the notion of strong arcs in a fuzzy graph was introduced bybhutani and rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. in mordeson and yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.in this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Lukasiewicz n-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the al...

A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. ...

The aim of this paper is to introduce the notions of interval valued (∈,∈ ∨q)-fuzzy Boolean (implicative, positive implicative and fantastic) filters in BL-algebras and to investigate some related properties. Some characterizations of these generalized fuzzy filters are derived. Finally, the relations among these generalized fuzzy filters are discussed. It is proved that an interval valued (∈,∈...

The Multiple Attribute Group Decision Making (MAGDM) problems are investigated in which all the information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices, and the information about attribute weights is partially known. Three different models are utilized for calculating the completely unknown attribute weights which are then used for aggr...

The concept of quasi-coincidence of an interval-valued fuzzy set is considered. By using this new idea, the notion of interval-valued (α, β)−fuzzy k−ideals of semirings is introduced, which is a generalization of a fuzzy k−ideal. Also some related properties are studied and in particular, the interval-valued (∈,∈ ∨q)−fuzzy k−ideals in a semiring will be investigated. Finally, the concept of imp...

On the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine...

Fuzzy valued measure ([7], [10], [3], [5]) is a natural generalization of a set valued measure ([6]). Infinite addition is defined ([12]) as a Zadeh’s extension principle of continuity. In [9], using an additive fuzzy valued measure, an integral of single valued function is defined and some basic properties are given. In this paper we proceed to investigate specific properties of integrals in f...

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first p...

This paper presents a new method for document retrieval using fuzzy-valued concept networks, where the relevant degrees between the concepts in a fuzzy-valued concept network are represented by arbitrary shapes of fuzzy numbers. There are two kinds of relevant relationships between any two concepts in a fuzzy-valued concept network, i.e., fuzzy positive association and fuzzy negative associatio...