Generalized Roughness of (∈, ∈ ∨q)-Fuzzy Ideals in Ordered Semigroups - Azmat Hussain; Muhammad İrfan Ali; Tahir Mahmood (Journal of New Theory)
Ordered semigroups (OSGs) is a significant algebraic structure havingpartial ordered with associative binary operation. OSGs have broadapplications in various fields such as coding theory, automata theory, fuzzyfinite state machines and computer science etc. In this manuscript weinvestigate the notion of generalized roughness for fuzzy ideals in OSGs onthe basis of isotone and monotone mappings. Then the notion of approximationis boosted to the approximation of fuzzy bi-ideals,~approximations fuzzyinterior ideals and approximations fuzzy quasi-ideals in OSGs andinvestigate their related properties. Furthermore(\isin;,\isin;\or;q)-fuzzy ideals are the generalization of fuzzy ideals. Also thegeneralized roughness for (\isin;,\isin;\or;q)-fuzzy ideals,fuzzy bi-ideals and fuzzy interior ideals have been studied in OSGs anddiscuss the basic properties on the basis of isotone and monotone mappings