Generalized Rough Fuzzy Ideals in Quantales

Abstract

The paper examines the generalized rough fuzzy ideals of quantales. There are some intrinsic relations between fuzzy prime (primary) ideals of quantales and generalized rough fuzzy prime (primary) ideals of quantales. Homomorphic images of "generalized rough ideals, generalized rough prime (primary) ideals, and generalized rough fuzzy prime (primary) ideals" which are incited by quantale homomorphism are examined.

Roughness in Hypervector Spaces

“…In the modules [7] and rings [8], Davvaz looked at roughness. Qurashi and Shabir [9,10] explored rough subsets in quantales and quantale modules. Shabir and others studied roughness in S-acts [11] and in ordered semigroups [11].…”

Topological Structures of Lower and Upper Rough Subsets in a Hyperring

“…Shabir and Irshad [13] applied roughness in ordered semigroups. In [14][15][16][17][18][19][20][21][22], authors studied roughness in different hyperstructures. Fuzzy sets were also considered by many authors, for instance, Fotea and Davvaz [23] studied fuzzy hyperrings.…”

Fuzziness and Roughness in Hyperquantales

“…Davvaz et al in [6] applied Atanassov's intuitionistic fuzzy set theory to quantales. In [29,30], Saqib and Shabir studied relationship between generalized rough sets and quantale by using fuzzy ideals of quantale.…”