A New Methodology for Solving Piecewise Quadratic Fuzzy Cooperative Continuous Static Games

Xiao, He; Zhang, Xiaoju; Lin, Dong; Khalifa, Hamiden Abd El-Wahed; Edalatpanah, S. A.

doi:10.1155/2022/5314322

Cited by 2 publications

(2 citation statements)

References 45 publications

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“…In [37], the authors focused on the probabilistic linguistic matrix games based on the fuzzy theories. Some resarchers studied several methodologies on fuzzy cooperative games and fuzzy non-cooperative games [38], [39]. Li and Tu [40] developed a new method to solving general intuitionistic fuzzy matrix games, which takes into account the degree of acceptance that general intuitionistic fuzzy constraints can be violated.…”

Section: Introductionmentioning

confidence: 99%

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

Debnath,

Kamacı

2023

Pamukkale J Eng Sci

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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. 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 yaklaşımlarındastratejiler 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 gen...

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Section: Introductionmentioning

confidence: 99%

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

Debnath,

Kamacı

2023

Pamukkale J Eng Sci

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“…In recent years, numerous authors have studied games under uncertainty, including Garg et al [21], Khalifa et al [22,23], Xiao et al [24], Rasoulzadeh et al [25], Zanjani et al [26], Das [27], Veeramani et al [28], and Mao et al [29]. Osman [30,31] analyzed the solvability set, stability set of the first kind, and stability set of the second kind for parametric convex nonlinear programming.…”

Section: Introductionmentioning

confidence: 99%

Toward Multi-Objective Optimization Approach for Solving Cooperative Continuous Static Games under Fuzzy Environment

Alhanouf,

Hamiden,

Muhammad

2023

IJFIS

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This study focuses on the analysis of cooperative continuous static games involving multiple players (n-players) with fuzzy parameters present in both the cost functions and the right-hand side of constraints. The fuzzy parameters used in this study are described by piecewise quadratic fuzzy numbers that are known for their accurate representation. Specifically, we introduce close interval approximations as a reliable method for handling piecewise quadratic fuzzy numbers. The study defines and investigates the stability set of the second kind in a fuzzy environment, where differentiability is not assumed. The determination of this stability set is an essential aspect of the study. To illustrate the concepts presented, a numerical example is provided, offering a practical demonstration of the proposed framework.

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A New Methodology for Solving Piecewise Quadratic Fuzzy Cooperative Continuous Static Games

Cited by 2 publications

References 45 publications

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

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

Toward Multi-Objective Optimization Approach for Solving Cooperative Continuous Static Games under Fuzzy Environment

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