Delayed Renewal Process In Uncertain Environments

In this dissertation, as extensions of a delayed renewal process in a stochastic environment, delayed renewal processes in fuzzy, random fuzzy and fuzzy random environments are discussed, respectively. Furthermore, homogeneous Poisson process in random fuzzy and fuzzy random environments are researched.The groundwork is as follows:Firstly, the delayed renewal process in a fuzzy environment is discussed. Relations between the renewal number and the interarrival times are addressed. And the fuzzy style of elementary renewal theorem is given.Secondly, the delayed renewal process in a random fuzzy environment is discussed. And then, the random fuzzy style of elementary renewal theorem, Blackwell renewal theorem and Smith key renewal theorem are respectively given. Furthermore, as an extension of the random fuzzy delayed process, the random fuzzy equilibrium process — one particular case of the random fuzzy delayed process is introduced. Consequently, propositions on the random fuzzy equilibrium process are considered. In addition, the question whether such a process has the original propositions under a random thinning transform is analyzed.Thirdly, the homogeneous Poisson process in a random fuzzy environment is discussed. As one of applications and an extension of the random fuzzy Poisson process, some propositions on random fuzzy compound Poisson process are studied. In addition, the question whether such a process has the original propositions under a random thinning transform and a superposition transform is researched.Fourthly, the delayed renewal process in a fuzzy random environment is considered. And then, the fuzzy random style of elementary renewal theorem, Blackwell renewal theorem and Smith key renewal theorem are respectively given. as an extension of the fuzzy random delayed process, the fuzzy random equilibrium process — one particular case of the fuzzy random delayed process is introduced. Consequently, propositions on the fuzzy random equilibrium process are addressed. In addition, the question whether such a process has the original propositions under a random thinning transform is analyzed.Lastly, the homogeneous Poisson process in a fuzzy random environment is studied. As one of applications and an extension of the random fuzzy Poisson...