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Year 2020, Issue: 31, 48 - 54, 30.06.2020

Abstract

References

  • H.S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40 (1934) 914 - 920.
  • M. Henriksen, Ideals in semiringss with commutative addition, Amer. Math. Soc. Notices, 6(1958) 321.
  • K. Iizuka, On the Jacobson radical of semiring, Tohoku Math.J., 11(2) (1959)409-421
  • D.R.La Torre, On h-ideals and k-ideals in hemirings, Publ. Math. Debrecen 12(1965), 219-226.
  • M.M.K.Rao, \Gamma-semirings-1, Southeast Asian Bull. of Math., 19(1995), 49-54
  • L.A.Zadeh, Fuzzy Sets, Information and Control, 8(1965), 338 - 353.
  • K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1983) 87 - 96.
  • P. Sarkar and S. Kar, Interval-Valued Primary Fuzzy Ideal of Non-commutative Semigroup, In- ternational Journal of Applied and Computational Mathematics, 3(4) (2017), 3945 - 3960.
  • J. Casasnovas andF Rossello, Scalar and fuzzy cardinalities of crisp and fuzzy multisets, Interna- tional Journal of Intellegent Systems, Vol. 24, Issue 6, (2009), 587 - 623.
  • V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529 - 539.
  • Y. B. Jun and S. Z. Song, Hesitant fuzzy set theory applied to lters in MTL-algebras, Honam Math. J. 36 (2014), no. 4, 813 - 830.
  • R. M. Rodriguez, Luis Martinez and Francisco Herrera, Hesitant fuzzy linguistic term sets for decision making, IEEE Trans. Fuzzy Syst. 20, no. 1, (2012) 109 - 119.
  • V. Torra and Y. Narukawa, On hesitant fuzzy sets and decision, in: The 18th IEEE International Conference on Fuzzy Systems, pp. 1378 - 1382, Jeju Island, Korea, 2009.
  • G. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute decision making, Knowledge-Based Systems, 31 (2012), 176 - 182.
  • M. Xia and Z. S. Xu, Hesitant fuzzy information aggregation in decision making, Internat. J. Approx. Reason., 52 (2011), no. 3, 395 - 407.
  • M. Xia, Z. S. Xu, and N. Chen, Some hesitant fuzzy aggregation operators with their application in group decision making, Group Decision Negotiation, 22 (2013), 259 - 279.
  • Z. S. Xu and M. Xia, Distance and similarity measures for hesitant fuzzy sets, Inform. Sci., 181 (2011), no. 11, 2128 - 2138.
  • B. Zhu, Z. Xu, and M. Xia, Hesitant fuzzy geometric Bonferroni means, Inform. Sci., 205 (2012), 72 - 85.
  • Y. B. Jun and M. Khan, Hesitant fuzzy bi-ideals in semigroups, Commun. Korean Math. Soc. 30 (2015), No. 3, 143 - 154
  • T.K. Dutta, S.K. Sardar, On matrix \Gamma-semirings, Far East J. Math. Sci.,Vol 7, No. 1 (2002), 17 - 31.

Hesitant Fuzzy h-ideals of \Gamma-hemirings

Year 2020, Issue: 31, 48 - 54, 30.06.2020

Abstract

The purpose of this paper is to introduce and study hesitant fuzzy h-
ideals ( h-bi-ideals, h-quasi-ideals) of a \Gamma-hemiring. We investigate several properties of
these ideals. We show that hesitant fuzzy ideals are closed under intersection, carte-
sian product and composition. We also obtain some inter-relations between these
ideals and characterizations of h-regular \Gamma-hemiring.
-

