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INTERVAL-VALUED FUZZY GENERALIZED BI-IDEALS OF A SEMIGROUP

Lee, Keon-Chang;Kang, Hee-Won;Hur, Kul

  • Received : 2011.10.11
  • Accepted : 2011.10.26
  • Published : 2011.12.25

Abstract

We introduce the concept of an interval-valued fuzzy generalized bi-ideal of a semigroup, which is an extension of the concept of an interval-valued fuzzy bi-ideal (and of a noninterval-valued fuzzy bi-ideal and a noninterval-valued fuzzy ideal of a semi-group), and characterize regular semigroups, and both intraregular and left quasiregular semigroup in terms of interval-valued fuzzy generalized bi-ideals.

Keywords

interval-valued fuzzy set;interval-valued fuzzy ideal;interval-valued fuzzy bi-ideal;interval-valued fuzzy generalized bi-ideal

References

  1. R. Biswas, Rosenfeld's fuzzy subgroups with interval-values membership func- tions, Fuzzy Sets and Systems 63 (1995), 87-90.
  2. J. Calais, Semi-groups quasi-invariants, C.R.AcAd. Sci.Paris 252(1961), 2357- 2359.
  3. Minseok Cheong and K. Hur, Interval-valued fuzzy ideals and bi-ideals of a semi- group, To be sunmitted.
  4. J. Y. Choi, S. R. Kim and K. Hur, Interval-valued smooth topological spaces, Honam Math. J. 32(4) (2010), 711-738. https://doi.org/10.5831/HMJ.2010.32.4.711
  5. K. Hur, J. G. Lee and J. Y. Choi, Interval-valued fuzzy relations, J. Korean Institute of Intelligent Systems, 19(3) (2009), 425-431. https://doi.org/10.5391/JKIIS.2009.19.3.425
  6. M. B. Gorzalczany, A method of inference in approximate reeasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems 21 (1987), 1-17. https://doi.org/10.1016/0165-0114(87)90148-5
  7. H. W. Kang and K. Hur, Intuitionistic fuzzy ideals and bi-ideals, Honam Math. J. 26(3) (2004), 309-330.
  8. H. W. Kang and K. Hur, Interval-valued fuzzy subgroups and rings, Honam Math. J. 32(4) (2010), 593- 617. https://doi.org/10.5831/HMJ.2010.32.4.593
  9. S. Lajos, On generalized bi-ideals in semigroups, Coll. Math. Soc, Janos Bilyai, 20, Algebraic Theory of Semigroups (G. Ponak, Ed.), North-Holland (1979), 335-340.
  10. T. K. Monda and S. K. Samanta, Topology of interval-valued fuzzy sets, Indian J. Pure Appl. Math. 30 no. 1 (1999), 23-38.
  11. M. K. Roy and R. Biswas, Interval-valued fuzzy relations and Sanchez's approach for medical diagnosis, Fuzzy Sets and Systems 47 (1992), 35-38. https://doi.org/10.1016/0165-0114(92)90057-B
  12. L. A. Zadeh, Fuzzy sets, Inform. and Central 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  13. L. A. Zadeh, The concept of a linguistic variable and its application to approximate reason- ing I, Inform. Sci. 8 (1975), 199-249. https://doi.org/10.1016/0020-0255(75)90036-5

Cited by

  1. Lattices of Interval-Valued Fuzzy Subgroups vol.14, pp.2, 2014, https://doi.org/10.5391/IJFIS.2014.14.2.154
  2. Interval-Valued Fuzzy Congruences on a Semigroup vol.13, pp.3, 2013, https://doi.org/10.5391/IJFIS.2013.13.3.231
  3. Ω-INTERVAL-VALUED FUZZY SUBSEMIGROUPS IN A SEMIGROUP vol.37, pp.1, 2015, https://doi.org/10.5831/HMJ.2015.37.1.29
  4. INTERVAL-VALUED FUZZY SUBGROUPS vol.35, pp.4, 2013, https://doi.org/10.5831/HMJ.2013.35.4.565
  5. INTERVAL-VALUED FUZZY GROUP CONGRUENCES vol.38, pp.2, 2016, https://doi.org/10.5831/HMJ.2016.38.2.403
  6. INTERVAL-VALUED FUZZY SUBGROUPS AND LEVEL SUBGROUPS vol.35, pp.3, 2013, https://doi.org/10.5831/HMJ.2013.35.3.525

Acknowledgement

Supported by : Wonkwang University