Hiperesnek oyun teorisi modelleri ve çok kriterli karar vermede uygulamaları

Öz

Klasik oyun teorisi esnek küme yapıları için genişletilmiştir ve böylece esnek oyun teorisi, bulanık esnek oyun teorisi, sezgisel bulanık esnek oyun teorisi, nötrosofik esnek oyun teorisi tanıtılmıştır. Esnek oyun yaklaşımlarında getiri fonksiyonu, küme-değerli fonksiyondur ve çözüm elde etmek için küme işlemlerinin kullanılmasına izin verir, bu da onu pratikte çok uygun ve kolay uygulanabilir kılar. Ayrıca bu oyun yaklaşımlarında stratejiler nitelikler/parametreler olarak belirlenebilir. Yani, tüm bu esnek oyun teorileri, tek-nitelikli fonksiyonları kullanarak parametrik bilgileri işlemek için tasarlanmıştır. Ancak, çok-nitelikli fonksiyon kullanılarak elde edilen parametrik bilgileri işlemek için başka bir güçlü araca ihtiyaç vardır. Bu tür problemleri matematiksel olarak modellemek için hiperesnek küme kavramı önerilmiştir. Bu makalede, hiperesnek oyun teorisi adı verilen hiperesnek kümeye dayalı bir oyun teorisi modeli oluşturulmuştur. Bu oyun teorisinde, getiri fonksiyonu küme-değerli fonksiyondur ve stratejiler çok-nitelikli olarak seçilir. İki kişilik bir hyperesnek oyun geliştirilmiş ve bu tür oyunlar için farklı çözüm yöntemleri (hiperesnek eyer noktası yöntemi, hiperesnek eliminasyon yöntemi, hiperesnek Nash dengesi yöntemi gibi) üretilmiştir. Ayrıca önerilen yöntemler, gerçek hayatta karşılaşılabilecek oyun teorisi tabanlı karar verme problemlerine başarılı bir şekilde uygulanmıştır. Son olarak, iki kişilik hiperesnek oyun n-kişilik hiperesnek oyuna genişletilmiştir. Bir n-kişilik hiperesnek oyunun Nash dengesi tanımlanmış ve bu çözüm yöntemi için bir uygulama sunulmuştur.

Anahtar Kelimeler

• Hiperesnek kümeler
• Hiperesnek getiriler
• İki kişilik hiperesnek oyunlar
• n-kişilik hiperesnek oyunlar

Hypersoft game theory models and their applications in multi-criteria decision making

Abstract

The classical game theory has been extended for soft set structures, and thus, soft game theory, fuzzy soft game theory, intuitionistic fuzzy soft game theory, neutrosophic soft game theory have been introduced. The payoff function in the soft game approaches is the set-valued function and allows the use of set operations to obtain solution, which makes it very convenient and easily applicable in practice. Also, in these game approaches, the strategies can be determined as attributes/parameters. That is, all these soft game theories are designed to manipulate parametric information using a single-attribute function. However, another powerful tool is needed to process parametric information obtained using multi-attribute function. To model such problems mathematically, the concept of hypersoft set has proposed. In this paper, a game theory model based on hypersoft set called hypersoft game theory is constructed. In this game theory, payoff function is the setvalued function and the strategies are chosen as multi-attributes. A twoperson hypersoft game is developed and different solution methods (such as hypersoft saddle point method, hypersoft elimination method, hypersoft Nash equilibrium method) are produced for such games. Also, the proposed methods are successfully applied to game theory-based decision making problems that may be encountered in real life. Finally, the two-person hypersoft game is extended to the n-person hypersoft game. Nash equilibrium of an n-person hypersoft game is described and an application for this solution method is presented.

Keywords

• Hypersoft sets
• Hyperpayoffs
• two-person hypersoft games
• n-person hypersoft games

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