@INPROCEEDINGS { Rsds3506,
author = {Mukaidono, Masao}, 
title = {Kleene Algebras in Fuzzy Truth Values}, 
booktitle = {Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery}, 
conference = {International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery}, 
pages = {37--43}, 
publisher = {Japanese Research Group on Rough Sets}, 
address = {Tokyo, Japan}, 
month = {November}, 
year = 1996, 
editor = {Tsumoto, Shusaku and Kobayashi, Satoshi and Yokomori, Takashi and Tanaka, Hiroshi and Nakamura, Akira}, 
isbn = {4-947717-01-7}, 
abstract = {It is well known that fuzzy logic satisfies the axioms of Kleene algebra, that is fuzzy logic a model of Kleene algebra, just as the binary logic is a model of Boolean algebra. This is because the truth values, called numerical truth values, in fuzzy logic satisfy the axioms of Kleene algebra. On the other hand, numerical truth values are extended info interval truth values and fuzzy truth values in fuzzy logic. In this cases although interval truth values satisfy the axiom of De Morgan algebra, which is a weaker algebra than Kleene algebra, fuzzy truth values do not satisfy even the axioms of lattice. In this paper, after introducing truth values of fuzzy logic, describing the axioms of Kleene algebra and clarifying the fundamental properties of Kleene algebra, the conditions that subset of interval truth values and fuzzy truth values satisfy the axioms of Kleene algebra are explained and some simple examples of subsets of interval truth values and fuzzy truth values which satisfy the axioms of Kleene algebra are shown.}, 
keywords = {kleene algebra, fuzzy logic, numerical truth values, interval truth values, fuzzy truth values, }, 
}