Abstract
Recently, Yong-Ming Li proposed fuzzy systems based upon genuine manyvalued implications for SISO cases. From the opinion of application, it is expected that the fuzzy systems have monotonicity if both the antecedent and consequent parts of fuzzy rules are monotone. Hence we discuss the monotonicity of this fuzzy systems in this paper. However, some instances show that the fuzzy systems do not necessarily have monotonicity even if both antecedent and consequent parts of fuzzy rules have monotonicity. And then we give the sufficient conditions that the fuzzy systems based upon R-implications, some S-implications and some QL-implications have monotonicity. It is pointed out that our proofs are different with, strictly speaking, more complex than H. Seki’s proofs because there does not exist the uniform formula of output in Li’s system while H. Seki’s proofs have them.
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