On Fuzzy Ideal Cone Method to Capture Entire Fuzzy Nondominated Set of Fuzzy Multi-criteria Optimization Problems with Fuzzy Parameters

This paper deals with the computational aspect of the fuzzy ideal cone method by Ghosh and Chakraborty, Fuzzy ideal cone: a method to obtain complete fuzzy nondominated set of fuzzy multi-criteria optimization problems with fuzzy parameters, In: The Proceedings of IEEE International Conference on Fuzzy Systems 2013, FUZZ IEEE 2013, IEEE Xplore, pp. 1–8 to generate the complete fuzzy nondominated set of a fuzzy multi-criteria optimization problem. In order to formulate the decision feasible region, the concept of inverse points in fuzzy geometry is used. Relation between the fuzzy decision feasible sets evaluated through the inverse points and directly through the extension principle is reported. It is shown that under a certain monotone condition both the decision feasible sets are identical. This result can greatly reduce the computational cost of evaluating the decision feasible region. After evaluating the decision feasible region, criteria feasible region is formulated using the basic fuzzy geometrical ideas. An algorithmic implementation of the fuzzy ideal cone method is presented to find the complete fuzzy nondominated set of the fuzzy criteria feasible region.