Formalization of Human Categorization Process Using Interpolative Boolean AlgebraReport as inadecuate




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Mathematical Problems in Engineering - Volume 2015 2015, Article ID 620797, 8 pages -

Research Article

Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000 Belgrade, Serbia

Institute Mihajlo Pupin, University of Belgrade, Volgina 15, 11000 Belgrade, Serbia

Received 1 August 2014; Accepted 21 September 2014

Academic Editor: Shifei Ding

Copyright © 2015 Vladimir Dobrić et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Since the ancient times, it has been assumed that categorization has the basic form of classical sets. This implies that the categorization process rests on the Boolean laws. In the second half of the twentieth century, the classical theory has been challenged in cognitive science. According to the prototype theory, objects belong to categories with intensities, while humans categorize objects by comparing them to prototypes of relevant categories. Such categorization process is governed by the principles of perceived world structure and cognitive economy. Approaching the prototype theory by using truth-functional fuzzy logic has been harshly criticized due to not satisfying the complementation laws. In this paper, the prototype theory is approached by using structure-functional fuzzy logic, the interpolative Boolean algebra. The proposed formalism is within the Boolean frame. Categories are represented as fuzzy sets of objects, while comparisons between objects and prototypes are formalized by using Boolean consistent fuzzy relations. Such relations are directly constructed from a Boolean consistent fuzzy partial order relation, which is treated by Boolean implication. The introduced formalism secures the principles of categorization showing that Boolean laws are fundamental in the categorization process. For illustration purposes, the artificial cognitive system which mimics human categorization activity is proposed.





Author: Vladimir Dobrić, Darko Kovačević, Bratislav Petrović, Dragan Radojević, and Pavle Milošević

Source: https://www.hindawi.com/



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