A fuzzy definition of optimality for many-criteria optimization problems

When dealing with many-objectives optimization problems, the concepts of Pareto-optimality and Pareto-dominance are often inefficient in modeling and simulating human decision making. This leads to an unpractical size for the set of Pareto-optimal (PO) solutions, and an additional selection criteria among solutions is usually arbitrarily considered. In the paper, different fuzzy-based definitions of optimality and dominated solutions, being nonpreference based, are introduced and tested on analytical test cases, in order to show their validity and nearness to human decision making. Based on this definitions, different subsets of PO solution set can be computed using simple and clear information provided by the decision maker and using a parameter value ranging from zero to one. When the value of the above parameter is zero, the introduced definitions coincide with classical Pareto-optimality and dominance. When the parameter value is increased, different subset of PO solutions can be obtained corresponding to higher degrees of optimality.