Intuitionistic Fuzzy Entropy Measures Research Articles

An improved entropy function for the intuitionistic fuzzy sets with application to cloud vendor selection

This study proposes a novel entropy function for the intuitionistic fuzzy sets to improve the existing fuzzy entropy measure. We introduce an attitude-based entropy measure by methodically calculating the experts’ attitude values through variance approach. We discuss several important properties and present an example to demonstrate the applicability and efficacy of the proposed method. An illustrative example exhibits the effectiveness of the proposed intuitionistic fuzzy entropy functions and measures. We further show the superiority of the proposed intuitionistic fuzzy entropy measures over the existing measures.

Proposed Intuitionistic Fuzzy Entropy Measure Along With Novel Multicriteria Sorting Techniques

Recently, the major environmental change and a pandemic called COVID-19 have heavily impacted the economy, business, and health of each country. Moreover, the climatic changes and COVID-19 are calamities to human life. In other words, these two aspects threaten the existence of humans and the sustenance of the overall development of a country. These two factors particularly influence the tourism sector, so a strategy balancing environmental quality and dealing with the ill effects of COVID-19 is formulated to uplift the economic sectors. Atannasov’s intuitionistic fuzzy domain is used to model the environmental quality and COVID-19 due to the involvement of hesitancy and uncertainty. The precise measurement of the imprecision in the information is obtained with the help of entropy measure. The paper analyzes the two aspects using a novel entropy measure based on multiple criteria sorting (MCS). Here, the two MCS problems are solved with the help of two proposed techniques: TOPSIS-GREY-sort and ENTROPY-TOPSIS-GREY-sort. A case study showing the impact of COVID-19 in the Philippines and the environmental quality of Tehran (the capital city of Iran) are considered to validate the functioning of the proposed techniques. We use “A novel sorting method TOPSIS-SORT: an application for Tehran environmental quality evaluation (2016), Ekonomica a management,” and “Current Issues in Tourism 25.2(2022): 168–178, Taylor and Francis” for the comparative analysis.

Multi-Criteria Decision-Making Model using Intuitionistic Fuzzy Entropy and Variable Weight Theory

The aim of this research is to develop a new multi-criteria decision-making method that integrates an intuitionistic fuzzy entropy measure and variable weight theory to be implemented in different fields to provide a solution for MCDM problems when the available information is incomplete. A limited number of studies have considered determining decision maker’s weights by performing objective techniques, and almost all of these researches detected a constant weights for the decision makers. In addition, most of the MCDM studies were not formulated to perform sensitivity analysis. The new method is based on the TOPSIS model with an intuitionistic fuzzy entropy measure in the exponential-related function form and the engagement of the variable weight theory to determine weights for the decision-makers that vary as per attibutes. Lastly, a mathematical model was developed in this research to be as an input for developing the mobile-aplication based method in future for virtual use of the new MCDM method.

An intuitionistic fuzzy entropy approach for supplier selection

Due to apparent flexibility of Intuitionistic Fuzzy Set (IFS) concepts in dealing with the imprecision or uncertainty, these are proving to be quite useful in many application areas for a more human consistent reasoning under imperfectly defined facts and imprecise knowledge. In this paper, we apply notions of entropy and intuitionistic fuzzy sets to present a new fuzzy decision-making approach called intuitionistic fuzzy entropy measure for selection and ranking the suppliers with respect to the attributes. An entropy-based model is formulated and applied to a real case study aiming to examine the rankings of suppliers. Furthermore, the weights for each alternative, with respect to the criteria, are calculated using intuitionistic fuzzy entropy measure. The supplier with the highest weight is selected as the best alternative. This proposed model helps the decision-makers in better understanding of the weight of each criterion without relying on the mere expertise.

On a generalized entropy and dissimilarity measure in intuitionistic fuzzy environment with applications

Imprecision is an intrinsic characteristic of human behaviour. The concept of fuzziness is a well-recognized mechanism to quantify the imprecision and ambiguity of human judgement. In the last three decades, various extensions of fuzzy theory have been put forward. Intuitionistic fuzzy theory reveals some interesting aspects of approximate models. Intuitionistic fuzzy entropy measures the average amount of imprecision and ambiguity present in an intuitionistic fuzzy set. In this work, we propose flexible (generalized) measure of intuitionistic fuzzy (IF) entropy and establish its superiority over some existing IF-entropies. We introduce a generalized IF-dissimilarity measure and prove some of its properties. We also provide an improved TOPSIS method to handle multiple attribute group decision-making problem in intuitionistic fuzzy settings using our proposed IF-entropy, IF-dissimilarity and IF-correlation efficiency. We then investigates the performance of the proposed IF-dissimilarity in a pattern recognition problem and obtain encouraging results.

