Effect on Decision Making Processes of Pythagorean Fuzzy Set

Abstract

Pythagorean Fuzzy Set concept is a more flexible approach that encompasses fuzzy sets and intuitionistic fuzzy sets in the uncertainty modeling process. The concept offers a new approach for jointly evaluating membership and non-membership degrees. This approach allows decision makers to express uncertainty over a wider range. Therefore, Pythagorean fuzzy sets offer higher representational power than intuitionistic fuzzy sets and are particularly effective in solving complex problems such as multi-criteria decision making, risk analysis, expert systems. Decision making is an approach that aims to systematically analyze decision problems that consider multiple criteria. This method allows the decision maker to evaluate both qualitative and quantitative factors to make the most appropriate choice among alternatives. Among the most commonly used methods, AHP, TOPSIS and PROMETHEE are prominent, aiming to determine the relative advantages of alternatives under different assumptions. Today, fuzzy logic and its extended forms, intuitionistic and pythagorean fuzzy approaches, are frequently integrated into decision making processes to reduce the influence of uncertainty, expert judgment, and subjective assessments. This allows decision models to more effectively represent the complex and uncertain situations encountered in real life problems. This study presents an example of the impact of pythagorean fuzzy sets on decision-making processes.

Keywords

• Decision making
• fuzzy set
• pythagorean fuzzy set.

Pisagor Bulanık Kümesinin Karar Verme Süreçleri Üzerindeki Etkisi

Abstract

Pisagor Bulanık Küme kavramı, belirsizlik modelleme sürecinde bulanık kümeleri ve sezgisel bulanık kümeleri kapsayan daha esnek bir yaklaşımdır. Bu kavram, üyelik ve üye olmama derecelerini birlikte değerlendirmek için yeni bir yaklaşım sunar. Bu yaklaşım, karar vericilerin belirsizliği daha geniş bir aralıkta ifade etmelerini sağlar. Bu nedenle, Pisagor bulanık kümeleri, sezgisel bulanık kümelerden daha yüksek temsil gücü sunar ve çok kriterli karar verme, risk analizi, uzman sistemler gibi karmaşık sorunların çözümünde özellikle etkilidir. Karar verme, birden fazla kriteri dikkate alan karar problemlerini sistematik olarak analiz etmeyi amaçlayan bir yaklaşımdır. Bu yöntem, karar vericinin alternatifler arasında en uygun seçimi yapmak için hem nitel hem de nicel faktörleri değerlendirmesine olanak tanır. En yaygın kullanılan yöntemler arasında, farklı varsayımlar altında alternatiflerin göreceli avantajlarını belirlemeyi amaçlayan AHP, TOPSIS ve PROMETHEE öne çıkmaktadır. Günümüzde, belirsizliğin, uzman yargısının ve öznel değerlendirmelerin etkisini azaltmak için bulanık mantık ve genişletilmiş biçimleri olan sezgisel ve pisagor bulanık yaklaşımları sıklıkla karar verme süreçlerine entegre edilmektedir. Bu, karar modellerinin gerçek hayatta karşılaşılan karmaşık ve belirsiz durumları daha etkili bir şekilde temsil etmesine olanak tanır. Bu çalışma, pisagor bulanık kümelerinin karar verme süreçleri üzerindeki etkisine dair bir örnek sunmaktadır.

Keywords

• Karar verme
• bulanık küme
• pisagor bulanık küme

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