An Algorithm for Group Decision Making Problems via Soft Set Relations

Year 2025, Volume: 10 Issue: 1, 29 - 41, 29.06.2025

Nazan Polat

https://doi.org/10.33484/sinopfbd.1581388

Abstract

Decision-making is a critical process in various fields, often complicated by uncertainty and incomplete information. Soft set theory, introduced as a mathematical tool to handle such uncertainties, offers a flexible and efficient framework for addressing these challenges. The purpose of this study is developing a method by using graph representation of soft set relation for group decision making problems with several examples as application. The algorithm integrates key soft set relations, allowing for the systematic evaluation of alternatives against multiple criteria. Through a some of examples and case studies, effectiveness of the algorithm in decision-making applications is examined. Results show that the soft set-based approach provides a more adaptable and precise method for decision-making compared to traditional techniques, making it a valuable tool for complex decision environments.

Keywords

Soft Sets , Soft Set Relations , Group Decision Making Problems , Graph Representations of Soft Set Relations.

Grup Karar Verme Problemleri için Esnek Küme Bağıntılarıyla bir Algoritma

Abstract

Karar verme, çeşitli çalışma alanlarında genellikle belirsizlik ve eksik bilgi nedeniyle karmaşık hale gelen kritik bir süreçtir. Bu tür belirsizliklerle başa çıkmak için matematiksel bir araç olarak tanıtılan esnek küme teorisi, bu zorlukları ele almak için esnek ve etkili bir çerçeve sunar. Bu çalışmanın amacı, uygulama olarak birkaç örnekle grup karar verme problemleri için esnek küme ilişkisinin graf gösterimini kullanarak bir yöntem geliştirmektir. Algoritma, alternatiflerin birden fazla kritere göre sistematik olarak değerlendirilmesine olanak tanıyan temel esnek küme bağıntılarını kullanır. Örnekler aracılığıyla, algoritmanın karar verme uygulamalarındaki sağlamlığını ve etkinliğini gösterilmiştir. Sonuçlar, esnek küme tabanlı yaklaşımın, geleneksel tekniklere kıyasla karar verme için daha uyarlanabilir ve kapsamlı bir yöntem sağladığını ve karmaşık karar verme problemleri için değerli bir araç haline getirdiğini göstermektedir.

Keywords

Esnek kümeler , Esnek Küme Bağıntıları , Grup Karar Verme Problemleri , Esnek Küme Bağıntılarının Grafik Gösterimi.

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