The comparison concept plays a determining role in many problems related to object management in an Object-Oriented Database Model. Object comparison is appropriately managed in a crisp object-oriented context by means of the concepts of identity and value equality. However, when dealing with imprecise or imperfect objects, questions like ‘To which extent may two objects be the same one?’ or ‘H...

In this paper, we focus on multiobjective fuzzy random programming problems with simple recourse through a fractile optimization model, in which fuzzy random variables coefficients are involved in equality constraints, and random variables coefficients are involved in the objective functions. In the proposed method, equality constraints with fuzzy random variables are defined on the basis of a ...

The paper considers an early approach toward a (fuzzy) set theory with a graded membership predicate and a graded equality relation which had been developed by the German mathematician D. Klaua in 1965. In the context of the mathematical fuzzy logic MTL of left-continuous t-norms we discuss some properties of these graded relations. We compare the simultaneous recursive definitions of these rel...

A classical result for crisp choice functions shows the equivalence between Arrow axiom and the property of full rationality. In this paper we study a fuzzy form of Arrow axiom formulated in terms of the subsethood degree and of the degree of equality (of fuzzy sets). We prove that a fuzzy choice function verifies Fuzzy Arrow Axiom if and only if it is (fuzzy) full rational. We also show that t...

In general fuzzy linear regression, the coefficients of the fuzzy regression model are symmetric triangular fuzzy numbers, while we try to replace them by more general ones, which are asymmetric trapezoidal fuzzy numbers. Possibility of equality between two asymmetric trapezoidal fuzzy numbers is explained by possibility distribution. Two different models are presented in this paper. Furthermor...

Subsethood A ⊆ B and set equality A = B are among the basic notions of set theory. For traditional (“crisp”) sets, every element a either belongs to a set A or it does not belong to A, and for every two sets A and B, either A ⊆ B or A 6⊆ B. To describe commonsense and expert reasoning, it is advantageous to use fuzzy sets in which for each element a, there is a degree μA(a) ∈ [0, 1] to which a ...

The research in the field of the so called Fuzzy Mathematics can be conditionally devided into two mainstreams: the first one emphasizes on the study of different fuzzy structures (topological, algebraic, analytical, etc) on an ordinary set X, while for the second one the starting point are L-valued sets, that is a set equipped with some L-valued equality E : X × X → L (L being a lattice usuall...

Linear equality and inequality systems with fuzzy parameters defined by the extension principle are called possibilistic linear equality and inequality systems. The solution of these systems is defined in the sense of BellmanZadeh [1]. This paper investigate stability and continuity properties of the solution in the above-named systems.

in this paper we study a representation of a fuzzy subgroup $mu$ of a group $g$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  this representation is unique up to the number of components and their isomorphic copies. in the crisp group theory, this is a well-known theorem attributed to remak, krull, and schmidt. we consider the lattice of fuzzy subgroups and som...