Weak fuzzy implication algebras and induced structures

• Autorzy: Chajda I. , Emanovsky P. , Halas R.
• Języki publikacji: EN

Abstrakty

EN

The concept of fuzzy implication algebra is weakened replacing the exchange axiom by an essentially weaker version. To each such algebra a groupoid is assigned. We get conditions under which this groupoid is commutative and show when a fuzzy implication algebra becomes a lattice with antitone involutions on all sections.

Słowa kluczowe

EN

fuzzy implication; exchange identity; quasi-commutativity

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 1
• Strony: 1--14
• Opis fizyczny: Bibliogr. 7 poz., tab., rys.

Twórcy

autor

Chajda I.

autor

Emanovsky P.

autor

Halas R.

• Department of Algebra and Geometry Palacky University Olomouc Faculty of Sciences Tomkova 40 779 00 Olomouc, Czech Republic,

Bibliografia

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• [3] Liu Lian Zhen, Guo-jun Wang, Fuzzy implication algebra and MV-algebra, Fuzzy Systems Math. 12 (1998), 20-25.
• [4] Liu Lian Zhen, Li Kai Tai, Some properties of fuzzy implication algebras, preprint.
• [5] A. Ursini, Sulla varietádi algebre con una buona teoria degli ideali, Boll. Un. Mat. Ital. 6 (1972), 90-95.
• [6] Wang-ming Wu, Fuzzy implication algebra, Fuzzy Systems Math. 4 (1990), 56-63.
• [7] A. Wroński, BCK-algebras do not form a variety, Math. Japon., 28 (1983), 211-213.