Penalized Intuitionistic Fuzzy Goal Programming Method for Solving Multi-Objective Decision-Making Problems

Abstract

Many applicable problems have multi-goals that optimize simultaneously,
and decision-makers set imprecise aspiration levels for each goal.
Although such types of problems solved by fuzzy optimization are common
in the literature, intuitionistic fuzzy optimization techniques are
more efficient to handle than fuzzy and classical optimization. This research
study focused on establishing a novel method by combining the
penalty function method with an interactive goal programming methodology
for addressing multi-objective decision-making problems in an intuitionistic
fuzzy environment. One of the challenge that exists in the
literature of the optimization method under an imprecise decision environment is that it is not guaranteed to generate a Pareto-optimal solution for the introduced problem. Therefore, in order to ensure the
Pareto-optimality of the obtained solution, the suggested method has
developed a new aggregation operator, an appropriate relaxation of the
constraint set, and a well-structured extended Yager membership function.
In addition, unlike other methods in the literature, the suggested
method gives decision-makers the option to penalize the most unsatisfied
objective function at a specific attained solution instead of starting
from scratch and working their way through the problem. To illustrate
the proposed method, we used a numerical example.