considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. this paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong hausdorff topology.we study interrelationships between this theory and other fuzzy theories suchas intuitionis...

This article gives a tutorial introduction on label semantics framework on reasoning with uncertainty. Modelling real world problems typically involves processing uncertainty of two distinct types. These are uncertainty arising from a lack of knowledge relating to concepts which, in the sense of classical logic, may be well defined and uncertainty due to inherent vagueness in concepts themselve...

We revisit Zadeh's notion of "evidence the second kind" and show that it provides foundation for a general theory epistemic random fuzzy sets, which generalizes both Dempster-Shafer belief functions possibility theory. In this perspective, deals with generated by while induced sets. The more allows us to represent combine evidence is uncertain fuzzy. demonstrate application formalism statistica...

A probability density function verifies more demanding properties than a possibility measure. Probabilistic models ensure a predictable asymptotic behaviour. This should not be taken to suggest possibility theory should not be used. In fact, a histogram is a possibility measure and it is generally a better descriptor of a small sample of data than a probability density function regardless of it...

We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be de ned by letting T (Q) be the measure of the family of closed sets K which have nonempty intersection with Q. We prove an e ective version of Choquet's capacity theorem by showing that every computable capacity may be obta...

in this paper, we establish the theory of fuzzy ideal convergence on completely distributive lattices and give characterizations of some topological notions. we also study fuzzy limit structures and discuss the relationship between fuzzy co-topologies and fuzzy limit structures.

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...

This paper presents the theory and formalism of fuzzy causal probabilistic networks (FCPN) and show their current and potential applications in multisensor data fusion. A fuzzy causal probabilistic network (FCPN) is a directed acyclic graph representing the joint probability distributions of a set of fuzzy random variables describing a problem domain. FCPNs extend causal probabilistic networks ...

In this paper, the concepts of positive dependence and linearlypositive quadrant dependence are introduced for fuzzy random variables. Also,an inequality is obtained for partial sums of linearly positive quadrant depen-dent fuzzy random variables. Moreover, a weak law of large numbers is estab-lished for linearly positive quadrant dependent fuzzy random variables. Weextend some well known inequ...

In this paper, we introduce and study a random variational-like inclusion and its corresponding random proximal operator equation for random fuzzy mappings. It is established that the random variational-like inclusion problem for random fuzzy mappings is equivalent to a random fixed point problem. We also establish a relationship between random variational-like inclusion and random proximal ope...