For interval-valued fuzzy datasets, people have started to do research on interval-valued fuzzy rough sets and relevant models. However, these models could not be effectively applied to handle the real-valued datasets such as interval-valued fuzzy datasets as variable precision problems were not considered in interval-valued fuzzy rough sets. In this paper, fuzzy variable precision rough sets a...

The relationship between the intuitionistic fuzzy sets and the algebraic hyperstructures is described in this paper. The concept of the quasi-coincidence of an intuitionistic fuzzy interval valued with an interval-valued intuitionistic fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of an intuitionistic fuzzy point in intuitionistic fuzzy sets. By using thi...

Interval-valued fuzzy sets are based on the algebra of subintervals of the unit interval [0, 1]. We study valuations as a special type of measures on this algebra. We present a description of all valuations which preserve the standard fuzzy negation and extend the identity on the elements of the form (x, x). Consequences for sublattices are formulated. Keywords— Girard algebra, interval-valued ...

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 recording of interval-valued data has become a common practice nowadays. This paper presents some partitioning clustering algorithms for interval-valued data. The proposed methods furnish a partition of the input data and a corresponding prototype (a vector of intervals) for each cluster by optimizing an adequacy criterion which is based on suitable adaptive city-block distances between vec...

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...

Based on the Choquet integral and the generalized Shapley function, two new induced Atanassov’s interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov’s interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov’s interval-val...

Abstract.With respect to interval-valued hesitant fuzzy multi-attribute decision making, this study first presents a new ranking method for interval-valued hesitant fuzzy elements. In order to obtain the comprehensive values of alternatives, two induced generalized interval-valued hesitant fuzzy hybrid operators based on the Shapley function are defined, which globally consider the importance o...

We begin the paper studying the axioms that the indicators of the grade of inclusion of a fuzzy set in another fuzzy set must satisfy. Next, we present an expression of such indicator, ®rst for fuzzy sets and then for interval-valued fuzzy sets, analyzing in both cases their main properties. Then, we suggest an expression for the similarity measure between interval-valued fuzzy sets. Besides, w...