A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...

E cannot always use the classical methods to solve complicated problems in economics, engineering, social sciences, medical sciences etc. because different types of uncertainties are present in these theories. These days so many theories are available to deal with such type of uncertainties, such as, theory of fuzzy sets [1], theory of intuitionistic fuzzy sets [2], [3], theory of vague sets [4...

We give a framework to describe gauge theory on a certain class of commutative but nonassociative fuzzy spaces. Our description is in terms of an Abelian gauge connection valued in the algebra of functions on the cotangent bundle of the fuzzy space. The structure of such a gauge theory has many formal similarities with that of Yang-Mills theory. The components of the gauge connection are functi...

After introducing and developing fuzzy set theory, a lot of studies have been done to combine statistical methods and fuzzy set theory. This works, called fuzzy statistics, have been developed in some branches. In this article we review essential works on fuzzy estimation, fuzzy hypotheses testing, fuzzy regression, fuzzy Bayesian statistics, and some relevant fields. Zusammenfassung: Nach Entw...

The purpose of this paper is to provide a review of the current state of fuzzy logic theory in epidemiology, which is a recent area of research. We present four applications of fuzzy logic theory in epidemic problems, using linguistic fuzzy models, possibility measure, probability of fuzzy events and fuzzy decision making techniques. The results demonstrate that the applications of fuzzy sets i...

Intuitionistic fuzzy probabilities are an extension of the concept of probabilities with application in several practical problem solving tasks. The former are probabilities represented through intuitionistic fuzzy numbers, to indicate the uncertainty of the membership and nonmembership degrees in the value assigned to probabilities. Moreover, a dual hesitant fuzzy set (DHFS) is an extension of...

We proposed the theory of multi-fuzzy sets [Sabu and Ramakrishnan (2010a), (2011a)] as an extension of theories of fuzzy sets, L-fuzzy sets [Goguen (1967)] and intuitionistic fuzzy sets [Atanassov (1986)]. Theory of multi-fuzzy sets deals with multi-level fuzziness and multi-dimensional fuzziness. Our previous papers discussed the basic notions of multi-fuzzy sets, multi-fuzzy topology, and mul...

This paper marks the 50th anniversary of the publication of my first paper on fuzzy sets, “Fuzzy sets,” Information and Control, 1965. What is of historical interest is that initially—and for some time thereafter—my paper was an object of indifference, skepticism and derision. A prominent school of thought claimed that fuzzy set theory is probability theory in disguise. Positive comments were f...

in this paper, the capacitated location-routing problem with fuzzy demands (clrp-fd) is considered. the clrp-fd is composed of two well-known problems: facility location problem and vehicle routing problem. the problem has many real-life applications of which some have been addressed in the literature such as management of hazardous wastes and food and drink distribution. in clrp-fd, a set of c...