Fuzzy random renewal reward process and its applications (Q845310)

This paper is a continuation of [\textit{S. Wang, Y.-K. Liu} and \textit{J. Watada}, Comput. Math. Appl. 57, No. 7, 1232--1248 (2009; Zbl 1186.90039)]. Now, the authors discuss a renewal reward process with fuzzy random interarrival times and rewards under independence wrt. t-norms (T-independence). They derive a new fuzzy random renewal reward theorem for the long-run expected average reward. In contrast with fuzzy random renewal processes in papers by \textit{C. M. Hwang} [Fuzzy Sets Syst. 116, No.~2, 237--244 (2000; Zbl 0966.60081)], \textit{R. Zhao, W. Tang} and \textit{H. Yun} [Eur. J. Oper. Res. 169, No.~1, 189--201 (2006; Zbl 1101.60344)] and \textit{E. Popova} and \textit{H.-C. Wu} [Eur. J. Oper. Res. 117, No.~3, 606--617 (1999; Zbl 0937.90019)] whose results hold only for the minimum t-norm, the renewal theorem obtained in this paper can be applied to more general situations using the class of continuous Archimedean t-norms, such as the product t-norm, Dombi t-norm and Yager t-norm. Two examples (a multi-service system and a replacement problem) illustrate the results.