In this paper, an O-convergence theory of fuzzy nets is built in L-topological spaces by means of neighborhoods of fuzzy points. It has many nice properties. It can be used to characterize the closed set, open set, T2 separation axiom and fuzzy compactness. c © 2003 Elsevier B.V. All rights reserved.

In the setting of fuzzy choice functions (Georgescu [6]), we explore the relationships among known and new consistency axioms. Then we define the notion of sequential application of fuzzy choice functions, and investigate its normative implications. The Fuzzy Arrow Axiom is preserved by this sequential procedure, which ensures that full-rationality is preserved too.

The issues relating fuzzy sets definition are under consideration including the analogue for separation axiom, statistical interpretation and membership function representation by the conditional Probabilities.

Based on the axiom de nition of distance measure, some new formulas of fuzzy entropy induced by distance measure and some new properties of distance measure are given. A characterization of a -distance measure is a metric de ned on all fuzzy sets is obtained. c © 2001 Elsevier Science B.V. All rights reserved.

In this paper we introduce the conditional entropy without a fuzzy measure for the union of fuzzy partitions. We recall its properties and we solve the system of functional equations which derives from these conditions, taking into account the locality principle and the independence axiom.

We show by standard automated theorem proving methods and freely available automated theorem prover software that axiom (A2), stating that multiplicative conjunction implies its first member, is provable from other axioms in fuzzy logics BL and MTL without using axiom (A3), which is known to be provable from other axioms [1]. We also use freely available automated model generation software to s...

In this paper we introduce a definition of gradation of continuity ingraded fuzzy topological spaces and study its various characteristic properties.The impact of the grade of continuity of mappings over the N-compactnessgrade is examined. Concept of gradation is also introduced in openness, closed-ness, homeomorphic properties of mappings and T2 separation axiom. Effectof the grades interrelat...

Classical ontologies are not suitable to represent imprecise nor uncertain pieces of information. As a solution we will combine fuzzy Description Logics with a possibilistic layer. Then, we will show how to perform reasoning by relying on classical existing reasoners. Description Logics (DLs for short) are a family of logics for representing structured knowledge which have proved to be very use...

In this paper we explore fuzzy semantics for a wide class of normal modal systems enriched with multiple instances of the axiom of confluence and prove a general completeness result for such systems.