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...

We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy vers...

We extend the main idea of a fuzzy analysis of consensus introduced by Spillman, Spillman and Bezdek [12] that is based on a concept of a distance from consensus to a case when individual testimonies are individual intuitionistic fuzzy preference relations, as opposed to fuzzy preference relations commonly employed. Intuitionistic fuzzy preference relations, that in addition to a membership deg...

small polygroups are multi-valued systems that satisfy group-likeaxioms. using the notion of “belonging ($epsilon$)” and “quasi-coincidence (q)” offuzzy points with fuzzy sets, the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy subpolygroups isintroduced. the study of ($epsilon$, $epsilon$ $vee$ q)-fuzzy normal subpolygroups of a polygroupare dealt with. characterization and some of the fundam...

The n-dimensional fuzzy sets have been introduced as a generalization of interval-valued fuzzy sets, Atanassov’s intuitionistic and interval-valued intuitionistic fuzzy sets. In this paper we investigate t-norms on 3-dimensional sets which are joinmorphisms. Under some additional conditions we show that they can be represented using a representation which generalizes a similar representation fo...

The concept of quasi-coincidence of an interval valued fuzzy set is considered. By using this idea, the notion of interval valued (α, β)−fuzzy sub-implicative ideals of BCIalgebras is introduced, which is a generalization of a fuzzy sub-implicative ideal. Also some related properties are studied and in particular, the interval valued (∈,∈ ∨q)−fuzzy subimplicative ideals in a BCI-algebra will be...

In this paper, using fuzzy complex valued functions and fuzzy complex valued fuzzy measures ([11]) and interval-valued Choquet integrals ([2-6]), we define Choquet integral with respect to a fuzzy complex valued fuzzy measure of a fuzzy complex valued function and investigate some basic properties of them.