Renewal and renewal reward theorems for T-independent L-R fuzzy variables

Abstract

Hong [Fuzzy Optimization of Decision Making 13 (2014) 415-434, Information Sciences 228 (2013) 45-60.] considers the law of large numbers for T-independent weighted fuzzy variables whose underlying spaces are R p. He proved T-independent fuzzy renewal theorems and renewal reward theorems with respect to the necessity measure and the expected values of fuzzy variable by using the law of large numbers for weighted fuzzy variables on R p. In this paper, we obtained R 1-version of renewal theorems and renewal reward theorems for L-R fuzzy variables with not uniformly bounded spreads using the results of Hong from which all of the results of Wang and Liu [Applied Mathematical Modelling 39 (2015) 1536-1553] are immediate consequences of our results. An illustrative example is shown.