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On fuzzy renewal processes for fuzzy random variables and extended theorems
Author(s) -
Hwang ChaoMing,
Yang MiinShen
Publication year - 2011
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20457
Subject(s) - renewal theory , mathematics , fuzzy logic , fuzzy number , random variable , fuzzy measure theory , fuzzy set , mathematical economics , computer science , artificial intelligence , statistics
In this paper, we construct fuzzy renewal processes involving fuzzy random variables. We first extend the renewal processes to the fuzzy renewal processes where interarrival times, rewards, and stopping times are all fuzzy random variables. According to these fuzzy renewal processes, we then extend some theorems of renewal processes to those in fuzzy renewal processes. These are elementary renewal theorem, asymptotic expected average reward, and Wald's equation. In each part, we also give examples for applications. © 2010 Wiley Periodicals, Inc.