A New Approach to Fuzzy Random Variables and its Fuzzy Stochastic Orders Based on Ranking Concepts

A new approach of ranking concept of fuzzy random variables to stochastic ordering is investigated in this paper.  The stochastic orders of random variables are extend to the cases where the available data are imprecise quantities, rather than crisp. To do this, using some elements of fuzzy set theory, we suggest some stochastic orders like the hazard rate order, the fuzzy mean residual life order and fuzzy up mean residual life order and apply them to construct some new fuzzy stochastic orders for ranking fuzzy random variables. Also we study the characterizations and relationship between them.