Abstract
First, semigroup structure is constructed by providing binary operations for the crossing cubic set structure. The concept of commutative crossing cubic ideal is introduced by applying crossing cubic set structure to commutative ideal in BCK-algebra, and several properties are investigated. The relationship between crossing cubic ideal and commutative crossing cubic ideal is discussed. An example to show that crossing cubic ideal is not commutative crossing cubic ideal is given, and then the conditions in which crossing cubic ideal can be commutative crossing cubic ideal are explored. Characterizations of commutative crossing cubic ideal are discussed, and the relationship between commutative crossing cubic ideal and crossing cubic level set is considered. An extension property of commutative crossing cubic ideal is established, and the translation of commutative crossing cubic ideal is studied. Conditions for the translation of crossing cubic set structure to be commutative crossing cubic ideal are provided, and its characterization is processed.
Highlights
A crisp set A in a universe K can be described as its characteristic function ξA : K → {0, 1}.If we take an extension [0, 1] of the range {0, 1} in the characteristic function ξA : K → {0, 1}, we can obtain a new function ξ : K → [0, 1], and it is called the fuzzy set, which is introduced by Zadeh [1]
They identified the relationship between them. They provided conditions for crossing cubic structure to be closed crossing cubic ideal, and explored the conditions under which crossing cubic ideal is closed. They discussed characterizations of crossing cubic ideal, and we studied the translation of crossing cubic subalgebra and crossing cubic ideal
We provided two binary operations to assign a semigroup structure to the set of crossing cubic set structures and applied the crossing cubic set structure to commutative ideals of BCK-algebras and defined commutative crossing cubic ideal
Summary
A crisp set A in a universe K can be described as its characteristic function ξA : K → {0, 1}. Based on the need for tools necessary to process negative information, Jun et al [2] introduced the negative-valued function and applied it to the BCK/BCI-algebra. Abbas et al [11] introduced the concept of a cubic Pythagorean fuzzy set based on the Pythagorean fuzzy set and the interval value Pythagorean fuzzy set They developed a cubic Pythagorean fuzzy weighted mean operator and a cubic Pythagorean fuzzy weighted geometric operator, and they applied it to multi-attribute decision-making with unknown weight information. Jun et al [14] introduced crossing cubic set structure as an extension of bipolar fuzzy set, consisting of interval-valued fuzzy set and negative-valued function, and applied it to BCK-algebra. We find conditions for the translation of crossing cubic set structure to be commutative crossing cubic ideal, and consider its characterization
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
