In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that...

Given a fuzzy variable, what is the degree of difficulty of predicting the specified value that the fuzzy variable will take? Entropy provides a measure to characterize the fuzziness. Given some constraints, there are usually multiple compatible membership functions. Which membership function shall we take? The maximum entropy principle attempts to select the membership function that maximizes ...

Keywords: Fuzzy variable Independence Operation t-norm Convergence Law of large numbers a b s t r a c t T-independence of fuzzy variables is a more general concept than the classical independence. The objective of this study is to deal with some new properties of T-independent fuzzy variables. First of all, for any general t-norm, some criteria of T-independence are discussed for fuzzy variable...

This paper is concerned with H∞ filtering problem for T-S fuzzy systems with partly immeasurable premise variables. By using measurable premise variables of fuzzy models as the premise variables of fuzzy filters, a new fuzzy filter scheme is constructed. Further based on a class of line integral fuzzy Lyapunov functions, a convex condition for designing H∞ filters is proposed. In contrast to th...

Article Outline Glossary I. Definition of the Subject and Its Importance II. Introduction III. Mathematical modeling of imprecise data IV. Fuzzy random variables V. Statistical analysis of random fuzzy perceptions VI.1 Fuzzy estimators and fuzzy confidence intervals VI.2 Fuzzy statistical tests VII. Statistical analysis of random fuzzy variables VIII. Future directions Bibliography Glossary Fuz...

This paper studies an alternating renewal process when on-off times are random fuzzy variables. We provide a theorem concerning the long-term average expected service times of customers. Here, we do not use the α0-pessimistic value and the α0-optimistic value of fuzzy variables, we simulate the expected value of random fuzzy variables based on fuzzy simulation to calculate the long-term average...

This paper establishes a theory of decision making under uncertainty with fuzzy utilities. The extension of expected utility and stochastic dominance to the comparison of sets of random variables plays a crucial role. Their properties as fuzzy rankings are studied, and their definitions are further generalized to the comparison of fuzzy random variables. Also, a connection between expected util...