-Distributive and infinitely -distributive t-norms on complete lattices

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 2005 English Publisher:Elsevier BVJournal:Fuzzy Sets and Systems, volume 151, pages 341-352 (issn: 0165-0114,

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Authors: Funda Karaçal; Djavvat Khadjiev;

doi: 10.1016/j.fss.2004.06.013

-Distributive and infinitely -distributive t-norms on complete lattices

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Abstract

Abstract A relation between the direct decomposability of an infinitely ∨ -distributive t-norm on a complete lattice L and direct decompositions of the neutral element 1 of L is obtained. Some useful applications of this relation are given. In particularly, the description of all T 1 -lattices without infinitely ∨ -distributive t-norms on complete lattices and the description of all ∨ -distributive t-norms on lattices of length 2 are given. The paper also contains the solutions of two open problems.

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Karadeniz Technical University
Turkey

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