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INTERVAL-VALUED FUZZY SUBGROUPS AND RINGS

  • Kang, Hee-Won (Dept. of Mathematics Education, Woosuk University) ;
  • Hur, Kul (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
  • Received : 2010.07.26
  • Accepted : 2010.11.03
  • Published : 2010.12.25

Abstract

We introduce the concepts of interval-valued fuzzy sub-groups [resp. normal subgroups, rings and ideals] and investigate some of it's properties.

Keywords

References

  1. K.Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems,20(1986) 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
  2. K.Atanassov and G.Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy sets and Systems 31(1989) 343-349. https://doi.org/10.1016/0165-0114(89)90205-4
  3. Baldev Benerjee and Dhiren Kr.Basnet, Intuitionistic fuzzy subrings and ideals, J.Fuzzy Math 11(1)(2003) 139-155.
  4. R. Biswas, Rosenfeld's fuzzy subgroups with interval-valued membership functions. Fuzzy set and systems 63(1995) 87-90. https://doi.org/10.1016/0165-0114(94)90148-1
  5. D.Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88(1997) 81-89. https://doi.org/10.1016/S0165-0114(96)00076-0
  6. D.Coker and A.Haydar Es, On fuzzy compact ness in intuitionstic fuzzy topological spaces, J.Fuzzy Math. 3(1995) 899-909.
  7. M.B.Gorzalczany, A method of inference in approximate reasoning based on interval-values fuzzy, sets, Fuzzy sets and Systems 21(1987) 1-17. https://doi.org/10.1016/0165-0114(87)90148-5
  8. K.Hur, S.Y.Jang and H.W.Kang, Intuitionistic fuzzy subgroupoids, International Journal of Fuzzy Logic and Intelligent Systems 2(1)(2002) 92-147.
  9. K.Hur, H.W.Kang and H.K.Song, Intuitionistic fuzzy subgroups and subrings. Honam Math.J. 25(1)(2003) 19-41.
  10. K.Hur, J.G.Lee and J.Y.Choi, Interval-valued fuzzy relations. J. Korean Institute of Intelligent systems 19(3)(2009) 425-432. https://doi.org/10.5391/JKIIS.2009.19.3.425
  11. W.J.Liu Fuzzy invaiant subgroups and fuzzy ileds, Fuzzy sets and Systems 8(1982) 133-189. https://doi.org/10.1016/0165-0114(82)90003-3
  12. T.K.mondal and S.K.Samanta, Topology of interval-valued fuzzy sets, Indian J. Pure Appl. Math. 30(1)(1999) 20-38.
  13. L.A.Zadeh, Fuzzy sets, Inform and Control 8(1965) 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  14. L.A.Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inform. Sci 8(1975) 199-249. https://doi.org/10.1016/0020-0255(75)90036-5

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