On Soft Rough Topology with Multi-Attribute Group Decision Making

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 09 Jan 2019 English Publisher:MDPI AGJournal:Mathematics, volume 7, page 67 (eissn: 2227-7390,

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Authors: Muhammad Riaz; Florentin Smarandache; Atiqa Firdous; Atiqa Fakhar;

doi: 10.3390/math7010067 , 10.5281/zenodo.2862867 , 10.5281/zenodo.2862866

On Soft Rough Topology with Multi-Attribute Group Decision Making

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Abstract

Rough set approaches encounter uncertainty by means of boundary regions instead of membership values. In this paper, we develop the topological structure on soft rough set ( SR -set) by using pairwise SR -approximations. We define SR -open set, SR -closed sets, SR -closure, SR -interior, SR -neighborhood, SR -bases, product topology on SR -sets, continuous mapping, and compactness in soft rough topological space ( SRTS ). The developments of the theory on SR -set and SR -topology exhibit not only an important theoretical value but also represent significant applications of SR -sets. We applied an algorithm based on SR -set to multi-attribute group decision making (MAGDM) to deal with uncertainty.

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Keywords

<named-content content-type="inline"><inline-formula> <mml:math id="mm2000" display="block"> <mml:semantics> <mml:mi mathvariant="script">SR</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-compactness, <named-content content-type="inline"><inline-formula> <mml:math id="mm1997" display="block"> <mml:semantics> <mml:mi mathvariant="script">SR</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-set, <named-content content-type="inline"><inline-formula> <mml:math id="mm1998" display="block"> <mml:semantics> <mml:mi mathvariant="script">SR</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-topology, <named-content content-type="inline"><inline-formula> <mml:math id="mm1999" display="block"> <mml:semantics> <mml:mi mathvariant="script">SR</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-continuity, rough set, decision making

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