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Unified forms of the CDR method of approximate reasoning on Antanassov's intuitionistic fuzzy sets and its property analysis
Author(s) -
Li Jun,
Xu Xiaofu
Publication year - 2018
Publication title -
computational intelligence
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.353
H-Index - 52
eISSN - 1467-8640
pISSN - 0824-7935
DOI - 10.1111/coin.12170
Subject(s) - modus ponens , mathematics , type 2 fuzzy sets and systems , fuzzy set operations , fuzzy number , fuzzy logic , artificial intelligence , discrete mathematics , algorithm , fuzzy set , computer science
Two basic models of fuzzy reasoning are fuzzy modus ponens and fuzzy modus tollens. Correspondingly, the key point of intuitionistic fuzzy reasoning is to solve the problems of intuitionistic fuzzy modus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT). In many important algorithms of fuzzy reasoning, the Consequent Dilation Rule (CDR) method possesses the virtue of unconditional reductivity. This paper proposed an intuitionistic CDR (ICDR) method for IFMP and IFMT problems by extending the CDR method to the intuitionistic fuzzy reasoning. It was proved that the intuitionistic CDR methods, both for IFMP and IFMT, are unconditionally reductive in the circumstance of using residual intuitionistic implication operators. At the same time, the continuity, approximation properties and robustness of the CDR method in Łukasiewicz intuitionistic fuzzy reasoning space have been studied by using the new defined average natural distance between intuitionistic fuzzy sets.