Modeling risk attitudes in picture fuzzy multi-objective linear programming with chance constraints

Abstract

Picture fuzzy sets provide a flexible framework for simultaneously modeling uncertainty, neutrality, and refusal. This study proposes a novel solution method for chance-constrained multi-objective linear programming within a picture fuzzy context. We introduce a comprehensive definition of generalized trapezoidal picture fuzzy numbers (GTPFNs), with particular attention to ensuring coherent and shape-preserving arithmetic operations. To enhance computational efficiency, we adopt a risk-based simplification guided by the selected risk attitude and cost-benefit classification. Specifically, it reduces the coefficients represented by GTPFNs to a generalized trapezoidal representation. This makes the proposed approach more practical for large-scale decision problems, where optimistic, pessimistic, and intermediate attitudes of decision-makers are captured through possibility, necessity, and credibility measures, respectively. The method has been applied to single-and multi-objective problems defined in intuitionistic and picture fuzzy environments, considering both single and multiple height levels, using benchmark cases from the literature. Numerical results on benchmark problems confirm that the proposed approach is computationally tractable and faithfully reflects the prescribed risk attitudes of the decision-makers. As the risk parameter increases, sensitivity analysis shows that the solutions systematically become more conservative, with lower optimal values of the maximization-oriented objective function and tighter possibility-, credibility-, or necessity-based satisfaction levels.