Random Fuzzy Processes And The Application To Deteriorating Production Systems

Random fuzzy process is one type of uncertain process. It is the subject that studies on the modelling and analysis of the random fuzzy problems changing with time, and the study can be applied to a lot of fields such as management science, finance, economics, engineering and so on. Based on random fuzzy theory, this paper discusses the random fuzzy process and its application to the deteriorating production systems. Several important results are obtained.Based on random fuzzy theory, this paper presents the definition of random fuzzy Markov chain, and proves the existence theorem. The definitions and the expressions of k-step fuzzy transition probability and k-step fuzzy transition probability matrix of random fuzzy Markov chain are given. Homogeneous random fuzzy Markov chain and the concepts of reducible, intercommunicate, period and transient are studied. Moreover, random fuzzy walk and its application to G/G/1 queueing model is discussed, and random fuzzy Spitzer identity is proved.According to random fuzzy renewal reward theorem, this paper presents a random fuzzy economic manufacturing quantity (EMQ) model in a deteriorating process. It is assumed that the setup cost and the average holding cost are characterized as fuzzy variables and the elapsed time until shift is a random fuzzy variable. As a function of these parameters, the average total cost is also a random fuzzy variable, and the unimodality of its expected value is studied. To obtain the optimal run length and the minimum average cost, simultaneous perturbation stochastic approximation (SPSA) algorithm based on random fuzzy simulation is provided. Random fuzzy EMQ models with fuzzy deterioration, fuzzy linear deterioration and fuzzy exponential deterioration are presented, respectively. Numerical examples are presented in the end.