In this paper, based on fuzzy measurement data, a prediction method for probability distribution of electromagnetic wave leaked from electronic information equipment is proposed. More specifically, by applying the well-known probability measure of fuzzy events to the probability distribution in an orthogonal expansion series form reflecting systematically various types of correlation informatio...

2. Fuzzy stochastic processes First we give some mathematical notations regarding fuzzy numbers. Let (Ω,M, P ) be a probability space, where M is a σ-field and P is a non-atomic probability measure. R denotes the set of all real numbers, and let C(R) be the set of all non-empty bounded closed intervals. A ‘fuzzy number’ is denoted by its membership function ã : R → [0, 1] which is normal, upper...

Most of the existing approaches for fuzzy reliability analysis are based on fuzzy probability.  The aim of this paper is to describe fuzzy reliability using fuzzy differential equation. The reliability of a system in real world applications is affected by some uncertain parameters. Fuzzy reliability is a way to present the reliability function uncertainly using fuzzy parameters. In the proposed...

This paper proposes a new formalization of the classical probability-possibility relation, which is further confirmed as a much complex, but natural provability – reachability possibility probability fuzzy membership – integrability interconnection. Searching for the right context in which this relation can be consistently expressed for the particular case of experimentally obtained iris recogn...

This paper describes an extended relational database model based on probability theory and possibility theory. Fuzzy information and probabilistic information are incorporated into the relational databases simultaneously to represent fuzzy probability of events in the real-world applications. The tuples in such a relation are associated with a possibility distribution, and their attribute value...

Fuzzy random variable is a measurable function from a probability space to the set of fuzzy variables, while random fuzzy variable is a function from a credibility space to the set of random variables. The concepts of independent and identically distributed fuzzy random variables and random fuzzy variables are presented, and some useful properties are discussed.

This paper presents a proposition of the knowledge representation and the inference procedure including two types of uncertainty: probabilistic and fuzzy. Added weights to the fuzzy rule-based model state probabilities of fuzzy events in antecedents and consequents. The exemplary calculations are presented. Key-Words: Fuzzy sets, Knowledge representation, Inference procedure, Probability of fuz...

This paper discusses fuzzification of crisp domains into fuzzy classes providing fuzzy domains. Relationship between two fuzzy domains, Xi and Xj , is represented by a matrix, wij . If Xi and Xj have n and m elements of fuzzy data, respectively, then wij is n × m matrix. Our primary goal in this paper is to generate and provide some formulas for predicting interval probability in the relation t...

This paper is a reply to Laviolette and Seaman’s critical discussion of fuzzy set theory. Rather than questioning the interest of the Bayesian approach to uncertainty, some reasons why Bayesian find the idea of a fuzzy set not palatable are laid bare. Some links between fuzzy sets and probability that Laviolette and Seaman seem not to be aware of are pointed out. These links suggest that, contr...

This paper discusses fuzzification of crisp domains into fuzzy classes providing fuzzy domains. Relationship between two fuzzy domains, Xi and Xj , is represented by a matrix, wij . If Xi and Xj have n and m elements of fuzzy data, respectively, then wij is n × m matrix. The primary goal of the paper is to generate and provide some formulas for predicting interval probability in the relation to...