Roughness in hemirings

Some Algebraic Properties of Generalized Fuzzy Rough Approximations Derived by Fuzzy Set-Valued Homomorphism of LA-G-Semigroups

“…The definitions of the fuzzy set valued and the set valued homomorphism of LA-Γ-semigroups are given in the following [7]. [2,5,11,[34][35][36]). Proof.…”

TL-fuzzy set valued homomorphisms and generalized (I,T)-L-fuzzy rough sets on groups

“…Let G, H be groups. A mapping T : G → P(H) satisfying T(a)T(b) ⊆ T(ab) and (T(a)) −1 ⊆ T(a −1 ) for all a, b ∈ G is called set valued homomorphism of groups (see [2,5,10,[26][27][28]).…”

“…Yamak et al [27,28] investigated some properties of the generalized rough sets with respect to set-valued homomorphisms of rings and modules. And also see [1,2,10,26].…”

Generalized Rough Fuzzy Ideals in Quantales

“…Late years have seen its wide applications in algebraic systems, knowledge discovery, data mining, expert systems, pattern recognition, granular computing, graph theory, machine learning, partially ordered sets, and so forth [3][4][5][6][7][8][9][10][11][12][13][14][15]. It is noted that the significant concepts in the classical theory of rough set are the lower and upper approximations obtained from equivalence relation on a universal set.…”