Abstract: The present paper is focusing on the order, size and degree of the nodes of the interval-valued fuzzy graphs, which are isomorphic. Isomorphism between Interval-valued fuzzy graphs is proved to be an equivalence relation, whereas the Weak isomorphism is proved to be a partial order. Few properties of interval valued fuzzy graphs, which are self complementary, are discussed.

We study some properties of interval-valued fuzzy normal subgroups of a group. In particular, we obtain two characterizations of interval-valued fuzzy normal subgroups. Moreover, we introduce the concept of an interval-valued fuzzy coset and obtain several results which are analogous of some basic theorems of group theory.

A new accuracy function for the theory of interval-valued intuitionistic fuzzy set, which overcomes some difficulties arising in the existing methods for determining rank of interval-valued intuitionistic fuzzy numbers, is proposed by taking into account the hesitancy degree of interval-valued intuitionistic fuzzy sets. By comparing it with several proposed accuracy functions, the necessity and...

In this paper, we research the relationship between entropy and similarity of interval valued intuitionistic fuzzy sets in detail and prove eight theorems that entropy and similarity of interval valued intuitionistic fuzzy sets can be transformed to each other based on their axiomatic definitions. Finally, we propose some formulaes to calculate entropy and similarity of interval valued intuitio...

Grey systems and interval valued fuzzy sets appear to be similar concepts. This abstract provides a brief introduction to grey systems and compares them to interval valued fuzzy sets. We argue that grey system is similar to an interval fuzzy set, but has different properties. Grey systems focus on the interval range of the system property itself, but interval fuzzy sets consider the fuzzy membe...

The aim of this work is to analyze the interval canonical representation for fuzzy QL-implications and automorphisms. Intervals have been used to model the uncertainty of a specialist’s information related to truth values in the fuzzy propositional calculus: the basic systems are based on interval fuzzy connectives. Thus, using subsets of the real unit interval as the standard sets of truth deg...

In practical situations, interval-valued fuzzy sets are frequently encountered. In this paper, firstly, we present shadowed sets for interpreting and understanding interval fuzzy sets. We also provide an analytic solution to computing the pair of thresholds by searching for a balance of uncertainty in the framework of shadowed sets. Secondly, we construct errorsbased three-way approximations of...

Abstract. Theoretical concepts of graphs are highly utilized by computer scientists. Especially in research areas of computer science such as data mining, image segmentation, clustering image capturing and networking. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represe...

In the traditional fuzzy logic, the expert’s degree of certainty in a statement is described either by a number from the interval [0, 1] or by a subinterval of such an interval. To adequately describe the opinion of several experts, researchers proposed to use a union of the corresponding sets – which is, in general, more complex than an interval. In this paper, we prove that for such set-value...

Type-2 fuzzy sets are growing in popularity as, for certain applications they model uncertainty and imprecision better than type1 fuzzy sets. However, type-2 fuzzy sets can be difficult to understand and explain. Recent work has introduced embedded type-2 fuzzy sets and the Representation Theorem which enable us to discuss type-2 fuzzy sets in a different way. In particular they allow for alter...