Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

f-derivations on equality alebras

Document Type : Original Article

Author
sogol niazian
Faculty of Medicin-Tehran Medical Sciences, Islamic Azad University-Tehran-Iran
10.22034/jfsa.2024.437276.1195
Abstract
In this paper, we introduced the concept of f-derivation on equality algebra E by using the notions of inner and outer f-derivations. Then, we investigated some properties of (inner, outer) f-derivation and introduced some suitable conditions that they help us to define an f-derivation on E.
We defined kernel and fixed point sets of f-derivation on E and proved that under which condition they are filters of E. Finally, we proved that under some conditions the equivalence relations on (E, →, 1) coincide
with the equivalence relations on E with derivation d_f . Also, by using the properties of equality algebra, we made two outer f-derivations and by introducing an implication operation “\ri ” on the set of all these outer f-derivations, we showed that it make a BE-algebra and dual BCK-algebra.
Keywords
Equality algebra
f-derivation
outer (inner) derivation
filter
BE-algebra
dual BCK-algebra
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Fuzzy Systems and its Applications
Volume 6, Issue 2 - Serial Number 13
Open Access Statement
December 2024
Pages 269-298

  • Receive Date 23 January 2024
  • Revise Date 05 March 2024
  • Accept Date 25 June 2024