A Novel (R,S)-Norm Entropy Measure of Intuitionistic Fuzzy Sets and Its Applications in Multi-Attribute Decision-Making

Linguistic intuitionistic fuzzy multi-attribute bilateral matching considering satisfaction and fairness degree

Aiming at the multi-attribute bilateral matching problem with unknown attribute weights under a linguistic intuitionistic fuzzy environment, a decision method based on TODIM considering satisfaction and fairness degrees is proposed. First, the theories of linguistic intuitionistic fuzzy sets and bilateral matching are given, and the multi-attribute bilateral matching problem under a linguistic intuitionistic fuzzy environment is described. To solve this problem, according to linguistic intuitionistic fuzzy preference matrices, the overall attribute dominances are calculated based on TODIM; considering group consensus, a new method is proposed to calculate attribute weights based on linguistic intuitionistic fuzzy induced ordered weighted averaging (LIFIOWA) operator; then, the overall dominances of bilateral subjects are obtained by aggregating the overall attribute dominances and attribute weights. Furthermore, the overall dominances are standardized to calculate the satisfaction degrees of bilateral subjects; the fairness degrees of bilateral subjects are calculated considering the loss attenuation coefficient. Based on satisfaction degree matrices, fairness degree matrices and bilateral matching matrices, multiple bilateral matching models are established and then solved to obtain the optimal bilateral matching scheme. Finally, an example shows the effectiveness, reliability and accuracy of the proposed method. The research results indicate the following main characteristics of the proposed method: (1) A new method for calculating the unknown attribute weights using LIFIOWA operator is proposed. (2) According to the TODIM idea, a calculation method for fairness degree considering the loss attenuation coefficient is proposed. (3) Considering satisfaction and fairness degrees, multiple bilateral matching models under a linguistic intuitionistic fuzzy environment are established.

Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov's intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.

Q-Rung Probabilistic Dual Hesitant Fuzzy Sets and Their Application in Multi-Attribute Decision-Making

The probabilistic dual hesitant fuzzy sets (PDHFSs), which are able to consider multiple membership and non-membership degrees as well as their probabilistic information, provide decision experts a flexible manner to evaluate attribute values in complicated realistic multi-attribute decision-making (MADM) situations. However, recently developed MADM approaches on the basis of PDHFSs still have a number of shortcomings in both evaluation information expression and attribute values integration. Hence, our aim is to evade these drawbacks by proposing a new decision-making method. To realize this purpose, first of all a new fuzzy information representation manner is introduced, called q-rung probabilistic dual hesitant fuzzy sets (q-RPDHFSs), by capturing the probability of each element in q-rung dual hesitant fuzzy sets. The most attractive character of q-RPDHFSs is that they give decision experts incomparable degree of freedom so that attribute values of each alternative can be appropriately depicted. To make the utilization of q-RPDHFSs more convenient, we continue to introduce basic operational rules, comparison method and distance measure of q-RPDHFSs. When considering to integrate attribute values in q-rung probabilistic dual hesitant fuzzy MADM problems, we propose a series of novel operators based on the power average and Muirhead mean. As displayed in the main text, the new operators exhibit good performance and high efficiency in information fusion process. At last, a new MADM method with q-RPDHFSs and its main steps are demonstrated in detail. Its performance in resolving practical decision-making situations is studied by examples analysis.

Application of Exponential Jensen Picture Fuzzy Divergence Measure in Multi-Criteria Group Decision Making

A divergence measure plays a crucial part in discriminating two probability distributions and drawing inferences constructed on such discrimination. The intention of this study is to propose such a divergence measure based on Jensen inequality and exponential entropy in the settings of probability theory. Further, the idea has been generalized to fuzzy sets to familiarize a novel picture fuzzy divergence measure. Besides proposing the validity, some of its key properties are also deliberated. Finally, two illustrative examples are solved based on the proposed picture fuzzy divergence measure which shows the expediency and effectiveness of the proposed approach.

Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.

Evaluation of Sustainability Information Disclosure Based on Entropy

Disclosure of sustainability information is important for stockholders and governments. In order to evaluate the quality of sustainability information disclosure in heavily polluting industries, the quality of the disclosure is proposed to be evaluated from completeness, adequacy, relevance, reliability, normativeness and clarity aspects. The corresponding evaluation indicator system is constructed. Due to the ambiguity and complexity of the evaluation information, the intuitionistic fuzzy sets are applied to model the linguistic ratings. Entropy is used to derive the weight of experts, the object weight and the subject weight of the indicators. which are integrated when dealing with the evaluation information. The quality of sustainability information disclosure of seven representative companies in heavily polluting industries is evaluated. The importance of indicators and ranking of the companies are derived. Based on the evaluation results, the discussion and suggestions are also provided.