Dealing with typical values via Atanassov's intuitionistic fuzzy sets

This paper is an improved and extended version of our previous work2 2. Based on ‘On Some Typical Values for A-IFS’, by E. Szmidt and J. Kacprzyk Szmidt, E. and Kacprzyk, J. 2008. “On some typical values for Atanassov's intuitionistic fuzzy sets”. In Proceedings of the 4th international IEEE conference on intelligent systems IS'08, 13-2–13-7. Los Alamitos, CA: IEEE. [Google Scholar] which appeared in the Proceedings of the 4th International IEEE Conference on Intelligent Systems IS'08, pp. 13-2–13-7. on typicality in terms of Atanassov's intuitionistic fuzzy sets (to be called A-IFSs, for short)3 3. There is currently a discussion on the appropriateness of the name IFS introduced by Dubois et al. (2005 Dubois, D. 2005. Terminological difficulties in fuzzy set theory – the case of ‘intuitionistic fuzzy sets’. Fuzzy sets and systems, 156(3): 485–491. [Crossref], [Web of Science ®] , [Google Scholar]), and also Atanassov's (2005 Atanassov, K. 2005. Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper ‘terminological difficulties in fuzzy set theory – the case of intuitionistic fuzzy sets’. Fuzzy sets and systems, 156: 496–499. [Google Scholar]) response. This is, however, beyond the scope of this paper which will not be dealing with this issue. . We follow the line of reasoning known from psychological and cognitive sciences, in particular from linguistic experiments, and verify how those results work in the case of classification – a typical problem in computer science, decision sciences, etc. Our considerations concentrate on a typical example discussed in cognitive sciences – we investigate to which extent a linguistic representation in a psychological space (we start from nominal data – names are assigned to objects as labels) succeeds in predicting categories via A-IFSs. First, we consider a model of categories with a geometrical centroid model in which the similarity is defined in terms of a distance to 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. Finally, we discuss if the ‘reachable extreme ideals’ and ‘dominating frequency centres’ give comparative results. We show that A-IFSs make it possible to reflect a positive and negative information via the concept of membership and non-membership. Although the paper presents ongoing research, the results obtained are promising and point out the usefulness and strength of A-IFSs as a tool to account for more aspects of vague data and information.