Dealing with typical values by using Atanassov’s intuitionistic fuzzy sets

In this paper we consider the problem of determining typical values. We heavily refer to some results of linguistic experiments in psychology and cognitive science. Since analyzes employed in those areas, which make use of some considerations on how an object is typical to a category and its related so called contrast category, we propose the use of Atanassovpsilas intuitionistic fuzzy sets (to be called A-IFSs, for short). We follow the line of reasoning known from psychology and cognitive sciences, in particular those resulting from linguistic experiments, and verify how those results work in the case of classification, an omnipresent problem in computer science, decision sciences, etc. Our considerations concentrate around a typical example discussed in cognitive sciences. We start from nominal data, i.e. names are assigned to objects as labels, and we investigate to which extent a linguistic representation in a psychological space succeeds in predicting categories via the intuitionistic fuzzy sets. We only consider here a model of categories with a geometrical centroid model in which the similarity is defined in terms of a distance to the centroids. Next, we verify if the extreme ideals, which are important in cognitive processes when categories are learnt in the presence of the alternative (contrast) category, give comparative results. We show that Atanassovpsilas intuitionistic fuzzy sets make it possible to reflect a positive and negative information via the concept of membership and non-membership. Though the paper presents an ongoing research, the first results obtained are promising and point out the usefulness and strength of Atanassovpsilas intuitionistic fuzzy sets as a tool to account for more aspects of vague data and information.