Fuzzy Relations

Fuzzy relations are considered as softer models for expressing the strength of links between elements. Starting in early seventies, fuzzy relations have been defined, investigated, and applied in many different ways e.g., in fuzzy modeling, fuzzy diagnosis, and fuzzy control. They also have applications in fields such as Artificial Intelligence, Psychology, Medicine, Economics, and Sociology. In this monograph/thesis, we aim to study fuzzy equivalence relations in context of a modified definition of transitivity. This definition is formulated with the aim that it would provide a solution to the Poincare Paradox, which accompanies every definition of crisp and fuzzy transitiviy previously designed. Motivated by Debreu''s work in economics several existence theorems for numerical representation of max-min transitive symmetric fuzzy orderings are also given . Readership: Mathematicians and computer scientists, economists, engineers, psychologists and medicine researchers.