On intuitionistic fuzzy order-α divergence and entropy measures with MABAC method for multiple attribute group decision-making

The development of information measures associated with fuzzy and intuitionistic fuzzy sets is an important research area from the past few decades. Divergence and entropy are two significant information measures in the intuitionistic fuzzy set (IFS) theory, which have gained wider attention from researchers due to their extensive applications in different areas. In the literature, the existing information measures for IFSs have some drawbacks, which make them irrelevant to use in application areas. In order to obtain more robust and flexible information measures for IFSs, the present work develops and studies some parametric information measures under the intuitionistic fuzzy environment. First, the paper reviews the existing intuitionistic fuzzy divergence measures in detail with their shortcomings and then proposes four new order-α divergence measures between two IFSs. It is worth mentioning that the developed divergence measures satisfy several elegant mathematical properties. Second, we define four new entropy measures called order-α intuitionistic fuzzy entropy measures in order to quantify the fuzziness associated with an IFS. We prove basic and advanced properties of the order-α intuitionistic fuzzy entropy measures for justifying their validity. The paper shows that the introduced measures include various existing fuzzy and intuitionistic fuzzy information measures as their special cases. Further, utilizing the conventional multi-attributive border approximation area comparison (MABAC) model, we develop an intuitionistic fuzzy MABAC method to solve real-life multiple attribute group decision-making problems. Finally, the proposed method is demonstrated by using a practical application of personnel selection.

An intuitionistic fuzzy $$(\delta , \gamma )$$ ( δ , γ ) -norm entropy with its application in supplier selection problem

In this communication, based on the concept of $$(\delta , \gamma )$$ -norm entropy, an $$(\delta , \gamma )$$ -norm intuitionistic fuzzy entropy measure is introduced in the settings of intuitionistic fuzzy set theory. Some of its major properties are also proved. The performance of the proposed entropy measure is demonstrated using numerical examples. Based on the proposed intuitionistic fuzzy (IF) entropy, a new multiple-attribute decision-making method (MADM) considering the merits of subjective and objective weights has been introduced. Two methods of finding the weights of attributes are discussed. The proposed MADM method is effectively explained with the help of supplier selection example.

Generalized Intuitionistic Fuzzy Entropy Measure of Order α and Degree β and Its Applications to Multi-Criteria Decision Making Problem

The objective of this manuscript is divided into two fold. Firstly, a more generalized intuitionistic fuzzy entropy measure of order and degree has been presented for measuring the degree of fuzziness of the set with a proof of its validity. A structured linguistic variable has been taken as an illustrative example to show its validity and superiority than the existing measures. Furthermore, based on this measure, an approach to deal with multi-criteria decision making (MCDM) problem is developed. Finally, a practical example is provided to illustrate the decision making process. A computed result is compared with the help of existing results. A sensitivity analysis on the different values of the parameters will make a decision maker more choice for accessing their results.

R-norm entropy on intuitionistic fuzzy sets

Fuzzy sets have led to study of vague phenomena. Generalizations of fuzzy sets have led to deeper analysis of these types of studies. The problem that then arises is to finding quantitative measures for vagueness and other features of these phenomena. In the present paper, based on the concept of R-norm fuzzy entropy, an R-norm intuitionistic fuzzy entropy measure is proposed in the setting of intuitionistic fuzzy set theory. This measure is a generalized version of R-norm fuzzy entropy proposed by Hooda in 2004. Some properties of this measure are proved. Finally, a numerical example is given to show that the proposed entropy measure for intuitionistic fuzzy set is reasonable by comparing it with other existing intuitionistic fuzzy entropy measures.

Generalized Exponential Entropy on Intuitionistic Fuzzy Sets

Based on the concept of intuitionistic fuzzy entropy, this paper proposes a generalized parametric exponential intuitionistic fuzzy entropy measure. This measure is a generalized version of exponential intuitionistic fuzzy entropy proposed by Verma and Sharma, and its validity as an intuitionistic fuzzy entropy is verified. Further, some interesting properties of this measure are also analyzed, and an example shows that this measure is nonmonotone.

