A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators

Interval-valued algebras and fuzzy logics

In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter

More on neutrosophic soft rough sets and its modification

This paper aims to introduce and discuss anew mathematical tool for dealing with uncertainties, which is a combination of neutrosophic sets, soft sets and rough sets, namely neutrosophic soft rough set model. Also, its modification is introduced. Some of their properties are studied and supported with proved propositions and many counter examples

Neutrosophic Sets and Systems, Vol. 10, 2015

This volume is a collection of thirteen papers, written by different authors and co-authors (listed in the order of the papers): J. J. Peng and J. Q. Wang, E. Marei, S. Kar, K. Basu, S. Mukherjee, I. M. Hezam, M. Abdel-Baset and F. Smarandache, K. Mondal, S. Pramanik, A. Ionescu, M. R. Parveen and P. Sekar, B. Teodorescu, D. Kour and K. Basu, P. P. Dey and B. C. Giri, A. A. A. Agboola. In first paper, the authors studied Multi-valued Neutrosophic Sets and its Application in Multi-criteria Decision-Making Problems. More on neutrosophic soft rough sets and its modification is discussed in the second paper. Solution of Multi-Criteria Assignment Problem using Neutrosophic Set Theory are studied in third paper. In fourth paper, Taylor Series Approximation to Solve Neutrosophic Multiobjective Programming Problem. Similarly in fifth paper, Decision Making Based on Some similarity Measures under Interval Rough Neutrosophic Environment is discussed. In paper six, Neutralité neutrosophique et expressivité dans le style journalistique is studied by the author. Neutrosophic Semilattices and Their Properties given in seventh paper. Liminality and Neutrosophy is proposed in the next paper. Application of Extended Fuzzy Program-ming Technique to a real life Transportation Problem in Neutrosophic environment in the next paper. Further, TOPSIS for Single Valued Neutrosophic Soft Expert Set Based Multi-attribute Decision Making Problems is discussed by the authors in the tenth paper. In eleventh paper, Neutrosophic Quadruple Numbers, Refined Neutrosophic Quadruple Numbers, Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers have been studied by the author. In the next paper, On Refined Neutrosophic Algebraic Structures. At the end, Neutrosophic Actions, Prevalence Order, Refinement of Neutrosophic Entities, and Neutrosophic Literal Logical Operators are introduced by the author

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