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A novel new correlation measure for cubic Pythagorean fuzzy sets related to structures of $KU$-ideals on $KU$-algebras

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In this paper, the concepts of cubic Pythagorean $KU$-ideals are introduced and several properties are investigated. Also, relations between cubic Pythagorean $KU$-ideals and cubic Pythagorean ideals are given. The pre-image of cubic Pythagorean $KU$-ideals under homomorphism of $KU$-algebras are defined and how the pre-image of cubic Pythagorean $KU$-ideals under homomorphism of $KU$-algebras become cubic Pythagorean $KU$-ideal are studied. Moreover, the Cartesian product of cubic Pythagorean $KU$-ideals in Cartesian product $KU$-algebras is given. Finally, novel new correlation coefficient between two cubic Pythagorean fuzzy sets are also studied.

Abstract

In this paper, the concepts of cubic Pythagorean $KU$-ideals are introduced and several properties are investigated. Also, relations between cubic Pythagorean $KU$-ideals and cubic Pythagorean ideals are given. The pre-image of cubic Pythagorean $KU$-ideals under homomorphism of $KU$-algebras are defined and how the pre-image of cubic Pythagorean $KU$-ideals under homomorphism of $KU$-algebras become cubic Pythagorean $KU$-ideal are studied. Moreover, the Cartesian product of cubic Pythagorean $KU$-ideals in Cartesian product $KU$-algebras is given. Finally, novel new correlation coefficient between two cubic Pythagorean fuzzy sets are also studied.

참고문헌 (31)

  1. K. Is´eki, "On BCI-algebras", Mathematics Seminar Notes, 8(1), pp.125~130 (1980)
  2. K. Is´eki, "An introduction to the theory of BCK-algebras", Mathematica Japonica, 23(1), pp.1~26 (1978)
  3. K. Is´eki, "Ideal theory of BCK-algebras", Mathematica Japonica, 21(4), pp.351~366 (1976)
  4. C. Prabpayak, "On ideals and congruence in KU-algebras", Scientia Magna international book series, 5(1), pp.54~57 (2009)
  5. C. Prabpayak, "On isomorphisms of KU-algebras", Scientia Magna international book series, 5(3), pp.25~31 (2009)
  6. L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
  7. O. G. Xi, "Fuzzy BCK-algebras", Math. Japon, 36(5), pp.935~942 (1991)
  8. K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20, pp.87~96 (1986)
  9. T. Gerstenkorn, "Correlation of intuitionistic fuzzy sets", Fuzzy sets Systems, 44, pp.39~43 (1991)
  10. Samy M. Mostafa, "Interval-valued fuzzy KU-ideals in KU-algebras", International Mathematical Forum, 6(64), pp.3151~3159 (2011)
  11. Samy M. Mostafa, "Intuitionistic fuzzy KUideals in KU-algebras", Int. J. of Mathematical Sciences and Applications, 1(3), pp.1379~1384 (2011)
  12. Naveed Yaqoob, "Cubic KU-Ideals of KU-algebras", International Scholarly Research Network ISRN Algebra, 2012, pp.19~ (2012)
  13. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning. I", Inform. Sci, 8, pp.199~249 (1975)
  14. Samy M. Mostafa, "Fuzzy ideals of KU-Algebras", Int. Math. Forum, 6(63), pp.3139~3149 (2011)
  15. Samy M. Mostafa, "Anti-fuzzy KU-ideals of KU-algebras", International Journal of Algebra and Statistics, 1(1), pp.92~99 (2012)
  16. Moin A. Ansari, "Intersection soft ideals and their quotients on KU-algebras", AIMS Mathematics, 6(11), pp.12077~12084 (2021)
  17. Ali N. A. Koam, "On an extension of KU-algebras", AIMS Math, 6, pp.1249~1257 (2021)
  18. 정영배, "A novel extension of cubic sets and its applications in $BCK", BCI$-algebras, 2017, pp.14(5), 475~486[DOI]
  19. Y. B. Jun, "Cubic sets", Ann. Fuzzy Math. Inform, 4(1), pp.83~98 (2012)
  20. Pythagorean membership grades in multi-criteria decision making, "R. R. Yager", Machine Intelligence Institute, Iona College, ~, pp.Technical report MII-3301 (2013)
  21. S. S. Ahn, "The (2, 3)-fuzzy set and its application in BCK-algebras and BCI-algebras", J. Math. Computer Sci, 27, pp.118~130 (2022)
  22. 전영배, "The (m, n)-fuzzy set and its application in BCK-algebras", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 24(1), pp.17~29 (2022), 기초자연과학연구소[DOI]
  23. T. M. Al-shami, "SR-fuzzy sets and their weighted aggregated operators in application to decision-making", Hindawi Journal of Function Spaces, 2022, pp.14~ (2022)
  24. Y. A. Salih, "CR-fuzzy sets and their applications", J. Math. Computer Sci, 28, pp.171~181 (2023)
  25. H. Z. T Ibrahim, "(3, 2)-fuzzy sets and their applications to topology and computational optimal choices", Intelligence and Neuroscience, 2021, pp.14~ (2021)
  26. 백종일, "Correlation coefficient between intuitionistic single-valued neutrosophic sets and its applications", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 23(1), pp.81~105 (2022), 기초자연과학연구소[DOI]
  27. D. A. Chiang, "Correlation of fuzzy sets", Fuzzy Sets and Systems, 102, pp.221~226 (1999)
  28. A. Bryniarska, "The n-Pythagorean fuzzy sets", Symmetry, 12, pp.1772~ (2020)
  29. T. Senapati, "Fermatean fuzzy sets", Journal of Ambient Intelligence and Humanized Computing, 11, pp.663~674 (2020)
  30. K. Atanassov, "Interval-valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 31, pp.343~349 (1989)
  31. Z. S. Xu, "On correlation measures of intuitionistic fuzzy sets", Lect. Notes Comput. Sci, 4224, pp.16~24 (2006)

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