Virtual Logic-Based Fuzzy Parameterized Fuzzy Hypersoft Sets: An Algorithmic Framework for Improved Decision-Making

Öz

The primary aim of this study is to address potential inaccuracies in membership values expressed by decision-makers when dealing with uncertainty in complex environments. To achieve this, the concept of virtual logic is incorporated as a refinement mechanism. Building on this foundation, we construct the notion of a virtual fuzzy parameterized fuzzy hypersoft set (vfp-fhs-set) by integrating virtual logic with hypersoft sets, which are designed to more effectively represent the components of parameter sets. Through this integration, a novel hybrid mathematical model is introduced, enhancing parameterization with fuzzy membership values and providing a more robust framework for decision-making under uncertainty. Several fundamental set operations associated with this structure are formally examined to establish its theoretical soundness. Furthermore, a decision-making algorithm based on vfp-fhs-sets is proposed and illustrated with an application, demonstrating the practical utility of the model. Comparative analysis with existing approaches highlights the advantages of incorporating virtual logic, particularly in improving precision and reliability in the ranking of alternatives.

Anahtar Kelimeler

• fp-fhs-set
• vfp-fhs-set
• Algorithm
• Decision-making

Sanal Mantık Tabanlı Bulanık Parametreli Bulanık Hiper Yumuşak Kümeler: Gelişmiş Karar Verme İçin Algoritmik Bir Çerçeve

Öz

Bu çalışmanın temel amacı, karmaşık ortamlarda belirsizlikle başa çıkarken karar vericiler tarafından ifade edilen üyelik değerlerindeki olası yanlışlıkları ele almaktır. Bunu başarmak için, sanal mantık kavramı bir iyileştirme mekanizması olarak dahil edilmiştir. Bu temel üzerine inşa ederek, sanal mantığı parametre kümelerinin bileşenlerini daha etkili bir şekilde temsil etmek üzere tasarlanmış hiperyumuşak kümelerle entegre ederek sanal bulanık parametreli bulanık hiperyumuşak küme (vfp-fhs-kümesi) kavramını inşa ediyoruz. Bu entegrasyon yoluyla, bulanık üyelik değerleriyle parametrelendirmeyi geliştiren ve belirsizlik altında karar alma için daha sağlam bir çerçeve sağlayan yeni bir hibrit matematiksel model tanıtılmıştır. Bu yapıyla ilişkili birkaç temel küme işlemi, teorik sağlamlığını belirlemek için resmi olarak incelenmiştir. Ayrıca, vfp-fhs-kümeleri tabanlı bir karar alma algoritması önerilmiş ve bir uygulama ile gösterilerek modelin pratik faydası gösterilmiştir. Mevcut yaklaşımlarla karşılaştırmalı analiz, özellikle alternatiflerin sıralanmasında hassasiyeti ve güvenilirliği artırmada sanal mantığın dahil edilmesinin avantajlarını vurgulamaktadır.

Anahtar Kelimeler

• fp-fhs-küme
• vfp-fhs-küme
• Algoritma
• Karar verme

Kaynakça

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