Using Compensatory Fuzzy Logic to Model an Investor’s Preference Regarding Portfolio Stock Selection within Markowitz’s Mean–Variance Framework

We analyse the use of Compensatory FuzzyLogic (CFL) applied to an optimisation model to reflect aninvestor’s preferences regarding portfolio stock selection. CFL is a framework that allows the construction of fuzzy predicates using fuzzy parametrised linguistic variables. Although the potential of a CFL predicate to model preferences is high, to the best of our knowledge, this is the first use of this strategy to do so. Real datafrom the Mexican Stock Exchange was employed to create a test instance. Portfolios were obtained using the Particle Swarm Optimisation algorithm. By maximising the degree of truth of the predicate representing the investor’s preferences, the model is able to reflect investor profiles regarding the return–risk relation of the portfolios. Three artificial investor profiles were defined during the experimentation; the model was able to reflectall of these preferences.