This paper discusses two topics on fuzzy random variables in decision making. One is a new evaluation method of fuzzy random variables, and the other is to present a mathematical model in financial engineering by fuzzy random variables. The evaluation method is introduced as mean values defined by fuzzy measures, and it is also applicable to fuzzy numbers and fuzzy stochastic process defined by...

8 This work deals with the simulation of fuzzy random variables, which can be used 9 to model various realistic situations, where uncertainty is not only present in form 10 of randomness but also in form of imprecision, described by means of fuzzy sets. 11 Utilizing the common arithmetics in the space of all fuzzy sets only induces a conical 12 structure. As a consequence, it is difficult to di...

A random fuzzy variable is a function from a credibility space to the set of random variables. Chance distribution is a type of mathematical description of random fuzzy variables. This paper presents a sufficient and necessary condition for chance distribution of random fuzzy variables.

In this paper, we will discuss two special classes of mathematical programming models with fuzzy random variables. In the first model, a linear programming problem with fuzzy decision variables and fuzzy random coefficients is introduced. Then an algorithm is developed to solve the model based on fuzzy optimization method and fuzzy ranking method. In the second model, a fuzzy random quadratic s...

Fuzziness plays an essential role in the real world. Fuzzy set theory has been developed very fast since it was introduced by Zadeh (1965) [1]. A fuzzy set was characterized with its membership function by Zadeh. The term fuzzy variable was fist introduced by Kaufmann (1975) [2], and then appeared in Zadeh (1978) [3] and Nahmias (1978) [4] as a fuzzy set of real numbers. In order to establish t...

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...

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...

In the paper a new concept of modeling uncertainty is presented, based on the theory of fuzzy random variables. By this means, a super-ordinate uncertainty model is made available which includes the models developed so far, based on random variables and fuzzy variables as special cases. The fuzzy random variables are accounted for as input values in the fuzzy probabilistic structural analysis a...

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...