Hesitant intuitionistic fuzzy ideals of $\Gamma$-semirings

Debabrata Mandal

EN

Hesitant intuitionistic fuzzy ideals of $\Gamma$-semirings

Abstract

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.

Keywords

Hesitant,intuitionistic,ideal,cartesian product,intersec- tion,regular

References

[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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Debabrata Mandal ^*
India

Publication Date

May 30, 2020

Submission Date

April 27, 2019

Acceptance Date

May 1, 2020

Published in Issue

Year 2020 Volume: 9 Number: 1

IZ

https://izlik.org/JA88LN63LT

APA

Mandal, D. (2020). Hesitant intuitionistic fuzzy ideals of $\Gamma$-semirings. Journal of New Results in Science, 9(1), 44-52. https://izlik.org/JA88LN63LT

AMA

1.Mandal D. Hesitant intuitionistic fuzzy ideals of $\Gamma$-semirings. JNRS. 2020;9(1):44-52. https://izlik.org/JA88LN63LT

Chicago

Mandal, Debabrata. 2020. “Hesitant Intuitionistic Fuzzy Ideals of $\Gamma$-Semirings”. Journal of New Results in Science 9 (1): 44-52. https://izlik.org/JA88LN63LT.

EndNote

Mandal D (May 1, 2020) Hesitant intuitionistic fuzzy ideals of $\Gamma$-semirings. Journal of New Results in Science 9 1 44–52.

IEEE

[1]D. Mandal, “Hesitant intuitionistic fuzzy ideals of $\Gamma$-semirings”, JNRS, vol. 9, no. 1, pp. 44–52, May 2020, [Online]. Available: https://izlik.org/JA88LN63LT

ISNAD

Mandal, Debabrata. “Hesitant Intuitionistic Fuzzy Ideals of $\Gamma$-Semirings”. Journal of New Results in Science 9/1 (May 1, 2020): 44-52. https://izlik.org/JA88LN63LT.

JAMA

1.Mandal D. Hesitant intuitionistic fuzzy ideals of $\Gamma$-semirings. JNRS. 2020;9:44–52.

MLA

Mandal, Debabrata. “Hesitant Intuitionistic Fuzzy Ideals of $\Gamma$-Semirings”. Journal of New Results in Science, vol. 9, no. 1, May 2020, pp. 44-52, https://izlik.org/JA88LN63LT.

Vancouver

1.Debabrata Mandal. Hesitant intuitionistic fuzzy ideals of $\Gamma$-semirings. JNRS [Internet]. 2020 May 1;9(1):44-52. Available from: https://izlik.org/JA88LN63LT