On identifying fuzzy knees in fuzzy multi-criteria optimization problems
- 60 Downloads
This paper introduces and analyzes the idea of fuzzy knee in fuzzy multi-criteria optimization problems. The fuzzy decision feasible region of the problem is constructed under a fuzzy inequality relation that is defined with the help of same points in fuzzy geometry. Then, fuzzy criteria feasible region is obtained through the image of the fuzzy decision feasible region by the criteria-vector-valued mapping. For the constructed fuzzy criteria feasible region, we define fuzzy knee and then propose a method to capture the fuzzy knee regions, along with the complete fuzzy Pareto set. All the studied ideas and methodologies are supported with suitable examples and pictorial illustrations. An engineering application of the presented method is also given.
KeywordsFuzzy multi-criteria optimization Same points Fuzzy inequality Fuzzy knee
Mathematics Subject Classification90C70 90C29
The author is truly thankful to the anonymous reviewers and editors for their valuable comments and suggestions to improve the paper. The author gratefully acknowledges the financial support through Early Career Research Award (ECR/2015/000467), Science & Engineering Research Board, Government of India.
- 8.Deb, K.: Multi-objective evolutionary algorithms: introducing bias among pareto-optimal solutions. In: Advances in Evolutionary Computing, pp. 263–292. Springer, New York (2003)Google Scholar
- 12.Ghosh, D., Chakraborty, D.: Ideal cone: a new method to generate complete pareto set of multi-criteria optimization problems. In: Mathematics and Computing 2013, pp. 171–190. Springer, New York (2014)Google Scholar
- 21.Rachmawati, L., Srinivasan, D.: A multi-objective evolutionary algorithm with weighted-sum niching for convergence on knee regions. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 749–750. ACM, New York (2006)Google Scholar
- 24.Wang, X., Ruan, D., Kerre, E.E.: Mathematics of Fuzziness. Basic Issues, vol. 245. Springer, New York (2009)Google Scholar