Interval Type II Parametric Trapezoidal Fuzzy Number Approximation of Interval Type II Exponential Fuzzy Number Based on The Expected Interval

Abstract

Type I fuzzy numbers are used in some decision-making problems to handle the uncertainty. The membership degrees of Type I fuzzy numbers are crisp numbers. However, the events in which the membership degrees may be shown by fuzzy numbers may exist in the real life problems. In that cases, the Type II fuzzy numbers can be used. The usage of the simpler form of the fuzzy number is seen as an advantage for the avoiding of complex calculations in some studies. Considering this, the interval Type II parametric trapezoidal fuzzy number approximation of the interval Type II exponential fuzzy number has been found by a constrained optimization problem in which the equalities between expected intervals are used and the formulas have been given in this study.

Keywords

• Type II fuzzy number
• exponential fuzzy number
• parametric trapezoidal fuzzy number
• approximation
• optimization

Beklenen Aralığa Dayanan Aralık Tip II Üssel Bulanık Sayının Aralık Tip II Parametrik Yamuk Bulanık Sayı Yakınsaması

Abstract

Tip I bulanık sayıları belirsizliği ele almak için bazı karar verme problemlerinde kullanılmaktadır. Tip I bulanık sayılarının üyelik dereceleri adi sayılardır. Ancak gerçek yaşam problemlerinde, üyelik derecelerinin bulanık sayılar ile gösterilebileceği olaylar var olabilir. Bu gibi durumlarda, Tip II bulanık sayıları kullanılabilir. Bulanık sayının daha basit bir formunun kullanılması bazı çalışmalarda karmaşık hesaplamalardan kaçınmak için bir avantaj olarak görülmektedir. Bu durum dikkate alınarak, bu çalışmada aralık Tip II üssel bulanık sayının aralık Tip II parametrik yamuk bulanık sayı yakınsaması, beklenen aralıkların eşitliklerinin kullanıldığı bir kısıtlı optimizasyon problemi ile bulunmuş ve formüller verilmiştir.

Keywords

• Tip II bulanık sayı
• üssel bulanık sayı
• parametrik yamuk bulanık sayı
• optimizasyon
• yakınsama
• optimizasyon

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