Interpolative Boolean Algebra for Generalizations of Intuitionistic Fuzzy Sets

Milošević, Pavle; Petrović, Bratislav

doi:10.2991/eusflat-19.2019.94

Cited by 2 publications

(2 citation statements)

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“…This paper continues the work begun in [7,30], where we studied the possibility of introducing operations inspired by interpolative Boolean algebra [31] (IBA) in IFS theory. Herein, we aim to propose the LBIFS-IBA approach and to study its properties in detail.…”

Section: Introductionmentioning

confidence: 64%

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

2021

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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 μA+νA>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.

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Section: Introductionmentioning

confidence: 64%

“…Finally, graphical interpretation of GAIFS6 given in [39] is not correct. It is noticed and elaborated for instance in [25,29,30].…”

Section: Gaifs Gaifs Gaifs Gaifsmentioning

confidence: 87%