Affiliations: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India
Note: [] Corresponding author. Debjani Chakraborty, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721 302, India. E-mails: debjani@maths.iitkgp.ernet.in; debdas.email@gmail.com (Debdas Ghosh).
Abstract: Decision making processes in imprecise environments are usually addressed by fuzzy multi-criteria optimization problems. It is significantly natural that complete information about non-dominated set for fuzzy multi-criteria optimization problem not only facilitates decision making process, but also helps the process to undergo in a proper mathematical way. However, in the literature no methodology is found yet to capture entire fuzzy non-dominated set. Thus, this paper attempts to generate complete fuzzy non-dominated set of fuzzy multi-criteria optimization problem. This is the main objective of the paper. The proposed study mainly focuses to observe the problem from fuzzy geometrical framework. In the studied methodology, at first, fuzzy decision feasible region is constructed through a newly proposed fuzzy inequality relation using same points in fuzzy geometry. Then, fuzzy non-dominated set is formulated under a new definition of fuzzy Pareto set. Finally, modified normal boundary intersection method is being used to capture the fuzzy Pareto set of the problem. Proposed definitions and methodologies are supported by several numerical examples and pictorial illustrations.
Keywords: Fuzzy multi-criteria optimization, modified normal boundary intersection method, same points, fuzzy inequality
