Sheffer Stroke Nelson Algebras and Fuzzy Structures
Project no. 22747 · Status: Kapanmış · 2021
Summary
<p>In this study, Sheffer stroke Nelson algebras (briefly, s-Nelson algebras), (ultra) ideals, quasisubalgebras and quotient sets on these algebraic structures are introduced. The relationships between s-Nelson and Nelson algebras are analyzed. Also, it is shown that a s-Nelson algebra is a bounded distributive modular lattice, and the family of all ideals forms a complete distributive modular lattice. A congruence relation on s-Nelson algebra is determined by its ideal and quotient s-Nelson algebras are constructed by this congruence relation. It is indicated that a quotient s-Nelson algebra defined by the ultra ideal is totally ordered and that the cardinality of the quotient is less than or equals to 2. Moreover, (hesitant) fuzzy structures on s-Nelson algebras are given. Then relationships between (inf-hesitant) fuzzy quasisubalgebras and quasi-subalgebras are described on s-Nelson algebras. Indeed, (ultra infhesitant) fuzzy ideals are constructed by means of (ultra) ideals on these algebraic structures and vice versa. Finally, it is illustrated that every (inf-hesitant) fuzzy ideal of a s-Nelson algebra is the (inf-hesitant) fuzzy quasi-subalgebra, and that the inverse is satisfied under the special condition.</p><p><br></p><p>Keywords: Sheffer stroke, Nelson algebra, s-Nelson algebra, (ultra inf-hesitant fuzzy) ideal, (ultra inf-hesitant fuzzy) quasi-subalgebra. </p>