A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra

Pavle Milošević, Bratislav Petrović and Ivana Dragović
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Pavle Milošević: Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000 Belgrade, Serbia
Bratislav Petrović: Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000 Belgrade, Serbia
Ivana Dragović: Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000 Belgrade, Serbia

Mathematics, 2021, vol. 9, issue 17, 1-21

Abstract: One of the main issues in IFS theory are generalizations of intuitionistic fuzzy set (IFS) definition as well as IFS operations. In this paper, we present the LBIFS-IBA approach by applying operations based on interpolative Boolean algebra (IBA) on generalized IFS. Namely, LBIFS are defined as a special case of Liu’s generalized IFS with the maximal interpretational surface. By extending the interpretational surface, the descriptive power of the approach is enhanced, and therefore the problematic situations when ? A + ? A > 1 can be modeled. In addition, IBA-based algebra secures Boolean properties of the proposed approach. Considerable attention is given to comprehension of uncertainty within LBIFS-IBA, i.e., we propose a novel manner of uncertainty interpretation by treating values from [?1,1] interval. In order to prove its importance, we compare LBIFS-IBA with several well-known IFS generalizations, showing that only our approach offers meaningful uncertainty interpretation is all selected cases. Additionally, we illustrate the practical benefits of LBIFS-IBA by applying it to an example of modeling Japanese candlesticks for price charting and paying special attention to uncertainty interpretation.

Keywords: LBIFS-IBA approach; generalization of intuitionistic fuzzy sets; IFS-interpretational triangle; interpolative Boolean algebra; uncertainty interpretation; Japanese candlestick modeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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