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The quintuple implication principle of fuzzy reasoning based on interval-valued S-implication. (English) Zbl 1400.68221

Summary: Interval-valued fuzzy reasoning is an important issue in approximate reasoning and decision making under fuzzy and uncertainty. To improve the quality of interval-valued fuzzy reasoning, this paper proposes the quintuple implication principle (QIP) of fuzzy reasoning based on interval-valued S-implication in order to solve interval-valued fuzzy modus ponens (IFMP) and interval-valued fuzzy modus tollens (IFMT). We first present the QIP solutions of IFMP and IFMT for interval-valued S-implications, then discuss the reductivity and continuity of fuzzy reasoning with QIP method for interval-valued S-implications. Finally, we also provide several examples to illustrate and substantiate our theoretical developments.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
03B52 Fuzzy logic; logic of vagueness
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