Hesitant fuzzy hyperideals of ordered semihypergroups

Muhammad Farooq, Muhammad Izhar, Asghar Khan, Kostaq Hila

Abstract


Hesitant fuzzy sets introduced by Torra and Narukawa present a powrerful tool for study of hesitancy in decision making. In this paper, we introduce the notions of hesitant fuzzy product, characteristic hesitant fuzzy set, hesitant fuzzy hyperideals and hesitant fuzzy interior hyperideals of ordered semihypergroups. We characterize regular and intra-regular ordered semihypergroups by the properties of their hesitant fuzzy hyperideals and hesitant fuzzy interior hyperideals. We introduce the notion of hesitant fuzzy simple ordered semihypergroups. Furthermore, some characterizations of hesitant fuzzy simple ordered semihypergroups by means of hesitant fuzzy hyperideals and hesitant fuzzy interior hyperideals are provided.

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References


S.S. Ahn, K.J. Lee, Y.B. Jun, Ideal theory in ordered semigroups based on hesitant fuzzy sets, Honam J. Mathematical 38 (2016), no. 4, 783-794.

A. Ali, M. Khan, F.G. Shi, Hesitant fuzzy ideals in Abel- Grassmanns groupoid, Ital. J. Pure Appl. Math. 35 (2015), 536-556.

B. Davvaz, Semihypergroup theory, Elsevier/Academic Press, Amsterdam, 2016.

M. Farooq, A. Khan, B. Davvaz, Characterizations of ordered semihypergroups by the properties of their intersectional-soft generalized bi-hyperideals, Soft Comput. 22 (2018), no. 9, 3001-3010.

Y.B. Jun, S.Z. Song, G. Muhiuddin, Hesitant fuzzy semigroups with a frontier, J. Intell. Fuzzy Syst. 30 (2016), 1613-1618.

Y.B. Jun, K.J. Lee, C.H. Park, Hesitant fuzzy semigroups with two frontiers, Commun. Korean Math. Soc. 31 (2016), no. 1, 17-25.

N. Kehayopulu, M. Tsingelis, On hypersemigroups, Pure Mathematics and Applications 25 (2015), no. 2, 151-156.

A. Khan, M. Farooq, B. Davvaz, Int-soft interior-hyperideals of ordered semihypergroups, Int. J. Anal. Appl. 14 (2017), no. 2, 193-202.

F. Marty, Sur une generalization de la notion de group, In: Proceedings of the 8th Congress Math. Scandinaves, Stockholm, Sweden, 1934, 45-49.

S. Naz, M. Shabir, On soft semihypergroups, J. Intell. Fuzzy Syst. 26 (2014), 2203-2213.

S. Naz, M. Shabir, On prime soft bi-hyperideals of semihypergroups, J. Intell. Fuzzy Syst. 26 (2014), 1539-1546 .

R.M. Rodriguez, L. Martinez, F. Herrera, Hesitant fuzzy linguisticterm sets for decision making, IEEE Trans. Fuzzy Syst. 20 (2012), no. 1, 109-119.

J. Tang, B. Davvaz, Y.F. Luo, A study on fuzzy interior hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 36 (2016), 125-146.

J. Tang, A. Khan, Y.F. Luo, Characterization of semisimple ordered semihypergroups in terms of fuzzy hyperideals, J. Intell. Fuzzy Syst. 30 (2016), 1735-1753.

J. Tang, B. Davvaz, X.Y. Xie, N. Yaqoob, On fuzzy interior Γ-hyperideals in ordered Γ-semihypergroups, J. Intell. Fuzzy Syst. 32(2017), 2447-2460.

N. Tipachot, B. Pibaljommee, Fuzzy interior hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 36 (2016), 859-870.

A. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529-539.

V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision, In: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, 1378-1382.

L.A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338-353.




DOI: https://doi.org/10.52846/ami.v51i2.1872