Zoran Stojaković

On fuzzy ideals in BCC-algebras

The purpose of this paper is description of properties of fuzzy BCC-ideals in BCC-algebras and its images. We describe also an extension of a fuzzy BCC-ideal μ of a given BCC-subalgebra S of X to a fuzzy BCC-ideal μ of X such that μ and μ have the same image.

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.

Single identities for varieties equivalent to quadruple systems

Abstract If H is a subgroup of the symmetric group S4, then a 3-groupoid (S, f) is called H-permutable if f(xσ(1), xσ(2), xσ(3)) = xσ(4) ↔ f(x1, x2, x3) = x4 for every σ ∈ H. Some classes of generalized idempotent H-permutable 3-groupoids are equivalent to Steiner, Mendelsohn and other quadruple systems. We prove that the variety of generalized idempotent H-permutable 3-groupoids can be defined by a single identity for every subgroup H of S4 which contains at least one permutation σ such that σ(4) / 4.

On Rusakov's n-ary rs-groups

AbstractProperties of n-ary groups connected with the affine geometry are considered. Some conditions for an n-ary rs-group to be derived from a binary group are given. Necessary and sufficient conditions for an n-ary group

Self-orthogonal cyclicn-quasigroups

\left\langle {\theta ,b} \right\rangle

Self-orthogonal cyclic n-quasigroups.

-derived from an additive group of a field to be an rs-group are obtained. The existence of non-commutative n-ary rs-groups which are not derived from any group of arity m2 is proved.

INTEGRAL WITH RESPECT TO FUZZY MEASURE IN FINITE DIMENSIONAL BANACH SPACES 1

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.