in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

8 This article investigates the consistency of interval fuzzy preference relations based on interval 9 arithmetic, and new definitions are introduced for additive consistent, multiplicative consistent 10 and weakly transitive interval fuzzy preference relations. Transformation functions are put 11 forward to convert normalized interval weights into consistent interval fuzzy preference relations...

We present a new and natural interpretation of fuzzy sets and fuzzy relations where the basic notions and operations have quite natural meanings. We interpret fuzzy sets and fuzzy relations in a cumulative Heyting valued model for intuitionistic set theory, and de0ne the basic notions and operations naturally in the model. As far as fuzzy sets and fuzzy relations are considered as extensions of...

Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...

In this paper, a quadratic programming (FFQP) problem is considered in which all of the cost coefficients, constraints coefficients, and right hand side of the constraints are characterized by L-R fuzzy numbers. Through this paper, the concept of α- level of fuzzy numbers for the objective function, and the order relations on the fuzzy numbers for the constraints are considered.  To optimize th...

We study graded properties (α–properties) of fuzzy relations, which are parameterized versions of fuzzy relation properties defined by L.A. Zadeh. Namely, we take into account fuzzy relations which are: α–reflexive, α– irreflexive, α–symmetric, α–antisymmetric, α–asymmetric, α–connected, α–transitive, where α ∈ [0, 1]. We also pay our attention to the composed versions of these basic properties...

in this paper, new definitions of $l$-fuzzy closure operator, $l$-fuzzy interior operator, $l$-fuzzy remote neighborhood system, $l$-fuzzy neighborhood system and $l$-fuzzy quasi-coincident neighborhood system are proposed. it is proved that the category of $l$-fuzzy closure spaces, the category of $l$-fuzzy interior spaces, the category of $l$-fuzzy remote neighborhood spaces, the category of ...

In this contribution connections between input fuzzy relations R1, . . . ,Rn on a set X and the output fuzzy relationRF = F(R1, . . . ,Rn) are studied. F is a function of the form F : [0, 1]n → [0, 1] and RF is called an aggregated fuzzyrelation. In the literature the problem of preservation, by a function F, diverse types of properties of fuzzy relationsR1, . . . ,Rn is examined. Here, it is c...

In this paper we consider some properties of intuitionistic fuzzy preference relations. We pay attention to preservation of intuitionistic fuzzy preference relations by aggregation operations. In particular, we know, that a special kind of aggregation operations (lattice operations) do not preserve intuitionistic fuzzy preference relations. We describe the operations which preserve intuitionist...

Since upper and lower approximations could be induced from the rough set structures, rough sets are considered as approximations. The concept of fuzzy rough sets was proposed by replacing crisp binary relations with fuzzy relations by Dubois and Prade. In this paper, we introduce and investigate some properties of intuitionistic fuzzy rough approximation operators and intuitionistic fuzzy relat...