$(3,3,\sqrt[3]{\cdot})$-picture fuzzy structures of a $BCC$-ideal of $BCC$-algebras and their correlation coefficient
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A picture fuzzy set is one of the generalizations of Atanassove's (IFSs) fuzzy set. Under this environment, in this manuscript, we familiarize a new type of extensions of fuzzy sets called cubic root fuzzy sets (briefly, $\sqrt[3]{\cdot}$-Fuzzy sets) and Fermatean fuzzy sets to contrast $(3,3,\sqrt[3]{\cdot})$-picture sets. We introduce the notion of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals of $BCC$-algebras. After then, we study the homomorphic image and inverse image of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals under homomorphism of $BCC$-algebras. Moreover, the Cartesian product of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals of $BCC$-algebras is given. Finally, we introduce the concept of correlation for $(3,3,\sqrt[3]{\cdot})$-picture fuzzy sets, which is a new extension of the correlation of Atanassove's IFSs and investigated several properties.
Abstract
A picture fuzzy set is one of the generalizations of Atanassove's (IFSs) fuzzy set. Under this environment, in this manuscript, we familiarize a new type of extensions of fuzzy sets called cubic root fuzzy sets (briefly, $\sqrt[3]{\cdot}$-Fuzzy sets) and Fermatean fuzzy sets to contrast $(3,3,\sqrt[3]{\cdot})$-picture sets. We introduce the notion of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals of $BCC$-algebras. After then, we study the homomorphic image and inverse image of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals under homomorphism of $BCC$-algebras. Moreover, the Cartesian product of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals of $BCC$-algebras is given. Finally, we introduce the concept of correlation for $(3,3,\sqrt[3]{\cdot})$-picture fuzzy sets, which is a new extension of the correlation of Atanassove's IFSs and investigated several properties.
참고문헌 (33)
- K. Is´eki, "An introduction to the theory of BCK-algebras", Mathematica Japonica, 23(1), pp.1~26 (1978)
- K. Is´eki, "On BCI-algebras", Mathematics Seminar Notes, 8(1), pp.125~130 (1980)
- A. Wron ′ski, "BCK-algebras do not form a variety", Math. Japon, 28(2), pp.211~213 (1983)
- Y. Komori, "The class of BCC-algebras is not a variety", Math. Japonica, 29, pp.391~394 (1984)
- W. A. Dudek, "A new characterization of ideals in BCC-algebras", Novi Sad J. Math, 29, pp.139~145 (1999)
- W. A. Dudek, "On ideals and congruences in BCC-algebras", Czechoslovak Mathematical Journal, 48(1), pp.21~29 (1998)
- L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
- K, Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20, pp.87~96 (1986)
- O. G. Xi, "Fuzzy BCK-algebra", Math. Japon, 36, pp.935~942 (1991)
- W. A. Dudek, "Normalizations of fuzzy BCC-ideals in BCC-algebras", Math. Moravica, 3, pp.17~24 (1999)
- B. C. Cuong, "Picture fuzzy sets", Journal of Computer Science and Cybernetics, 30, pp.409~420 (2014)
- B. C. Cuong, "Picture fuzzy sets ˆOC¸ ˆo a new concept for computational intelligence problems", Proceedings of the Third World Congress on Information and Communication Technologies WIICT (2013)
- B. C. Cuong, "Some fuzzy logic operators for picture fuzzy sets", Seventh International Conference on Knowledge and Systems Engineering (2015)
- R. R. Yager, "Pythagorean fuzzy subsets", Proceedings of the 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA, 2013, 57~61[DOI]
- Pythagorean membership grades in multi-criteria decision making, "R. R. Yager", Machine Intelligence Institute, Iona College, ~, pp.Technical report MII-3301 (2013)
- H. Z. Ibrahim, "(3, 2)-Fuzzy sets and their applications to topology and computational optimal choices", Intelligence and Neuroscience, 2021, pp.14~ (2021)
- T. Senapati, "Fermatean fuzzy sets", Journal of Ambient Intelligence and Humanized Computing, 11, pp.663~674 (2020)
- T. Gerstenkorn, "Correlation of intuitionistic fuzzy sets", Fuzzy sets Systems, 44, pp.39~43 (1991)
- H. Bustince, "Correlation of interval-valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 74, pp.237~244 (1995)
- D. H. Hong, "Correlation of intuitionistic fuzzy sets in probability spaces", Fuzzy Sets and Systems, 75, pp.77~81 (1995)
- D. H. Hong, "A note on correlation of interval-valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 95, pp.113~117 (1998)
- W. L. Hung, "Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets", Int. J. Uncertain Fuzziness Knowl Based Syst, 9, pp.509~516 (2001)
- W. L. Hung, "Correlation of intuitionistic fuzzy sets by centroid method", Inform. Sci, 144, pp.219~225 (2002)
- H. B. Mitchell, "A correlation coefficient for intuitionistic fuzzy sets", Int. J. Intell. Syst, 19, pp.483~490 (2004)
- W. A. Dudek, "On proper BCC-algebras", Bull. Inst. Math. Academia Sinica, 20, pp.137~150 (1992)
- W. A. Dudek, "Fuzzy BCC-ideals in BCC-algebras", Math. Montisnigri, 10, pp.21~30 (1999)
- A. Bryniarska, "The n-Pythagorean fuzzy sets", Symmetry, 12, pp.1772~ (2020)
- S. S. Ahn, "The (2, 3)-fuzzy set and its application in BCK-algebras and BCI-algebras", J. Math. Computer Sci, 2, pp.118~130 (2022)
- Y. B. Jun, "The (m; n)-fuzzy set and its application in BCK-algebras", Anna. Fuzzy Math. Inform, 24(1), pp.17~29 (2022)
- T. M. Al-shami, "SR-fuzzy sets and their weighted aggregated operators in application to decision-making", Journal of Function Spaces, 2022, pp.14~ (2022)
- Y. A. Salih, "CR-fuzzy sets and their applications", J. Math. Computer Sci, 28, pp.171~181 (2023)
- D. A. Chiang, "Correlation of fuzzy sets", Fuzzy Sets Systems, 102, pp.221~226 (1999)
- Z. S. Xu, "On correlation measures of intuitionistic fuzzy sets", Lect. Notes Comput. Sci, 4224, pp.15~24 (2006)