A note on UP-hyperalgebras

Abstract

We introduce the concept of UP-hyperalgebras which is a generalization of UP-algebras, and investigate some related properties. Moreover, we introduce the concepts of UP-hypersubalgebras, UP-hyperideals of types 1 and 2, and s-UP-hyperideals of types 1 and 2 in UPhyperalgebras and give some relations among these concepts. We try to show that these concepts are independent by some examples. Furthermore, the closed condition and the R-condition of a nonempty subset are discussed.

Characteristic Picture Fuzzy Sets and Level Subsets in UP (BCC)-Algebras

“…Among many algebraic structures, algebras of logic form important class of algebras. Examples of these are BCK-algebras [16], BCI-algebras [17], BE-algebras [23], UP-algebras [11], fully UPsemigroups [12], topological UP-algebras [28], UP-hyperalgebras [14], extension of KU/UP-algebras [27] and others. They are strongly connected with logic.…”

Lattice Valued Fuzzy Sets in UP (BCC)-Algebras

“…Among many algebraic structures, algebras of logic form important class of algebras. Examples of these are BCK-algebras [16], BCI-algebras [17], β-algebras [27], BG-algebras [24], BP-algebras [1], UP-algebras [11], fully UP-semigroups [12], topological UP-algebras [32], UP-hyperalgebras [14], extension of KU/UP-algebras [31] and others. They are strongly connected with logic.…”

Picture fuzzy sets in UP-algebras by means of a special type

“…Among many algebraic structures, algebras of logic form important class of algebras. Examples of these are BCK-algebras [15], BCI-algebras [16], BE-algebras [17], UP-algebras [10], fully UP-semigroups [11], topological UP-algebras [20], UP-hyperalgebras [13], extension of KU/UP-algebras [19] and others. They are strongly connected with logic.…”