본문 바로가기
KERD
논문KCI 등재

Cubic bipolar structures of $BCC$-ideal on $BCC$-algebras

이정곤|허걸|S. M. Mostafa
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2020.08|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제20권 제1호|pp. 89-103|DOI 10.30948/afmi.2020.20.1.89

0

조회

0

다운로드

1

인용

0

참고문헌

키워드

$BCC$-algebraFuzzy $BCC$-ideal(Cubic bipolar) $BCC$-idealCartesian product of cubic bipolar $BCC$-ideal

초록

In this paper, we introduce the concept of cubic bipolar $BCC$-ideal and investigate several properties. Also, we give relations between cubic bipolar $BCC$-ideal and cubic bipolar $BCC$-ideal. The image and the pre-image of cubic bipolar $BCC$-ideal in $BCC$-algebras are defined and how the image and the pre-image of cubic bipolar $BCC$-ideal in $BCC$-algebras become cubic bipolar $BCC$-ideal are studied. Moreover, the Cartesian product of cubic bipolar $BCC$-ideal in Cartesian product $BCC$-algebras is given.

Abstract

In this paper, we introduce the concept of cubic bipolar $BCC$-ideal and investigate several properties. Also, we give relations between cubic bipolar $BCC$-ideal and cubic bipolar $BCC$-ideal. The image and the pre-image of cubic bipolar $BCC$-ideal in $BCC$-algebras are defined and how the image and the pre-image of cubic bipolar $BCC$-ideal in $BCC$-algebras become cubic bipolar $BCC$-ideal are studied. Moreover, the Cartesian product of cubic bipolar $BCC$-ideal in Cartesian product $BCC$-algebras is given.

참고문헌 (26)

  1. K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20, pp.87~96 (1986)
  2. W. A. Dudek, "On proper BCC-algebras", Bull. Inst. Math. Academia Sinica, 20, pp.137~150 (1992)
  3. W. A. Dudek, "A new characterization of ideals in BCC-algebras", Novi Sad J. Math, 29, pp.139~145 (1999)
  4. W. A. Dudek, "Fuzzy BCC-ideals in BCC-algebras", Math. Montisnigri, 10, pp.21~30 (1999)
  5. W. A. Dudek, "Normalizations of fuzzy BCC-ideals in BCC-algebras", Math. Moravica, 3, pp.17~24 (1999)
  6. W. A. Dudek, "On ideals and congruences in BCC-algebras", Czechoslovak Math. J, 48(123), pp.21~29 (1998)
  7. M. B. Gorzalczany, "A method of inference in approximate reasoning based on interval-valued fuzzy sets", Fuzzy sets and Systems, 21, pp.1~17 (1987)
  8. K. Iseki, "On BCI-algebras", Mathematics Seminar Notes, 8(1), pp.125~130 (1980)
  9. K. Iseki, "An introduction to the theory of BCK-algebras", Mathematica Japon-ica, 23(1), pp.1~26 (1978)
  10. K. Iseki, "Ideal theory of BCK-algebras", Mathematica Japonica, 21(4), pp.351~366 (1976)
  11. Y. B. Jun, "Cubic subalgebras and ideals of BCK", BCI-algebras, 2010, pp.44(2), 239~250
  12. Young Bae Jun, "Cubic q-ideals of BCI-algebras", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 1(1), pp.25~34 (2011), 기초자연과학연구소
  13. Y. B. Jun, "Cubic structures applied to ideals of BCI-algebras", Computers & Mathematics with Applications, 62(9), pp.3334~3342 (2011)
  14. Y. B. Jun, "Cubic sets", Ann. Fuzzy Math. Inform, 4(1), pp.83~98 (2012)
  15. Y. Komori, "The class of BCC-algebras is not a variety", Math. Japonica, 29, pp.391~394 (1984)
  16. K. J. Lee, "Bipolar fuzzy subalgerbas and bipolar fuzzy ideals of BCK", BCI- algerbas, ~
  17. K. M. Lee, "Bipolar-valued fuzzy sets and their operations", Proc. Int. Conf. on Intelligent Technologies, pp.307~312 (2000)
  18. K. M. Lee, "Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets", J. Fuzzy Logic Intelligent Systems, 14(2), pp.125~129 (2004)
  19. T. K. Mondal, "Topology of interval-valued fuzzy sets", Indian J. Pure Appl. Math, 30(1), pp.133~189 (1999)
  20. X. Ougen, "Fuzzy BCK-algebra", Math. Japon, 36(5), pp.935~942 (1991)
  21. M. Riaz, "bipolar fuzzy ordered weighted geometric aggregation operators and their application using internal and external cubic bipolar fuzzy data", Computational and Applied Mathematics, pp.38~87 (2019)
  22. M. Riaz, "Cubic bipolar fuzzy set with application to multi criteria group decision making", Group Decis Negotiation
  23. T. Senapati, "Cubic intuitionistic structures applied to ideals of BCI-algebras", An St Univ Ovidius Constanta, 25(2), pp.213~232 (2019)
  24. T. Senapati, "Cubic Intuitionistic Implicative Ideals of BCK-Algebras Proceedings of the National Academy of Sciences", India Section A: Physical Sciences (2020)
  25. A. Wronski, "BCK-algebras do not form a variety", Math. Japon, 28(2), pp.211~213 (1983)
  26. L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)

관련 논문AI추천

Interval-valued intuitionistic cubic structures of medial ideals on $BCI$-algebras허걸, 김준희, 이정곤, 정민석, S. M. Mostafa기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2020 · 제19권 제2호Cubic q-ideals of BCI-algebrasChang Su Kim, Jeong Gi Kang, Young Bae Jun기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2011 · 제1권 제1호A novel extension of cubic sets and its applications in $BCK/BCI$-algebras정영배기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제14권 제5호Bipolar fuzzy a-ideals of BCI-algebras이경자, 전영배대한수학회 · 대한수학회논문집2011 · 제26권 제4호(T, S)-bipolar Pythagorean structures of fuzzy medial-ideals허걸, 백종일, 한상현, Abdel Rahman S. Al-Adawy, S. M. Mostafa기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2022 · 제24권 제3호Topology of cubic bipolar structures and its application on Q-algebra허걸, 이정곤, Fatema. F. Kareem, S. M. Mostafa기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2021 · 제21권 제1호

이 간행물의 다른 논문 (6건)

Almost-s-Hurewicz ditopological texture spacesMoiz ud Din Khan, Hafiz Ullahpp. 1-13Applications of interval \textit{t}-norm fuzzy ideals of hemirings with interval valued characteristic functionSanaa Anjum, Tasawar Abbas, Bilal Ahmadpp. 15-27Fuzzy Bernstein Stancu difference operator of rough $I$-core of double sequences with weighted statistical convergence and its applicationsN. Subramanian, Bipan Hazarika, A. Indumathi, A. Esipp. 29-53Compactness in soft $S$-metric spacesVefa Cafarli, Sadi Bayramov, Cigdem Gunduz Araspp. 55-65Inverse domination in bipolar fuzzy graphsMahioub M. Q. Shubatah, Saqr H. AL-Emranypp. 67-77
원문 보기