A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra
Апстракт
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 (mu)A+nu(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.
Кључне речи:
uncertainty interpretation / LBIFS-IBA approach / Japanese candlestick modeling / interpolative Boolean algebra / IFS-interpretational triangle / generalization of intuitionistic fuzzy setsИзвор:
Mathematics, 2021, 9, 17Издавач:
- MDPI, Basel
DOI: 10.3390/math9172115
ISSN: 2227-7390
WoS: 000694412800001
Scopus: 2-s2.0-85114244463
Институција/група
Fakultet organizacionih naukaTY - JOUR AU - Milošević, Pavle AU - Petrović, Bratislav AU - Dragović, Ivana PY - 2021 UR - https://rfos.fon.bg.ac.rs/handle/123456789/2151 AB - 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 (mu)A+nu(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. PB - MDPI, Basel T2 - Mathematics T1 - A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra IS - 17 VL - 9 DO - 10.3390/math9172115 UR - conv_2551 ER -
@article{ author = "Milošević, Pavle and Petrović, Bratislav and Dragović, Ivana", year = "2021", 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 (mu)A+nu(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.", publisher = "MDPI, Basel", journal = "Mathematics", title = "A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra", number = "17", volume = "9", doi = "10.3390/math9172115", url = "conv_2551" }
Milošević, P., Petrović, B.,& Dragović, I.. (2021). A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra. in Mathematics MDPI, Basel., 9(17). https://doi.org/10.3390/math9172115 conv_2551
Milošević P, Petrović B, Dragović I. A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra. in Mathematics. 2021;9(17). doi:10.3390/math9172115 conv_2551 .
Milošević, Pavle, Petrović, Bratislav, Dragović, Ivana, "A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra" in Mathematics, 9, no. 17 (2021), https://doi.org/10.3390/math9172115 ., conv_2551 .