Evaluation of Fuzzy Pareto Solution Set by Using Fuzzy Relation Based Clustering Approach For Fuzzy Multi-Response Experiments
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
References
- KHURI, A.I., CORNELL, M., Response Surfaces, Marcel Dekker Inc., New-York, 1996.
- MYERS, R.H., MONTGOMERY, D.C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley and Sons, New York, 2002.
- BOX, G.E.P., DRAPER, N.R., Response Surface Mixtures and Ridge Analysis, John Wiley and Sons, New Jersey, 2007.
- ZADEH, L.A., Fuzzy Sets, Information and Control, Vol.8, 338-353, 1965.
- SILVA, R.C., YAMAKAMI, A., Definition of fuzzy Pareto-optimality by using possibility theory, IFSAEUSFLAT 2009, 1234-1239, 2009.
- XIE, H., LEE, Y.C., Process Optimization Using a Fuzzy Logic Response Surface Method, IEEE Transactions on Components, Packaging, and Manufacturing Technology-Part A, Vol.17, No.2, 1994. PRASAD, K., NATH, N., Comparison of Sugarcane Juice Based Beverage Optimisation Using Response Surface Methodology with Fuzzy Method, Sugar Tech, Vol.4, No.3-4, 109-115, 2002.
- LU, D., ANTONY, J., Optimization of multiple responses using a fuzzy-rule based inference system, International Journal of Production Research, Vol.40, No.7, 1613-1625, 2002.
- SHARMA, V., Multi Response Optimization of Process Parameters Based on Taguchi-Fuzzy Model for Coal Cutting by Water Jet Technology, International Journal on Design and Manufacturing Technologies, Vol.4, No.1, 10-14, 2010.
- Figure 5. Clustering results of fuzzy non-dominated solutions for 0.70
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
References
- KHURI, A.I., CORNELL, M., Response Surfaces, Marcel Dekker Inc., New-York, 1996.
- MYERS, R.H., MONTGOMERY, D.C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley and Sons, New York, 2002.
- BOX, G.E.P., DRAPER, N.R., Response Surface Mixtures and Ridge Analysis, John Wiley and Sons, New Jersey, 2007.
- ZADEH, L.A., Fuzzy Sets, Information and Control, Vol.8, 338-353, 1965.
- SILVA, R.C., YAMAKAMI, A., Definition of fuzzy Pareto-optimality by using possibility theory, IFSAEUSFLAT 2009, 1234-1239, 2009.
- XIE, H., LEE, Y.C., Process Optimization Using a Fuzzy Logic Response Surface Method, IEEE Transactions on Components, Packaging, and Manufacturing Technology-Part A, Vol.17, No.2, 1994. PRASAD, K., NATH, N., Comparison of Sugarcane Juice Based Beverage Optimisation Using Response Surface Methodology with Fuzzy Method, Sugar Tech, Vol.4, No.3-4, 109-115, 2002.
- LU, D., ANTONY, J., Optimization of multiple responses using a fuzzy-rule based inference system, International Journal of Production Research, Vol.40, No.7, 1613-1625, 2002.
- SHARMA, V., Multi Response Optimization of Process Parameters Based on Taguchi-Fuzzy Model for Coal Cutting by Water Jet Technology, International Journal on Design and Manufacturing Technologies, Vol.4, No.1, 10-14, 2010.
- Figure 5. Clustering results of fuzzy non-dominated solutions for 0.70
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | April 1, 2013 |
| Submission Date | November 20, 2012 |
| Acceptance Date | December 25, 2012 |
| Published in Issue | Year 2013 Volume: 17 Issue: 1 |
