Random Fuzzy Alternating Renewal Processes

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 fuzzy vectors. It provides a theorem on the limit value of the average chance of a given random fuzzy event in terms of 'system being on at time t'. The resultant model coincides with that attainable by stochastic analysis when the random fuzzy vectors degenerate to random vectors.