A survey of fuzzy implication algebras and their axiomatization |
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Affiliation: | Department of Mathematics, Faculty of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China |
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Abstract: | The theory of fuzzy implication algebras was proposed by Professor Wangming Wu in 1990. The present paper reviews the following two aspects of studies on FI-algebras: concepts, properties and some subclasses of FI-algebras; axiomatization of the class of FI-algebras and some of its important subclasses. The main results are summarized in the current paper, the relationships between FI-algebras and several classes of important fuzzy algebras are discussed, such as BL-algebras, MTL-algebras, and residuated lattices, and propositional calculus systems of several special classes of FI-algebras are shown. |
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Keywords: | Non-classical logics Fuzzy implication algebra Regular fuzzy implication algebra Heyting type fuzzy implication algebras PFI-algebra BCK-algebra |
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