Based upon previous studies on laws of large numbers for fuzzy, random, fuzzy random and random fuzzy variables, We go further to explore weak law of large numbers(WLLN) for hybrid variables comprising fuzzy random variables and random fuzzy variables. we mainly prove Chebyshev WLLN, Poisson WLLN, Bernoulli WLLN, Markov WLLN and Khintchin WLLN for hybrid variables based on chance measure.

The variance of fuzzy random variables often appears in fuzzy random programming problems. Based on the definition of the variance of a fuzzy random variable, this paper attempts to deduce several formulas for the variances of trapezoidal fuzzy random variables, in which the randomness is characterized by uniform distribution. Firstly, we give the moment formulas for trapezoidal fuzzy variables...

Recently, Zhao et al. [Fuzzy Optimization and Decision Making (2007) 6, 279-295] characterized the interarrival times as fuzzy random variables and presented a fuzzy random elementary renewal theorem on the limit value of the expected renewal rate of the process in the fuzzy random renewal process. They also depicted both the interarrival times and rewards are depicted as fuzzy random variables...

In this paper, a two-stage fuzzy random programming for a management problem in terms of water resources allocation having fuzzy random variable coefficients and decision vector of random variables is studied. The first results show the fact that a fuzzy pseudorandom optimal solution of a two-stage fuzzy random programming may be resolved into a two of pseudorandom optimal solutions of relative...

variables Continuity theorems and chance distribution of random fuzzy Email alerting service here right-hand corner of the article or click Receive free email alerts when new articles cite this article-sign up in the box at the top A random fuzzy variable is a function from a possibility space to the set of random variables. In this paper, some mathematical properties of a random fuzzy variable...

Random fuzzy theory offers an appropriate mechanism to model random fuzzy phenomena, with a random fuzzy variable defined as a function from a credibility space to a collection of random variables. Based on this theory, this paper presents the results of an investigation into the representation of properties of alternating renewal processes that are described by sequences of positive random fuz...

This paper studies reliability optimization of a series-parallel system with fuzzy random lifetimes. A fuzzy random reliability model is developed to maximize the system reliability. Since the reliability function consists of fuzzy random parameters, classical mathematical programming methods is not applicable to the reliability model. Therefore, in order to solve the model, a fuzzy random simu...

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...