Hesitant intuitionistic fuzzy ideals of $\Gamma$-semirings

Hesitant intuitionistic fuzzy ideals of $\Gamma$-semirings

In this paper, we have defined hesitant intuitionistic fuzzy ideals, hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals of a $\Gamma$-semiring and obtain some of their related properties. We have discussed some inter-relations between these ideals. We also obtain some characterizations of regular $\Gamma$-semiring.

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  • [1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1983) 87 - 96.
  • [2] T.K. Dutta, S.K. Sardar, On matrix ?-semirings, Far East J. Math.Sci.,Vol 7, No. 1 (2002), 17 - 31.
  • [3] Y. B. Jun and M. Khan, Hesitant fuzzy bi-ideals in semigroups, Commun.Korean Math. Soc. 30 (2015), No. 3, pp. 143 - 154
  • [4] Y. B. Jun and S. Z. Song, Hesitant fuzzy set theory applied to lters inMTL-algebras, Honam Math. J. 36 (2014), no. 4, 813 - 830.
  • [5] M.M.K.Rao, ?-semirings-1, Southeast Asian Bull. of Math., 19(1995)49-54
  • [6] R. M. Rodriguez, Luis Martinez and Francisco Herrera, Hesitant fuzzy lin-guistic term sets for decision making, IEEE Trans. Fuzzy Syst. 20 (2012),no. 1, 109 - 119.
  • [7] A. Rosenfeld, "Fuzzy groups", J. Math. Anal. Appl. 35(1971) 512 - 517
  • [8] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529 - 539.
  • [9] V. Torra and Y. Narukawa, On hesitant fuzzy sets and decision, in: The18th IEEE International Conference on Fuzzy Systems, pp. 1378 - 1382,Jeju Island, Korea, 2009.
  • [10] H.S. Vandiver, Note on a simple type of algebra in which cancellation lawof addition does not hold, Bull. Amer. Math. Soc. 40 (1934) 914 - 920.
  • [11] G. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute decision making, Knowledge-Based Systems 31 (2012), 176- 182.
  • [12] M. Xia and Z. S. Xu, Hesitant fuzzy information aggregation in decisionmaking, Internat. J. Approx. Reason. 52 (2011), no. 3, 395 - 407.
  • [13] M. Xia, Z. S. Xu, and N. Chen, Some hesitant fuzzy aggregation operators with their application in group decision making, Group DecisionNegotiation 22 (2013), 259 - 279.
  • [14] Z. S. Xu and M. Xia, Distance and similarity measures for hesitant fuzzysets, Inform. Sci. 181 (2011), no. 11, 2128 - 2138.
  • [15] B. Zhu, Z. Xu, and M. Xia, Hesitant fuzzy geometric Bonferroni means,Inform. Sci. 205 (2012), 72 - 85.
  • [16] L.A.Zadeh, "Fuzzy Sets", Information and Control, 8(1965)338 - 353.