The objective of this chapter is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership functions and rough membership functions, between core and support of fuzzy set theory and lower and upper appro...

It is pointed out that the moments of phase-space particle density at freeze-out can be determined from the coincidence probabilities of the events observed in multiparticle production. A method to measure the coincidence probabilities is described and its validity examined. Recently we have proposed [1] a method for measuring the average of the particle density in multiparticle phase space. Ge...

This research addresses system reliability analysis using weakest t-norm based approximate intuitionistic fuzzy arithmetic operations, where failure probabilities of all components are represented by different types of intuitionistic fuzzy numbers. Due to the incomplete, imprecise, vague and conflicting information about the component of system, the present study evaluates the reliability of sy...

Many problems in scientific investigation generate nonprecise data incorporating nonstatistical uncertainty. A nonprecise observation of a quantitative variable can be described by a special type of membership function defined on the set of all real numbers called a fuzzy number or a fuzzy interval. A methodology for constructing control charts is proposed when the quality characteristics are v...

By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered. Resulting system has various interactions including diffusion to left and right, two-particle interactions AαAβ → AγAδ and the extended n-particle drop-push interac...

Abstract: In conventional reliability analysis, the failure probabilities of the components of a system are treated as exact values. It is often difficult to obtain data for failure probabilities under changing environmental conditions. Hence fuzzy sets are used to analyze the fuzzy system reliability, where a fuzzy number represents the reliability of each component. Chen [14] analyzed the fuz...

Original scientific paper A Fuzzy Skinner Operant Conditioning Automaton (FSOCA) is constructed based on Operant Conditioning Mechanism with Fuzzy Set theory. The main character of FSOCA automaton is: the fuzzed results of state by Gaussian function are used as fuzzy state sets; the fuzzy mapping rules of fuzzyconditioning-operation replace the stochastic "conditioning-operant" mapping sets. So...

The purpose of this paper is to create an interval estimation of the fuzzy system reliability for the repairable multistate series-parallel system (RMSS). Two-sided fuzzy confidence interval for the fuzzy system reliability is constructed. The performance of fuzzy confidence interval is considered based on the coverage probability and the expected length. In order to obtain the fuzzy system rel...

The classical fuzzy classifier consists of rules each one describing one of the classes. In this paper a new fuzzy model structure is proposed where each rule can represent more than one classes with different probabilities. The obtained classifier can be considered as an extension of the quadratic Bayes classifier that utilizes mixture of models for estimating the class conditional densities. ...