprzyk entropy, the weighted De Luca–Termini entropy, the weighted score function based entropy, and the weighted min–max entropy, are also given. According to the minimum entropy principle, we establish the programming model to generate optimal weight of criteria, and present the corresponding multicriteria decision making method. Finally, two illustrative examples are given to verify the developed approach.

Two effective measures of intuitionistic fuzzy entropy

Based on the concept of fuzzy entropy, two effective measures of intuitionistic fuzzy entropy are proposed in intuitionistic fuzzy information, and then the essential properties of these measures are introduced. These measures are a generalized version of the fuzzy entropy and a complementarity of existing entropy for intuitionistic fuzzy sets. Based on this generalization, a connection between the concepts of the fuzzy entropy and the intuitionistic fuzzy entropy is established. Finally, a numeral example is given to show that the information measures of the proposed intuitionistic fuzzy entropy are reasonable and effective by the comparison of the proposed entropy and existing entropy.

Subsethood, entropy, and cardinality for interval-valued fuzzy sets—An algebraic derivation

In this paper a unified formulation of subsethood, entropy, and cardinality for interval-valued fuzzy sets (IVFSs) is presented. An axiomatic skeleton for subsethood measures in the interval-valued fuzzy setting is proposed, in order for subsethood to reduce to an entropy measure. By exploiting the equivalence between the structures of IVFSs and Atanassov's intuitionistic fuzzy sets (A-IFSs), the notion of average possible cardinality is presented and its connection to least and biggest cardinalities, proposed in [E. Szmidt, J. Kacprzyk, Entropy for intuitionistic fuzzy sets, Fuzzy Sets and Systems 118 (2001) 467–477], is established both algebraically and geometrically. A relation with the cardinality of fuzzy sets (FSs) is also demonstrated. Moreover, the entropy-subsethood and interval-valued fuzzy entropy theorems are stated and algebraically proved, which generalize the work of Kosko [Fuzzy entropy and conditioning, Inform. Sci. 40(2) (1986) 165–174; Fuzziness vs. probability, International Journal of General Systems 17(2–3) (1990) 211–240; Neural Networks and Fuzzy Systems, Prentice-Hall International, Englewood Cliffs, NJ, 1992; Intuitionistic Fuzzy Sets: Theory and Applications, Vol. 35 of Studies in Fuzziness and Soft Computing, Physica-Verlag, Heidelberg, 1999] for FSs. Finally, connections of the proposed subsethood and entropy measures for IVFSs with corresponding definitions for FSs and A-IFSs are provided.

Fuzzy entropy on intuitionistic fuzzy sets: Research Articles

In this article we exploit the concept of probability for defining the fuzzy entropy of intuitionistic fuzzy sets (IFSs). We then propose two families of entropy measures for IFSs and also construct the axiom definition and properties. Two definitions of entropy for IFSs proposed by Burillo and Bustince in 1996 and Szmidt and Kacprzyk in 2001 are used. The first one allows us to measure the degree of intuitionism of an IFS, whereas the second one is a nonprobabilistic-type entropy measure with a geometric interpretation of IFSs used in comparison with our proposed entropy of IFSs in the numerical comparisons. The results show that the proposed entropy measures seem to be more reliable for presenting the degree of fuzziness of an IFS. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 443–451, 2006.

Fuzzy entropy on intuitionistic fuzzy sets

In this article we exploit the concept of probability for defining the fuzzy entropy of intuitionistic fuzzy sets (IFSs). We then propose two families of entropy measures for IFSs and also construct the axiom definition and properties. Two definitions of entropy for IFSs proposed by Burillo and Bustince in 1996 and Szmidt and Kacprzyk in 2001 are used. The first one allows us to measure the degree of intuitionism of an IFS, whereas the second one is a nonprobabilistic-type entropy measure with a geometric interpretation of IFSs used in comparison with our proposed entropy of IFSs in the numerical comparisons. The results show that the proposed entropy measures seem to be more reliable for presenting the degree of fuzziness of an IFS. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 443–451, 2006.

On entropy for intuitionistic fuzzy sets applying the Euclidean distance

Recently, Szmidt and Kacprzyk[Fuzzy Sets and Systems 118(2001) 467-477] proposed a non-probabilistic-type entropy measure for intuitionistic fuzzy sets. Tt is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them. They showed that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of <TEX>$F\bigcapF^c and F\bigcupF^c$</TEX>, while applying the Hamming distances. In this note, while applying the Euclidean distances, it is also shown that the proposed measure can be defined in terms of the ratio of some function of intuitionistic fuzzy cardinalities: of <TEX>$F\bigcapF^c and F\bigcupF^c$</TEX>.