References

  • H.S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40 (1934) 914 - 920.
  • M. Henriksen, Ideals in semiringss with commutative addition, Amer. Math. Soc. Notices, 6(1958) 321.
  • K. Iizuka, On the Jacobson radical of semiring, Tohoku Math.J., 11(2) (1959)409-421
  • D.R.La Torre, On h-ideals and k-ideals in hemirings, Publ. Math. Debrecen 12(1965), 219-226.
  • M.M.K.Rao, \Gamma-semirings-1, Southeast Asian Bull. of Math., 19(1995), 49-54
  • L.A.Zadeh, Fuzzy Sets, Information and Control, 8(1965), 338 - 353.
  • K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1983) 87 - 96.
  • P. Sarkar and S. Kar, Interval-Valued Primary Fuzzy Ideal of Non-commutative Semigroup, In- ternational Journal of Applied and Computational Mathematics, 3(4) (2017), 3945 - 3960.
  • J. Casasnovas andF Rossello, Scalar and fuzzy cardinalities of crisp and fuzzy multisets, Interna- tional Journal of Intellegent Systems, Vol. 24, Issue 6, (2009), 587 - 623.
  • V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529 - 539.
  • Y. B. Jun and S. Z. Song, Hesitant fuzzy set theory applied to lters in MTL-algebras, Honam Math. J. 36 (2014), no. 4, 813 - 830.
  • R. M. Rodriguez, Luis Martinez and Francisco Herrera, Hesitant fuzzy linguistic term sets for decision making, IEEE Trans. Fuzzy Syst. 20, no. 1, (2012) 109 - 119.
  • V. Torra and Y. Narukawa, On hesitant fuzzy sets and decision, in: The 18th IEEE International Conference on Fuzzy Systems, pp. 1378 - 1382, Jeju Island, Korea, 2009.
  • G. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute decision making, Knowledge-Based Systems, 31 (2012), 176 - 182.
  • M. Xia and Z. S. Xu, Hesitant fuzzy information aggregation in decision making, Internat. J. Approx. Reason., 52 (2011), no. 3, 395 - 407.
  • M. Xia, Z. S. Xu, and N. Chen, Some hesitant fuzzy aggregation operators with their application in group decision making, Group Decision Negotiation, 22 (2013), 259 - 279.
  • Z. S. Xu and M. Xia, Distance and similarity measures for hesitant fuzzy sets, Inform. Sci., 181 (2011), no. 11, 2128 - 2138.
  • B. Zhu, Z. Xu, and M. Xia, Hesitant fuzzy geometric Bonferroni means, Inform. Sci., 205 (2012), 72 - 85.
  • Y. B. Jun and M. Khan, Hesitant fuzzy bi-ideals in semigroups, Commun. Korean Math. Soc. 30 (2015), No. 3, 143 - 154
  • T.K. Dutta, S.K. Sardar, On matrix \Gamma-semirings, Far East J. Math. Sci.,Vol 7, No. 1 (2002), 17 - 31.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Debabrata Mandal This is me

Publication Date June 30, 2020
Submission Date April 27, 2019
Published in Issue Year 2020 Issue: 31

Cite

APA Mandal, D. (2020). Hesitant Fuzzy h-ideals of \Gamma-hemirings. Journal of New Theory(31), 48-54.
AMA Mandal D. Hesitant Fuzzy h-ideals of \Gamma-hemirings. JNT. June 2020;(31):48-54.
Chicago Mandal, Debabrata. “Hesitant Fuzzy H-Ideals of \Gamma-Hemirings”. Journal of New Theory, no. 31 (June 2020): 48-54.
EndNote Mandal D (June 1, 2020) Hesitant Fuzzy h-ideals of \Gamma-hemirings. Journal of New Theory 31 48–54.
IEEE D. Mandal, “Hesitant Fuzzy h-ideals of \Gamma-hemirings”, JNT, no. 31, pp. 48–54, June 2020.
ISNAD Mandal, Debabrata. “Hesitant Fuzzy H-Ideals of \Gamma-Hemirings”. Journal of New Theory 31 (June 2020), 48-54.
JAMA Mandal D. Hesitant Fuzzy h-ideals of \Gamma-hemirings. JNT. 2020;:48–54.
MLA Mandal, Debabrata. “Hesitant Fuzzy H-Ideals of \Gamma-Hemirings”. Journal of New Theory, no. 31, 2020, pp. 48-54.
Vancouver Mandal D. Hesitant Fuzzy h-ideals of \Gamma-hemirings. JNT. 2020(31):48-54.


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