A Multiobjective Genetic Fuzzy System with Imprecise Probability Fitness for Vague Data

When questionnaires are designed, each factor under study can be assigned a set of different items. The answers to these questions must be merged in order to obtain the level of that input. Therefore, it is typical for data acquired from questionnaires that each of the inputs and outputs are not numbers, but sets of values. In this paper, we represent the information contained in such a set of values by means of a fuzzy number. A fuzzy statistics-based interpretation of the semantic of a fuzzy set is used for this purpose, as we consider that this fuzzy number is a nested family of confidence intervals for the value of the variable. The accuracy of the model is expressed by means of an interval-valued function, derived from a definition of the variance of a fuzzy random variable. A multicriteria genetic learning algorithm, able to optimize this interval-valued function, is proposed. As an example of the application of this algorithm, a practical problem of modeling in marketing is solved