| In order to study the fuzzy reasoning method closer to human thinking mode, K. T. Atanassov, an American scholar, proposed the concept of intuitionistic fuzzy sets. Because intuitionistic fuzzy sets show great potential in the practical applications, so numerous scholars prefer to this theory. In just a few decades, it can be described as rich fruits on theory of intuitionistic fuzzy sets, the study of intuitionistic fuzzy sets has been involved in decision analysis artificial intelligence, extension flutter, logical algebra and other areas. In the field of logic algebra, the scholars get fuzzy filters and intuitionistic fuzzy sets together, introduced the concept of intuitionistic fuzzy filters. The first part of this paper defines the concept of intuitionistic fuzzy filters on FI algebras. By intuitionistic fuzzy filters, a congruence relation is introduced on FI algebras and its basic nature is further studied. We look forward to the study of the algebraic structure of FI to play a role in promoting.Since the introduction of the concept of T-mold by Menger in 1942, it has been applied in many fields, including probabilistic metric spaces, semigroup theory, func-tional equations theory, fuzzy logic theory. Based on the article intuitionistic fuzzy filters on lattice implication algebras by Pei Zheng, the second part of this article combine intuitionistic fuzzy filters and T-mold. We introduce T1, T2 intuitionis-tic fuzzy filters and T1, T2 intuitionistic fuzzy related filters, and study the related properties of T1, T2 intuitionistic fuzzy filters and Ti, T2 intuitionistic fuzzy associ-ation filters, and gives equivalent characterizations. We hope this works provide a reference for further study on other filters of lattice implication algebras.This paper is organized as follows:The first chapter is preliminaris. In this chapter, we introduce the preliminary concepts, examples, and results of FI algebras and fuzzy implication algebras.The second chapter studies intuitionistic fuzzy filters and congruence realation of fuzzy implication algebras. In this chapter, we introduce the concept of intu-itive fuzzy filters in a fuzzy implication algebras and provide equivalent description. We discuss a congruence relation induced by intuitionistic fuzzy filters and some properties are also discussed.The third chapter studies two kinds of intuitionistic fuzzy filters. In lattice implication algebras, by combining intuitionistic fuzzy filters and T-mold, we in-troduce two kinds of intuitionistic fuzzy filters, extend the concept of intuitionistic fuzzy filters, study their properties, and give their equivalent characterizations. |
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