Journal
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
Volume 55, Issue 6, Pages 1369-1382Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ijar.2014.01.001
Keywords
Intuitionistic fuzzy sets; Fuzzy reasoning; Residual implications; Triple I method; Reductivity
Categories
Funding
- National Natural Science Foundation of China [61134004, 11101253]
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Two basic inference models of fuzzy reasoning are fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). The Triple I method is a very important method to solve the problems of FMP and FMT. The aim of this paper is to extend the Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets. In the paper, we first investigate the algebra operators' properties on the lattice structure of intuitionistic fuzzy information and provide the unified form of residual implications which indicates the relationship between intuitionistic fuzzy implications and fuzzy implications. Then we present the intuitionistic fuzzy reasoning version of the Triple I principles based on the models of intuitionistic fuzzy modus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT) and give the Triple I method of intuitionistic fuzzy reasoning for residual implications. Moreover, we discuss the reductivity of the Triple I methods for IFMP and IFMT. Finally, we propose a-Triple I method of intuitionistic fuzzy reasoning. (c) 2014 Elsevier Inc. All rights reserved.
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