Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

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...

In this communication, we study decision influence diagrams using fuzzy sets and fuzzy random variables t,o model problems in which assessing real-valued ~t i l i t~ies , and employing real-valued random variables t o model random magnit,udes, are considered to be too restrictive. We propose conditions allowing us to solve decision influence diagrams when uncertainty magnitudes are formalized b...

A central object of study in the field of algorithmic randomness are notions of randomness for sequences, i.e., infinite sequences of zeros and ones. These notions are usually defined with respect to the uniform measure on the set of all sequences, but extend canonically to other computable probability measures. This way each notion of randomness induces an equivalence relation on the computabl...

This study, fundamentals of fuzzy block theory, and its application in assessment of stability in underground openings, has surveyed. Using fuzzy topics and inserting them in to key block theory, in two ways, fundamentals of fuzzy block theory has been presented. In indirect combining, by coupling of adaptive Neuro Fuzzy Inference System (NFIS) and classic block theory, we could extract possibl...

This paper presents a multi-product multi-period inventory problem with random replenishment intervals and fuzzy costs under space and shortage level constraints. Since the costs (purchasing, holding and backordering) related to inventory system are often imprecise and the replenishment intervals are random in real life, the proposed model is also fuzzy-random Here, the replenishment intervals ...