Modeling Contexts as Fuzzy Propositions in Optimization Problems

Decisions made in areas such as economics, engineering, industry, and medical sciences are usually based on finding and interpreting solutions to optimization problems. When modeling an optimization problem, it should be clear that people do not make decisions in a vacuum or in isolation from the reality. So, there is always a decision-making context that, in addition to the natural constraints of the problem, acts as a filter on the candidate solutions available. If this fact is omitted, optimal but useless solutions to the problem can be obtained. In this article, we propose a systematic way of modeling contexts based on fuzzy propositions and two approaches (a priori and a posteriori) for solving optimization problems under their influence. In the proposed a priori approach, the context is explicitly included in the mathematical model of the problem. As this approach may have a limited application due to the increasing number of constraints and their nature, an a posteriori approach is proposed, in which a set of solutions, obtained by any means (like exact algorithms, simulation, or metaheuristics), are checked for their suitability to the context by using a multicriteria decision-making methodology. A simple fish harvesting problem in a sustainability context and a tourist trip design problem in a pandemic context were solved for illustration purposes. Our results provide researchers and practitioners with a methodology for more effective optimization and decision making.

Automated summary

Decisions made in various fields such as economics, engineering, industry, and medical sciences rely on finding and interpreting solutions to optimization problems. It is important to consider the decision-making context as a filter, along with the natural constraints of the problem, to avoid obtaining optimal but irrelevant solutions. This article proposes a method of modeling contexts using fuzzy propositions and introduces two approaches (a priori and a posteriori) for solving optimization problems under their influence. The results provide researchers and practitioners with a methodology for more effective optimization and decision making.