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Journals / Turkish Journal of Mathematics and Computer Science / 2018 / Cilt: 10 - Sayı: 10

S P-Fuzzy Soft Ideals in Semigroups

Canan AKIN
ÜLKÜ KARAKAYA
Pages
22–32
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover it is indicated that an α-level soft set of a S P-fuzzysoft subset is a soft subsemigroup for all α ∈ [0, 1] if and only if the SP-fuzzy soft subset is a SP-fuzzy softsubsemigroup.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the definition of a new concept which is a member of the class ˜ (U, P) and which is referredto as UP-fuzzy soft subset of a soft set on the class (U, P) is introduced, where ˜ (U, P) denotes the fuzzy soft classand (U, P) denotes the soft class with the universal set U and the set of parameters P.
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Key Findings & Data:It is demonstrated that UP-fuzzysoft subsets provide De Morgan rules for restricted union and restricted intersection.
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Conclusion & Impact:Moreover it is indicated that an α-level soft set of a S P-fuzzysoft subset is a soft subsemigroup for all α ∈ [0, 1] if and only if the SP-fuzzy soft subset is a SP-fuzzy softsubsemigroup.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Özet

In this paper, the definition of a new concept which is a member of the class ˜ (U, P) and which is referredto as UP-fuzzy soft subset of a soft set on the class (U, P) is introduced, where ˜ (U, P) denotes the fuzzy soft classand (U, P) denotes the soft class with the universal set U and the set of parameters P. We give the definitionsof the complement and α-level soft set of a UP-fuzzy soft subset of a soft set. It is demonstrated that UP-fuzzysoft subsets provide De Morgan rules for restricted union and restricted intersection. Furthermore, considering asemigroup S as an universal set, this paper presents some new algebraic notions which are called S P-fuzzy softsubsemigroup and S P-fuzzy soft left (right, bi-, quasi, interior) ideal of a soft semigroup. We examine some basicproperties such as restricted union, extended union, restricted intersection, extended intersection and product of thefamilies of S P-fuzzy soft subsemigroups and S P-fuzzy soft left (right, bi-, quasi, interior) ideals. It is obtainedthat the restricted intersection of the family of S P-fuzzy soft subsemigroups is a S P-fuzzy soft subsemigroup ofthe restricted intersection of the family of soft sets. Moreover it is indicated that an α-level soft set of a S P-fuzzysoft subset is a soft subsemigroup for all α ∈ [0, 1] if and only if the SP-fuzzy soft subset is a SP-fuzzy softsubsemigroup.

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Cite This Article

AKIN, C., KARAKAYA, Ü. (2018). S P-Fuzzy Soft Ideals in Semigroups. Turkish Journal of Mathematics and Computer Science, Cilt: 10 - Sayı: 10, 22–32. https://ajindex.com/articles/374764

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