Abstract

This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we construct a computer-program for studying the foldness theory of P-ideals in BCI-algebras.

Highlights

  • The study of BCK/BCI-algebras was initiated by Iséki [1] as a generalization of the concept of set-theoretic difference and propositional calculus

  • This paper aims to introduce new notions of n-fold P-ideals and n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras

  • We construct some algorithms for studying the foldness theory of P-ideals in BCI-algebras

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Summary

Introduction

The study of BCK/BCI-algebras was initiated by Iséki [1] as a generalization of the concept of set-theoretic difference and propositional calculus. In (1965), Zadeh [2] was introduced the notion of a fuzzy subset of a set as a method for representing uncertainty. In 1991, Xi [3] defined fuzzy subsets in BCK/BCI-algebras. We redefined a P-ideal of BCI-algebras and studied the foldness theory of fuzzy P-ideals, P-weak ideals, fuzzy weak P-ideals, and weak P-weak ideals in BCI-algebras. This theory can be considered as a natural generalization of P-ideals. We construct some algorithms for studying the foldness theory of P-ideals in BCI-algebras

Preliminaries
Fuzzy n-Fold P-Ideals in BCI-Algebras
Fuzzy-Fold Weak P-Ideals in BCI-Algebras
Algorithms
Conclusions and Future Research
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