Generalized Roughness of (∈, ∈ ∨q)-Fuzzy Ideals in Ordered Semigroups

Authors : Azmat Hussain, Muhammad Irfan Ali, Tahir Mahmood

Pages : 32-53

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Publication Date : 2019-01-01

Article Type : Research

Abstract :Ordered semigroups (OSGs) is a significant algebraic structure having  partial ordered with associative binary operation. OSGs have broad  applications in various fields such as coding theory, automata theory, fuzzy  finite state machines and computer science etc. In this manuscript we  investigate the notion of generalized roughness for fuzzy ideals in OSGs on  the basis of isotone and monotone mappings. Then the notion of approximation  is boosted to the approximation of fuzzy bi-ideals,~approximations fuzzy  interior ideals and approximations fuzzy quasi-ideals in OSGs and  investigate their related properties. Furthermore   (\isin;,\isin;\or;q) -fuzzy ideals are the generalization of fuzzy ideals. Also the  generalized roughness for (\isin;,\isin;\or;q) -fuzzy ideals,  fuzzy bi-ideals and fuzzy interior ideals have been studied in OSGs and  discuss the basic properties on the basis of isotone and monotone mappings
Keywords : Fuzzy sets, Rough sets, Approximations of fuzzy ideals