Interval-valued intuitionistic fuzzy continuous weighted entropy and its application to multi-criteria fuzzy group decision making

In this paper, we propose the interval-valued intuitionistic fuzzy continuous weighted entropy which generalizes intuitionistic fuzzy entropy measures defined by Szmidt and Kacprzyk on the basis of the continuous ordered weighted averaging (COWA) operator. It is shown that the continuous entropy of interval-valued intuitionistic fuzzy set is the average of the entropies of its interval-valued intuitionistic fuzzy values (IVIFVs). We also establish the programming model to determine optimal weight of criteria with the principle of minimum entropy. Furthermore, we investigate the multi-criteria group decision making (MCGDM) problems in which criteria values take the form of interval-valued intuitionistic fuzzy information. An approach to interval-valued intuitionistic fuzzy multi-criteria group decision making is given, which is based on the weighted relative closeness and the IVIFV attitudinal expected score function. Finally, emergency risk management (ERM) evaluation is provided to illustrate the application of the developed approach.

Interval-valued Intuitionistic Fuzzy Weighted Entropy in Evaluation of Service Quality

The importance of measuring service quality perceived by customers is an issue since the service quality is a key to success in service oriented industry. The estimation of service quality should be carried out with suitable measurement scales according to the types of service provided. To the best of authors’ knowledge, there have been little discussion about the applications of interval-valued intuitionistic fuzzy sets- based evaluation in measuring service quality. This paper proposes an evaluation for service quality of five vehicle insurance companies using interval-valued intuitionistic fuzzy entropy measure. Linguistic data were collected from customers using a questionnaire. An averaged interval-valued intuitionistic fuzzy number is used to construct decision matrix. Interval-valued intuitionistic fuzzy weighted averaging operator is used to aggregate the interval-valued intuitionistic fuzzy numbers for alternatives. It is found that PCF Insurance was evaluated as the best vehicle insurance company in providing service quality to customers DOI: http://dx.doi.org/10.11591/ij-ict.v2i1.1525

Objective weights with intuitionistic fuzzy entropy measures and computational experiment analysis

It is important to properly assess the weights of attributes when solving multi-attribute decision problems because variations in the weights often influence the rankings of the alternatives. In this paper, we propose an alternative objective weighting method to generate objective weights based on intuitionistic fuzzy (IF) entropy measures, which depend on the nature of a decision matrix in an intuitionistic fuzzy environment. Instead of the traditional fuzzy entropy measure, which is characterized by using the discriminating power to calculate the attribute weights, the proposed approach adopts the IF entropy measure, which emphasizes the credibility of the data. The IF entropy measure applied here is derived from a geometric interpretation of intuitionistic fuzzy sets and incorporates the concept of a ratio of distance measures. We implement four distance measures in the proposed approach and compare them in a computational experiment. The experimental results indicate that different IF entropy measures used in weighting methods can generate distinct objective attribute weights. In particular, when the number of attributes increases, the discrepancy between the IF entropy measures increases.

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.

Determining objective weights with intuitionistic fuzzy entropy measures: A comparative analysis

In this paper, we propose a new objective weighting method that employs intuitionistic fuzzy (IF) entropy measures to solve multiple-attribute decision-making problems in the context of intuitionistic fuzzy sets. Instead of traditional fuzzy entropy, which uses the probabilistic discrimination of attributes to obtain attribute weights, we utilize the IF entropy to assess objective weights based on the credibility of the input data. We examine various measures for IF entropy with respect to hesitation degree, probability, non-probability, and geometry to calculate the attribute weights. A comparative analysis of different measures to generate attribute rankings is illustrated with both computational experiments as well as analyses of Pearson correlations, Spearman rank correlations, contradiction rates, inversion rates, and consistency rates. The experimental results indicate that ranking the outcomes of attributes not only depends on the type of IF entropy measures but is also affected by the number of attributes and the number of alternatives.

A COMPARATIVE ANALYSIS OF OBJECTIVE WEIGHTING METHODS WITH INTUITIONISTIC FUZZY ENTROPY MEASURES

ABSTRACT Instead of the traditional entropy measures which focus on the discrimination of attributes, we utilize the nature of intuitionistic fuzzy (IF) entropy measures which assess the weight of attributes based on the credibility of data to propose a new objective weighting method for solving the multiple attribute decision making (MADM) problems. In this proposed method, we executed various and the newest IF entropy measures introduced by Vlachos and Sergiadis [18], and Zeng and Li [25]. Both of them estimated the IF entropy from the viewpoint of membership and non-membership degree of intuitionistic fuzzy sets. A comparative analysis of experimental simulation which contains not only different combinations of given number of attributes and alternatives but also different IF entropy measures is designed to observe and discuss the outcomes. The experimental results indicated that different IF entropy measures applied in the weighting method would generate distinct weight values and the ranking of attributes even though the measures originated from the same theorem. Especially, the number of attributes decides the extent of similarity among IF entropy measures. With the new objective weighting method, the decision maker can combine it with his/her subjective weights to obtain a compromise attribute weights in MADM problems.