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

Year 2019, Issue: 26, 32 - 53, 01.01.2019

Azmat Hussain Muhammad İrfan Ali , Tahir Mahmood

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

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