Bivalent and other solutions of fuzzy relational equations via linguistic hedges

Abstract We show that the well-known results regarding solutions of fuzzy relational equations and their systems can easily be generalized to obtain criteria regarding constrained solutions such as solutions which are crisp relations. When the constraint is empty, constrained solutions are ordinary solutions. The generalization is obtained by employing intensifying and relaxing linguistic hedges, conceived in this paper as certain unary functions on the scale of truth degrees. One aim of the paper is to highlight the problem of constrained solutions and to demonstrate that this problem naturally appears when identifying unknown relations. The other is to emphasize the role of linguistic hedges as constraints. © 2011 Elsevier B.V. All rights reserved. Motivation Fuzzy relational equations play an important role in fuzzy set theory and its applications, see and every fuzzy relation U satisfying the first or the second equality is called a solution of the respective fuzzy relational equation. The nature of the unknown relationship represented by U may impose additional constraints on U. For example, one may require that U be a bivalent (crisp) relation (see Section 3 for an illustrative example). More generally

Application of fuzzy relations to test theory

На відміну від класичного ймовірного підходу, в даній статті розглядається метод генерування та оцінки тестів, заснований на нечіткому підході. Це призводить до завдань, які можуть бути вирішені в рамках нечітких реляційних рівнянь. Кілька прикладів ілюструють користь такого підходу.В отличие от классического вероятного подхода, в данной статье рассматривается метод генерирования и оценки тестов, основанный на нечетком подходе. Это приводит к задачам, которые могут быть решены в рамках нечетких реляционных уравнений. Несколько примеров иллюстрируют пользу такого подхода.Unlike the classical probability-based approach we consider the ge-neration and evaluation of tests based on a fuzzy approach. This leads to tasks which can be solved within the frame of fuzzy relational equations. Several examples illustrate the usefulness of our approach

Using intensifying hedges to reduce size of multi-adjoint concept lattices with heterogeneous conjunctors

Abstract. In this work we focus on the use of intensifying hedges as a tool to reduce the size of the recently introduced multi-adjoint concept lattices with heterogeneous conjunctors

Computer science: the hardware software and heart of IT

1st edition, 201

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Fuzzy Logic

The capability of Fuzzy Logic in the development of emerging technologies is introduced in this book. The book consists of sixteen chapters showing various applications in the field of Bioinformatics, Health, Security, Communications, Transportations, Financial Management, Energy and Environment Systems. This book is a major reference source for all those concerned with applied intelligent systems. The intended readers are researchers, engineers, medical practitioners, and graduate students interested in fuzzy logic systems