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On the characterisation of anti-fuzzy multigroups

P. A. Ejegwa|J. A. Awolola|J. M. Agbetayo|I. M. Adamu
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2021.06|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제21권 제3호|pp. 307-318|DOI 10.30948/afmi.2021.21.3.307

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참고문헌

키워드

Fuzzy subgroupsFuzzy subsetsFuzzy multisetsFuzzy multigroupsAnti-fuzzy multigroups

초록

The concept of fuzzy multigroups applies fuzzy multisets to the theory of groups. Fuzzy multigroup is the study of group structures in fuzzy multiset context. This article introduces anti-fuzzy multigroup and characterises certain of its properties. It is established that a fuzzy multiset with group as its underlying set is a fuzzy multigroup if and only if the complement of the fuzzy multiset is an anti-fuzzy multigroup. Certain results that discuss the alpha-cuts of anti-fuzzy multigroups are explored.

Abstract

The concept of fuzzy multigroups applies fuzzy multisets to the theory of groups. Fuzzy multigroup is the study of group structures in fuzzy multiset context. This article introduces anti-fuzzy multigroup and characterises certain of its properties. It is established that a fuzzy multiset with group as its underlying set is a fuzzy multigroup if and only if the complement of the fuzzy multiset is an anti-fuzzy multigroup. Certain results that discuss the alpha-cuts of anti-fuzzy multigroups are explored.

참고문헌 (42)

