In many applications, such as intelligent decision systems, there are usually random perturbations caused by the constant changing of real situations, thus the analysis of the robustness with respect to random perturbations is practically important. In the side of fuzzy methods, a corresponding problem arises: will a small random perturbation of fuzzy input cause a big variance of fuzzy output?...

By dealing with interarrival times as exponentially distributed fuzzy random variables, a fuzzy random homogeneous Poisson process and a fuzzy random compound Poisson process are respectively defined. Several theorems on the two processes are provided, respectively.

This article deals with an economic order quantity (EOQ) inventory model for items with imperfect quality in fuzzy stochastic environment, wherein shortages are allowed and completely backlogged. Fuzzy stochastic environment means linguistic ‘impreciseness’ and statistical ‘uncertainty’ both appear simultaneously. Due to uncertain demand trend, imperfect production process, natural disaster etc...

This study introduces the fuzzy Lyapunov function to the fuzzy PID control systems, modified fuzzy systems, with an optimized robust tracking performance. We propose a compound search strategy called conditional linear matrix inequality (CLMI) approach which was composed of the proposed improved random optimal algorithm (IROA) concatenated with the simplex method to solve the linear matrix ineq...

A fuzzy random variable is viewed as the imprecise observation of the outcomes in a random experiment. Since randomness and vagueness coexist in the same framework, it seems reasonable to integrate fuzzy random variables into imprecise probabilities theory. Nevertheless, fuzzy random variables are commonly presented in the literature as classical measurable functions associated to a classical p...

We show that analogously to classical probability theory the conditional expectation E ( ? ~ X ) of a fuzzy random variable Y w.r.t. a fuzzy random variable X is w.r.t. a suitable metric the best approximation o f ? by measurable functions ofX. Furthermore, several linear regression functions, i.e. best approximation of ? by linear functions o f z and examples for random LR-fuzzy numbers and Ga...

In this paper, we concern with SLLN for sums of independent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and ...

This article develops a method of ratio estimate in fuzzy sense. By both the simple random sampling and stratified random sampling, we can obtain the ratio estimate in usual statistical sense. However, the sampling data may be ambiguous in some uncertain circumstance. To solve such kind of problem, we probe into the simple random sampling and stratified random sampling in fuzzy sense, obtain th...