Interval-Valued Intuitionistic Hesitant Fuzzy Aggregation Operators and Their Application in Group Decision-Making

Hesitant fuzzy sets, permitting the membership of an element to be a set of several possible values, can be used as an efficient mathematical tool for modelling people’s hesitancy in daily life. In this paper, we extend the hesitant fuzzy set to interval-valued intuitionistic fuzzy environments and propose the concept of interval-valued intuitionistic hesitant fuzzy set, which allows the membership of an element to be a set of several possible interval-valued intuitionistic fuzzy numbers. The aim of this paper is to develop a series of aggregation operators for interval-valued intuitionistic hesitant fuzzy information. Then, some desired properties of the developed operators are studied, and the relationships among these operators are discussed. Furthermore, we apply these aggregation operators to develop an approach to multiple attribute group decision-making with interval-valued intuitionistic hesitant fuzzy information. Finally, a numerical example is provided to illustrate the application of the developed approach

Triangular Cubic Hesitant Fuzzy Einstein Hybrid Weighted Averaging Operator and Its Application to Decision Making

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Neutrosophic Theory and its Applications : Collected Papers - vol. 1

Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every entity together with its opposite or negation and with their spectrum of neutralities in between them (i.e. entities supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel\u27s dialectics (the last one is based on and only). According to this theory every entity tends to be neutralized and balanced by and entities - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Hence, in one hand, the Neutrosophic Theory is based on the triad , , and . In the other hand, Neutrosophic Theory studies the indeterminacy, labelled as I, with In = I for n ≥ 1, and mI + nI = (m+n)I, in neutrosophic structures developed in algebra, geometry, topology etc. The most developed fields of the Neutrosophic Theory are Neutrosophic Set, Neutrosophic Logic, Neutrosophic Probability, and Neutrosophic Statistics - that started in 1995, and recently Neutrosophic Precalculus and Neutrosophic Calculus, together with their applications in practice. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic). In neutrosophic logic a proposition has a degree of truth (T), a degree of indeterminacy (I), and a degree of falsity (F), where T, I, F are standard or non-standard subsets of ]-0, 1+[. Neutrosophic Probability is a generalization of the classical probability and imprecise probability. Neutrosophic Statistics is a generalization of the classical statistics. What distinguishes the neutrosophics from other fields is the , which means neither nor . And , which of course depends on , can be indeterminacy, neutrality, tie (game), unknown, contradiction, vagueness, ignorance, incompleteness, imprecision, etc