Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

Fuzzyhyper K-algebras based on fuzzyhyper operation

Document Type : Original Article

Authors
fahime mohammadzade 1
الهه mohammadzade 2
1 Department of Mathematics‎, ‎Faculty of Science‎, ‎Payame Noor University‎, ‎ Tehran‎, ‎Iran‎,
2 Payame noor university
10.22034/jfsa.2024.470204.1239
Abstract
Abstract. In this paper, first we redefine the concepts of fuzzy hyper BCK- algebra and fuzzy hyper K algebra that were previously introduced by Borzoui and Zahedi based on fuzzy sets, and obtain their results with our new definition. In other words, A fuzzy hyper operation on a set under certain conditions , is called a fuzzy hyper K-algebra . In particular, we show that under certain conditions the sum and product of two fuzzy hyper K-algebra is a fuzzy hyper K-algebra. In addition, we define the concept of a fuzzy hyper K-ideal based on the fuzzy operation and we examine that each fuzzy hyper K- deal is a weak fazzyhyper K-ideal but the converse is not true. Also, with the help of the congruence relationship on the fuzzy hyper $K$-algebras, we obtain quotient structures. In the end, we make a fuzzy hyper k- algebra, a hyper Kalgebra, and vice versa.
Keywords
Hyper K-algebra
Fuzzy hyper K-algebra
Fuzzy hyper BCK-algebra
Fuzzy hyper K-ideal
Subjects
 
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Fuzzy Systems and its Applications
Volume 7, Issue 2 - Serial Number 15
Open Access Statement
December 2024
Pages 65-86

  • Receive Date 28 July 2024
  • Revise Date 13 November 2024
  • Accept Date 02 December 2024