  1. L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
  2. A. Rosenfeld, "Fuzzy subgroups", J. Math. Anal. Appl, 35, pp.512~517 (1971)
  3. P. A. Ejegwa, "Frattini fuzzy subgroups of fuzzy groups", J. Univ. Math, 2(2), pp.175~182 (2019)
  4. J. M. Mordeson, "Fuzzy group theory" (2005), Springer-Verlag
  5. B. Seselja, "A note on fuzzy groups", Yugoslav J. Operation Res, 7(1), pp.49~54 (1997)
  6. R. Biswas, "Fuzzy subgroups and anti fuzzy subgroups", Fuzzy Set Syst, 35, pp.121~124 (1990)
  7. S. K. Majumdar, "On some properties of anti fuzzy subgroups", J. Mech. Cont. Math. Sci, 3(2), pp.337~343 (2008)
  8. B. O. Onasanya, "Some reviews in fuzzy subgroups and anti fuzzy subgroups", Ann. Fuzzy Math. Inform, 11(3), pp.377~385 (2016)
  9. B. O. Onasanya, "Review of some anti fuzzy properties of some fuzzy subgroups", Ann. Fuzzy Math. Inform, 11(6), pp.899~904 (2016)
  10. S. Zhengwei, "The anti-fuzzy subgroup of group", J. Liaoning Normal University(Natural Science), 18(2), pp.99~101 (1995)
  11. S. Gayen, "On a generalized notion of anti-fuzzy subgroup and some characterizations", Int. J. Eng. Advanced Tech, 8(3), pp.385~390 (2019)
  12. K. Atanassov, "Intuituinistic fuzzy sets", Fuzzy Set Syst, 20, pp.87~96 (1986)
  13. D. Y. Li, "The intuitionistic anti-fuzzy subgroup in group", Fuzzy Inf. Eng., ASC 54, pp.145~151 (2009), Springer-Verlag
  14. M. Lin, "Anti-intuitionistic fuzzy subgroup and its homomorphic image", Int. J. Applied Math. Stat, 43(13), pp.387~391 (2013)
  15. Dilshad Alghazzawi, "Algebraic Characteristics of Anti-Intuitionistic Fuzzy Subgroups Over a Certain Averaging Operator", IEEE Access, 8, pp.205014~205021 (2020), Institute of Electrical and Electronics Engineers (IEEE)[DOI]
  16. R. Muthuraj, "A study on intuitionistic multi-anti fuzzy subgroups", Applied Math. Sci, 1(2), pp.35~52 (2014)
  17. M. O. Massa’deh, "Structure properties of an intuitionistic anti-fuzzy M-subgroups", J. Applied Comput. Sci. Math, 7(14), pp.42~44 (2013)
  18. R. R. Yager, "On the theory of bags", Int. J. General Syst, 13, pp.23~37 (1986)
  19. D. Singh, "An overview of the applications of multisets", Novi Sad J. Math, 37(2), pp.73~92 (2007)
  20. R. Biswas, "An application of Yager’s bag theory in multicriteria based decision-making problems", Int. J. Intell. Syst, 14, pp.1231~1238 (1999)
  21. P. A. Ejegwa, "Correspondence between fuzzy multisets and sequences", Global J. Sci. Frontier Research : Math. Deci. Sci, 14(7), pp.61~66 (2014)
  22. S. Miyamoto, "Basic operations of fuzzy multisets", J. Japan Soc. Fuzzy Theory Syst, 8(4), pp.639~645 (1996)
  23. S. Miyamoto, "multiset model and methods for nonlinear document clustering for information retrieval", pp.273~283 (2004), Springer-Verlag
  24. K. Mizutani, "Algorithms of nonlinear document clustering based on fuzzy multiset model", Int. J. Intell. Syst, 23, pp.176~198 (2008)
  25. A. Syropoulos, "On generalized fuzzy multisets and their use in computation", Iranian J. Fuzzy Syst, 9(2), pp.113~125 (2012)
  26. P. A. Ejegwa, "Synopsis of the notions of multisets and fuzzy multisets", Ann. Commun. Math, 2(2), pp.101~120 (2019)
  27. T. K. Shinoj, "On some algebraic structures of fuzzy multisets", Ann. Fuzzy Math. Inform, 9(1), pp.77~90 (2015)
  28. P. A. Ejegwa, "Homomorphism of fuzzy multigroups and some of its properties", Appl. Appl. Math, 13(1), pp.114~129 (2018)
  29. P. A. Ejegwa, "On fuzzy multigroups and fuzzy submultigroups", J. Fuzzy Math, 26(3), pp.641~654 (2018)
  30. P. A. Ejegwa, "On abelian fuzzy multigroups", J. Fuzzy Math, 26(3), pp.655~668 (2018)
  31. A. Baby, "On abelian fuzzy multigroups and order of fuzzy multigroups", J. New Theory, 5(2), pp.80~93 (2015)
  32. P. A. Ejegwa, "On normal fuzzy submultigroups of a fuzzy multigroup", Theory Appl. Math. Comp. Sci, 8(1), pp.64~80 (2018)
  33. P. A. Ejegwa, "Direct product of fuzzy multigroups", J. New Theory, 28, pp.62~73 (2019)
  34. P. A. Ejegwa, "On the concept of fuzzy comultisets and its properties", TWMS J. Appl. Eng. Math, 10(4), pp.918~929 (2020)
  35. P. A. Ejegwa, "Some characterizations of fuzzy comultisets and quotient fuzzy multigroups", Ratio Mathematica, 38, pp.237~259 (2020)
  36. P. A. Ejegwa, "On generalized direct product of fuzzy multigroups", Ann. Commun. Math, 3(1), pp.35~45 (2020)
  37. P. A. Ejegwa, "Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures", pp.34~62 (2020), IGI Global Publisher
  38. P. A. Ejegwa, "On commutators of fuzzy multigroups", Earthline J. Math. Sci, 4(2), pp.189~210 (2020)
  39. P. A. Ejegwa, "Characteristic and Frattini fuzzy submultigroups of fuzzy multigroups", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 19(2), pp.139~155 (2020), 기초자연과학연구소[DOI]
  40. P. A. Ejegwa, "Some properties of alpha-cuts of fuzzy multigroups", J. Fuzzy Math, 28(1), pp.201~222 (2020)
  41. P. A. Ejegwa, "On alpha-cuts homomorphism of fuzzy multigroups", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 19(1), pp.73~87 (2020), 기초자연과학연구소[DOI]
  42. A. M. Ibrahim, "Fuzzification of some results on multigroups", J. Nigerian Assoc. Math. Physics, 32, pp.119~124 (2015)

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