In our earlier work we have developed the axiomatic theory of the scalar cardinality of interval-valued fuzzy sets following Wygralak’s axiomatic theory of scalar cardinalities of fuzzy sets. The cardinality has been defined as a mapping from the set of interval-valued fuzzy sets with finite support to the set of closed subintervals of [0,+∞). We have shown that each scalar cardinality of inter...

The purpose of this paper is to establish a general existence of equilibrium for generalized game in abstract convex space, where the preference correspondence has unionly open lower section and the constraint correspondence is transfer open valued. New notions of UA-mapping and UAmajorized mapping are introduced, in which the lower sections are unionly open. We first prove some new fixed point...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

Abstract_ _ We prove a common coincidence point theorem for a non-fuzzy mapping and a pair of fuzzy mappings under a ' contraction condition on a metric space in the context of Hausdor¤ metric on the family of fuzzy sets. Further, we establish a common coincidence point theorem on a metric space with the d1 metric on fuzzy sets, which extends a number of recent results. As applications, we obta...

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which conta...

We associate a 3-manifold to a multiple valued semi-conformal mapping on the 3-sphere and study the branching set of the corresponding covering projection. Some remarkable geometric structures occur.

In this paper we show that metric regularity and strong metric regularity of a set-valued mapping imply convergence of inexact iterative methods for solving a generalized equation associated with this mapping. To accomplish this, we first focus on the question how these properties are preserved under changes of the mapping and the reference point. As an application, we consider discrete approxi...