Mila Stojaković

Fuzzy conditional expectation

Abstract The fuzzy random variables defined on a complete σ-finite measure space are studied. Their fuzzy conditional expectation is defined and its properties are examined. A new metric in the set of integrably bounded fuzzy variables is introduced and completeness of that metric space is proved.

Fuzzy valued measure

Abstract The main purpose of this paper is to introduce and develop the notion of a fuzzy valued measure in separable Banach space. This definition of fuzzy valued measure is a natural generalization of the set-valued measure. Radon-Nikodým theorems for fuzzy valued measure are established.

On mappings with φ-contractive iterate at a point on generalized metric spaces

AbstractWe prove a set of fixed point theorems for mappings with φ-contractive iterate at a point in a class of generalized metric spaces. This is a generalization of some well-known results for Guseman and Matkowski types of fixed point results in metric and generalized metric spaces. MSC:47H10, 54H25.

Series of fuzzy sets

Series of fuzzy sets with weakly closed, weakly compact or compact @a-levels are considered. The basic space is Banach space. The subject of this paper is investigation of infinite addition of fuzzy sets and condition when the sum of @a-levels is equal to the @a-level of the sum. The results in this paper complement and complete some previous results proved by the same authors in Stojakovic and Stojakovic [Addition and series of fuzzy sets, Fuzzy Sets and Systems 83 (1996) 341-346] for the series with compact @a-levels.

Addition and series of fuzzy sets

Abstract Addition and series of fuzzy sets are considered. The answer when the sum of x-cuts is equal to the x-cut of sum is given.

On Ćirić generalization of mappings with a contractive iterate at a point in G-metric spaces

Main results of this paper are fixed point theorems for mappings with a generalized contractive iterate at a point in G-metric spaces which are generalizations of the well-known results in metric spaces.

Decomposition and representation of fuzzy valued measure

Abstract Fuzzy valued measure is a mapping which maps a σ -algebra to a set of fuzzy sets with convex compact α -level defined on a Banach space X . Decomposition and representation of fuzzy valued measure by a sequence of single-valued measures is given. The case when the set of images is the set of fuzzy numbers (that is, when X = R ) is considered.

Support Functions for Fuzzy Sets

The main purpose of this paper is to introduce and develop the notion of support functions for fuzzy sets. This approach gives the opportunity to investigate a lot of properties of fuzzy valued functions (functions with values in space of fuzzy sets defined on Banach space) using rich apparatus of functionals. In this paper we examine some aspects of measurability, integrability and measure theory.

Fixed point theorems and variational principle in fuzzy metric space

Abstract The variational principle and fixed point theorems for singlevalued and multivalued mappings in fuzzy metric space are given and their equivalence is proved.

Representation of fuzzy-valued mappings by the sequence of single-valued mappings

Abstract In this paper the analysis focusses on the important classes of fuzzy-valued mappings: • - measurable fuzzy-valued mappings, • - integrable fuzzy-valued mappings. Our aim is to discuss the problem of representation of such mappings by countable family of single-valued mappings. This is a most useful result, since it provides us with a remarkable list of alternative definitions, criteria and proofs of theorems related to this type of fuzzy mappings.