A Historical Account of Types of Fuzzy Sets and Their Relationships

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used

Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making

Recently proposed q-rung orthopair fuzzy set (q-ROFS) is a powerful and effective tool to describe fuzziness, uncertainty and vagueness. The prominent feature of q-ROFS is that the sum and square sum of membership and non-membership degrees are allowed to be greater than one with the sum of qth power of the membership degree and qth power of the non-membership degree is less than or equal to one. This characteristic makes q-ROFS more powerful and useful than intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS). The aim of this paper is to develop some aggregation operators for fusing q-rung orthopair fuzzy information. As the Muirhead mean (MM) is considered as a useful aggregation technology which can capture interrelationships among all aggregated arguments, we extend the MM to q-rung orthopair fuzzy environment and propose a family of q-rung orthopair fuzzy Muirhead mean operators. Moreover, we investigate some desirable properties and special cases of the proposed operators. Further, we apply the proposed operators to solve multi-attribute group decision making (MAGDM) problems. Finally, a numerical instance as well as some comparative analysis are provided to demonstrate the validity and superiorities of the proposed method

An Extended TODIM Method for Group Decision Making with the Interval Intuitionistic Fuzzy Sets

For a multiple-attribute group decision-making problem with interval intuitionistic fuzzy sets, a method based on extended TODIM is proposed. First, the concepts of interval intuitionistic fuzzy set and its algorithms are defined, and then the entropy method to determine the weights is put forward. Then, based on the Hamming distance and the Euclidean distance of the interval intuitionistic fuzzy set, both of which have been defined, function mapping is given for the attribute. Finally, to solve multiple-attribute group decision-making problems using interval intuitionistic fuzzy sets, a method based on extended TODIM is put forward, and a case that deals with the site selection of airport terminals is given to prove the method

Multi-criteria decision-making method based on intuitionistic trapezoidal fuzzy prioritised owa operator

In the real decision-making, there are many multiple attribute decision-making (MADM) problems, in which there exists the prioritised relationship among decision-making attributes. In this paper, with respect to the prioritised multi-criteria decision-making problems under intuitionistic trapezoidal fuzzy information, a new decision-making method on the basis of the intuitionistic trapezoidal fuzzy prioritised ordered weighted aggregation operator has been proposed. Firstly, the definitions, operational rules and characteristics of intuitionistic trapezoidal fuzzy numbers and POWA operator have been introduced. Then, intuitionistic trapezoidal fuzzy prioritised ordered weighted aggregation (ITFPOWA) operator has been defined as well as the computational method of associated weight, and some properties have been studied and proved. Furthermore, based on the ITFPOWA operator, an approach to the multi-criteria decision-making with intuitionistic trapezoidal fuzzy numbers has been established. Finally, an illustrative example has been given to prove the evaluation procedures of the developed approach and to demonstrate its practicality and validity

Fuzzy decision making: A bibliometric-based review

Fuzzy decision-making consists in making decisions under complex and uncertain environments where the information can be assessed with fuzzy sets and systems. The aim of this study is to review the main contributions in this field by using a bibliometric approach. For doing so, the article uses a wide range of bibliometric indicators including the citations and the h-index. Moreover, it also uses the VOS viewer software in order to map the main trends in this area. The work considers the leading journals, articles, authors and institutions. The results indicate that the USA was the traditional leader in this field with the most significant researcher. However, during the last years, this field is receiving more attention by Asian authors that are starting to lead the field. This discipline has a strong potential and the expectations for the future is that it will continue to grow

Algorithms for possibility linguistic single-valued neutrosophic decision-making based on COPRAS and aggregation operators with new information measures

The objective of this work is to introduce the concept of the possibility linguistic single-valued neutrosophic set (PLSVNS) for better dealing with the imprecise and uncertain information during the decision-making process. The prominent characteristics of this set are that it considers two distinctive sorts of information such as the membership, indeterminacy, non-membership degrees, and their corresponding possibility degree. In it, first, we stated some operational laws, score and accuracy functions, comparison laws between the pairs of the set. Then, we define weighted averaging and geometric aggregation operators (AOs) to collaborate the PLSVNSs into a single one. Further, we present two algorithms based on a complex proportional assessment (COPRAS) method and AOs based method under PLSVNS information to solve the decision-making problems. In these methods, the information related to weights of decision makers and criteria is determined with the help of a distance and entropy measures. Finally, a practical real-life example is provided to expose the materialness and the viability of our work

(α, β)−Pythagorean Fuzzy Numbers Descriptor Systems

By using pythagorean fuzzy sets and T-S fuzzy descriptor systems, the new (α, β)-pythagorean fuzzy descriptor systems are proposed in this paper. Their definition is given firstly, and the stability of this kind of systems is studied, the relation of (α, β)-pythagorean fuzzy descriptor systems and T-S fuzzy descriptor systems is discussed. The (α, β)-pythagorean fuzzy controller and the stability of (α, β)-pythagorean fuzzy descriptor systems are deeply researched. The (α, β)-pythagorean fuzzy descriptor systems can be better used to solve the problems of actual nonlinear control. The (α, β)-pythagorean fuzzy descriptor systems will be a new research direction, and will become a universal method to solve practical problems. Finally, an example is given to illustrate effectiveness of the proposed method

CROSA: Context-aware cloud service ranking approach using online reviews based on sentiment analysis

[EN] The explosion of cloud services over the Internet has raised new challenges in cloud service selection and ranking. The existence of a great variety of offered cloud services made the users think deeply about the most appropriate services that meet their needs and at the same time are adaptable to their context. Nowadays, online reviews are used for the purpose of enhancing the effectiveness of finding useful product information, having impact on the consumers' decision-making process. In this context, the current paper suggests a context-aware cloud service ranking approach using online reviews and based on sentiment analysis (CROSA). Its main objective is to ease the cloud service selection. The CROSA approach analyzes sentiments associated with service measurement index (SMI)-based service properties for each alternative cloud service. Moreover, it enhances the cloud service decision-making by supporting fuzzy sentiments through the intuitionistic fuzzy set theory and PROMETHEE II. The experimental results presented in this paper show that this approach is efficient and performing.Ben-Abdallah, E.; Boukadi, K.; Lloret, J.; Hammami, M. (2021). CROSA: Context-aware cloud service ranking approach using online reviews based on sentiment analysis. Concurrency and Computation: Practice and Experience. 33(7):1-16. https://doi.org/10.1002/cpe.5358S11633

Expert Estimates Averaging by Constructing Intuitionistic Fuzzy Triangles

The problem of ranking (sorting) of m alternatives is considered when experts evaluate each alternative according to k criteria. Functions of arithmetic and geometric averages are constructed for decision making. We present a generalization of this scheme when there are evaluation matrices of several experts and this information is aggregated in the form of triangular intuitionistic fuzzy numbers. Fuzzy triangles were constructed with different uncertainty levels, experts decision matrices and the number of experts varied from 2 to 5. Moreover, method for construction of experts decision probability matrices is proposed in the paper. Ranking results obtained by performing Monte Carlo simulations. Probabilities of errors are compared for arithmetic, geometric, fuzzy arithmetic and fuzzy geometric averages