Evaluation of Fuzzy Pareto Solution Set by Using Fuzzy Relation Based Clustering Approach For Fuzzy Multi-Response Experiments

Year 2013, Volume: 17 Issue: 1, 75 - 84, 01.04.2013

Özlem Türkşen Ayşen Apaydın

Abstract

The solution set of a multi-response experiment is characterized by Pareto solution set. In this paper, the multiresponse experiment is dealed in a fuzzy framework. The responses and model parameters are considered as triangular fuzzy numbers which indicate the uncertainty of the data set. Fuzzy least square approach and fuzzy modified NSGA-II (FNSGA-II) are used for modeling and optimization, respectively. The obtained fuzzy Pareto solution set is grouped by using fuzzy relational clustering approach. Therefore, it could be easier to choose the alternative solutions to make better decision. A fuzzy response valued real data set is used as an application.

Keywords

Fuzzy multi-response problem, fuzzy modeling, fuzzy NSGA-II, fuzzy Pareto solution set, fuzzy relational clustering

Bulanık Çok Yanıtlı Deneyler İçin Bulanık Pareto Çözüm Kümesinin Bulanık İlişkiye Dayalı Sınıflandırma Yaklaşımı İle Değerlendirilmesi

Abstract

The solution set of a multi-response experiment is characterized by Pareto solution set. In this paper, the multi-response experiment is dealed in a fuzzy framework. The responses and model parameters are considered as triangular fuzzy numbers which indicate the uncertainty of the data set. Fuzzy least square approach and fuzzy modified NSGA-II (FNSGA-II) are used for modeling and optimization, respectively. The obtained fuzzy Pareto solution set is grouped by using fuzzy relational clustering approach. Therefore, it could be easier to choose the alternative solutions to make better decision. A fuzzy response valued real data set is used as an application.

Keywords

Bulanık çok yanıtlı problem, bulanık modelleme, bulanık BSGA-II, bulanık Pareto çözüm kümesi, bulanık ilişkili sınıflandırma

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• Figure 5. Clustering results of fuzzy non-dominated solutions for 0.70  