Indian Journal of Science and Technology

Abstract

Background Objective: Lattice has been used in mathematics in 18th century. Modular lattice is one of the most important types of lattice. In18 Michal and Drewniak define a lattice which is generated by fuzzy implication. Method: In this paper we use 9 most frequently used implication and all of the full-fill the condition I(0, 0) = I(0, 1) = I(1, 1) = 1, I(1, 0) = 0 and are monotonic in both variable so they belong to FI. Finding: In this paper we present modular lattice generated by fuzzy implication. We show that these lattice lead to various algebraic structure on the set of almost fuzzy implication. We consider these implications and generate some formula for fuzzy implications thorough. Application/Improvement: Our investigations were inspired by paper of Czogula, Leski and Baczynski Drewniak and this paper is generalization of Michal and Drewniak paper “Lattice generated by fuzzy implication”. 2010 AMS Classification: 03G10, 03B05, 06B10, 04A72
Keyword: Fuzzy Implication, Fuzzy Implication Lattice, Lattice, Modular Lattice