The Encyclopedia of Neutrosophic Researchers - vol. 1

This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements

Interval-valued intuitionistic fuzzy soft graph

One of the theories designed to deal with uncertainty is the soft set theory. These collections were used due to a lack of membership functions in the fields of decision-making, systems analysis, classification, data mining, medical diagnosis, etc. Fuzzy graphs based on soft sets were developed alongside fuzzy graphs. Studying these graphs, examining the properties and operators on it, give special flexibility in dealing with indeterminate problems. In particular, most of the issues around us are mixed and operations are conveniently used in many combinatorial applications. Therefore, the study of operations have a significant effect on solving problems based on decisionmaking, medical, etc. In this paper, we introduce the notion of interval-valued intuitionistic fuzzy soft graphs, by combine concepts of interval-valued intuitionistic fuzzy graphs and fuzzy soft graphs. We also present several different types of operations including cartesian product, strong product and composition on interval-valued intuitionistic fuzzy soft graphs and investigate some properties of them.Publisher's Versio

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

Atanassov’s intuitionistic fuzzy translations of intuitionistic fuzzy subalgebras in BG-algebras

In this paper, the concepts of intuitionistic fuzzy translation to intuitionistic fuzzy subalgebras in BG-algebras are introduced. The notion of intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy subalgebras are introduced and several related properties are investigated. In this paper, the relationships between intuitionistic fuzzy translations and intuitionistic fuzzy extensions of intuitionistic fuzzy subalgebras are investigated.Publisher's Versio

Related Study of Soft Set and Its Application A Review

Abstract In the present paper some literature related to soft sets are collected. The literature is motivated by Molodsov