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## Generalized Roughness of (\isin;,\isin;\or;q)-Fuzzy Ideals in Ordered Semigroups

#### Azmat HUSSAİN [1] , Muhammad İrfan ALİ [2] , Tahir MAHMOOD [3]

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

Fuzzy sets, Rough sets, Approximations of fuzzy ideals
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Primary Language en Research Article Author: Azmat HUSSAİN Author: Muhammad İrfan ALİ Author: Tahir MAHMOOD Publication Date : January 1, 2019
 Bibtex @research article { jnt506392, journal = {Journal of New Theory}, issn = {2149-1402}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2019}, volume = {}, pages = {32 - 53}, doi = {}, title = {Generalized Roughness of (\\isin;,\\isin;\\or;q)-Fuzzy Ideals in Ordered Semigroups}, key = {cite}, author = {HUSSAİN, Azmat and ALİ, Muhammad İrfan and MAHMOOD, Tahir} } APA HUSSAİN, A , ALİ, M , MAHMOOD, T . (2019). Generalized Roughness of (\isin;,\isin;\or;q)-Fuzzy Ideals in Ordered Semigroups. Journal of New Theory , (26) , 32-53 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/42082/506392 MLA HUSSAİN, A , ALİ, M , MAHMOOD, T . "Generalized Roughness of (\isin;,\isin;\or;q)-Fuzzy Ideals in Ordered Semigroups". Journal of New Theory (2019 ): 32-53 Chicago HUSSAİN, A , ALİ, M , MAHMOOD, T . "Generalized Roughness of (\isin;,\isin;\or;q)-Fuzzy Ideals in Ordered Semigroups". Journal of New Theory (2019 ): 32-53 RIS TY - JOUR T1 - Generalized Roughness of (\isin;,\isin;\or;q)-Fuzzy Ideals in Ordered Semigroups AU - Azmat HUSSAİN , Muhammad İrfan ALİ , Tahir MAHMOOD Y1 - 2019 PY - 2019 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 32 EP - 53 VL - IS - 26 SN - 2149-1402-2149-1402 M3 - UR - Y2 - 2020 ER - EndNote %0 Journal of New Theory Generalized Roughness of (\isin;,\isin;\or;q)-Fuzzy Ideals in Ordered Semigroups %A Azmat HUSSAİN , Muhammad İrfan ALİ , Tahir MAHMOOD %T Generalized Roughness of (\isin;,\isin;\or;q)-Fuzzy Ideals in Ordered Semigroups %D 2019 %J Journal of New Theory %P 2149-1402-2149-1402 %V %N 26 %R %U ISNAD HUSSAİN, Azmat , ALİ, Muhammad İrfan , MAHMOOD, Tahir . "Generalized Roughness of (\isin;,\isin;\or;q)-Fuzzy Ideals in Ordered Semigroups". Journal of New Theory / 26 (January 2019): 32-53 . AMA HUSSAİN A , ALİ M , MAHMOOD T . Generalized Roughness of (\isin;,\isin;\or;q)-Fuzzy Ideals in Ordered Semigroups. JNT. 2019; (26): 32-53. Vancouver HUSSAİN A , ALİ M , MAHMOOD T . Generalized Roughness of (\isin;,\isin;\or;q)-Fuzzy Ideals in Ordered Semigroups. Journal of New Theory. 2019; (26): 53-32.

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