New category of the Fuzzy d-algebras

Abstract

The aim of this work is to introduce a new category of Fuzzy d-algebra called Γ-Fuzzy d-algebra. This notion is more useful than Fuzzy d-algebra because in the old case the degree of membership of any x [ X in the Fuzzy set does not depend on the structure of d-algebra X. Therefore, in this work, we introduced a new construction of Fuzzy d-algebra that is depended on structure of d-algebra. Also, we show that for any d-algebra there is a Γ-Fuzzy d-algebra. Further, this new construction helps us to find the interesting relation between Γ-Fuzzy d-algebra and edge d-algebra in this work. For any d-algebra, we determined unique Γ-Fuzzy topological space (X, G f ) using Γ-Fuzzy d-algebra. For any f [ X, a new class of d-is the set of all equivalence classes (X, * , f ) l . Finally, a new class of intuitionistic fuzzy set is called intuitionistic Γ-Fuzzy d-algebra is investigated and discussed. ARTICLE HISTORY

New Class of Doubt Bipolar Fuzzy Sub Measure Algebra

“…The related characteristics of BCK-algebras using the fuzzy group notion are examined [9]. Jun et al have also researched fuzzy features of numerous ideas in BCK/BCI/RHOalgebras [10][11][12][13][14][15][16][17][18][19][20][21]. Huang [22], on the other hand, are concerned with BCI algebra in other ways.…”

Fuzziness on Hopf Algebraic Structures with Its Application

“…The thought of fuzzy subcoalgebra was given by Chen [21] in 2009, and the thought of fuzzy subbialgebra was also given by Chen and Wenxu [22] in 2012. The concept of fuzziness was also applied in some other algebras in [23][24][25].…”

A new branch of bialgebraic structures: UP-bialgebras

“…Among many algebraic structures, algebras of logic form important class of algebras. Examples of these are BCK-algebras [1], BCI-algebras [2], KU-algebras [3], UP-algebra [4] and others (see [5,6]). BCK and BCIalgebras are two classes of logical algebras.…”