Constructing a Heyting semilattice that has Wajesberg property by using fuzzy implicative deductive systems of Hoops

Authors

  • M. M. Aaly Kologani
  • X.L. Xin chool of Mathematics, Northwest University, Xi'an, 710127, P.R. China
  • M. Mohseni Takallo
  • Y.B. Jun Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
  • Rajab Ali Borzooei Shahid Beheshti University

Keywords:

Hoop, fuzzy implicative deductive system, Brouwerian semilattice, Heyting algebra, Wajesberg hoop.

Abstract

In this paper, we defined the notions of $(\in,\in)$-fuzzy implicative deductive systems and $(\in,\in\vee q)$-fuzzy implicative deductive systems of hoops and studied some traits and tried to define some definitions that are equivalent to them. Thus by using the notion of $(\in,\in)$-fuzzy deductive system of hoop, we defined a new congruence relation on hoop and show that the algebraic structure that is made by it is a Brouwerian semilattice, Heyting algebra and Wajesberg hoop.

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Published

2021-11-03

Issue

Vol. 16

Section

Vol. 16, No. 9, (2022)

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