Modelling Contexts as Fuzzy Propositions in Optimisation Problems

Abstract

Decisions made in areas such as economics, engineering, industry and medical sciences are usually based on finding and interpreting solutions to optimisation problems. When modelling an optimisation 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 paper, we propose a systematic way of modelling contexts based on fuzzy propositions and two approaches (a priori and a posteriori) for solving optimisation 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 multi-criteria 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 optimisation and decision-making.