Korean J. Math.  Vol 28, No 4 (2020)  pp.753-774
DOI: https://doi.org/10.11568/kjm.2020.28.4.753

On interval valued intuitionistic fuzzy hyperideals of ordered semihypergroups

Somsak Lekkoksung, Nareupanat Lekkoksung

Abstract


We introduce the notion of interval valued intuitionistic fuzzy hyperideals, bi-hyperideals and quasi-hyperideals of an ordered semihypergroup. We characterize an interval valued intuitionistic fuzzy hyperideal of an ordered semihypergroup in terms of its level subset. Moreover, we show that interval valued intuitionistic fuzzy bi-hyperideals and quasi-hyperideals coincide only in a particular class of ordered semihypergroups. Finally, we show that every interval valued intuitionistic fuzzy quasi-hyperideal is the intersection of an interval valued intuitionistic fuzzy left hyperideal and an interval valued intuitionistic fuzzy right hyperideal.


Keywords


interval value intuitionistic fuzzy sets; interval value intuitionistic fuzzy hyperideals; ordered semihypergroups

Subject classification

20N20; 20M17; 20M99

Sponsor(s)

National Research Council of Thailand: NRCT

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References


S. Abdullah and K. Hila, Interval valued intuitionistic fuzzy set in Γ- semihypergroups, Int. J. Mach. Learn. & Cyber. 7 (2016), 217–228. (Google Scholar)

K. T. Atanassov and G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst. 31 (1989), 343–349. (Google Scholar)

M. Azhar, N. Yaqoob, M. Gulistan and M. Khalaf, On (∈, ∈ qk )-fuzzy hyperideals in ordered LA-semihypergroups, Disc. Dyn. Nat. Soc. (2018), Article ID 9494072, 13 pages. (Google Scholar)

P. Bonansinga and P. Corsini, On semihypergroup and hypergroup homomorphisms, Boll. Un. Mat. Ital. 6 (1982), 717–727. (Google Scholar)

B. Davvaz and S. Omidi, Basic notions and properties of ordered semihyperrings, Categ. General Alg. Struct. Appl. 4 (2016), 43–62. (Google Scholar)

M. Gulistan, N. Yaqoob, S. Kadry and M. Azhar, On generalized fuzzy sets in ordered LA-semihypergroups, Proc. Est. Acad. Sci. 68 (2019) 43–54. (Google Scholar)

D. Heidari and B. Davvaz, On ordered hyperstructures, U.P.B. Sci. Bull. Series A. 73 (2011), 85–96. (Google Scholar)

N. Kehayopulu and M. Tsingelis, Fuzzy ideal in ordered semigroups, Quasigroups Related Systems. 15 (2007), 279–289. (Google Scholar)

D. Krishnaswamy, J. Jayaraj and T. Anitha, Interval-valued intuitionistic fuzzy bi-ideals in ternary semirings, Rom. J. Math. Comput. Sci. 6 (2006), 6–15. (Google Scholar)

F. Marty, Sur une g ́en ́eralization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm. (1934), 45–49. (Google Scholar)

S. Z. Song, H. Bordbar and Y. B. Jun, A new type of hesitant fuzzy subalgebras and ideals in BCK/BCI-algebras, J. Intell. Fuzzy Syst. 32 (2009), 2009–2016. (Google Scholar)

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

N. Tipachot and B. Pibaljommee, Fuzzy interior hyperideals in ordered semihy-pergroups, Ital. J. Pure Appl. Math. 36 (2016), 859–870. (Google Scholar)

T. Vougiouklis, On some representation of hypergroups, Ann. Sci. Univ. Clermont-Ferrand II Math. 26 (1990), 21–29. (Google Scholar)

X. Wang, L. Dong and J. Yan, Maximum ambiguity based sample selection in fuzzy decision tree induction, IEEE Trans. Knowl. Data Eng. 24 (2012), 1491–1505. (Google Scholar)

N. Yaqoob and M. Gulistan, Partially ordered left almost semihypergroups, J. Egyptian Math. Soc. 23 (2015) 231–235. (Google Scholar)

N. Yaqoob, M. Gulistan, J. Tang, and M. Azhar, On generalized fuzzy hyperideals in ordered LA-semihypergroups, Comput. Appl. Math. 38 (2019) 124. (Google Scholar)

L. A. Zadeh, Fuzzy set, Inform. Control. 8 (1965), 338–353. (Google Scholar)

L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning—II, Inform. Sci. 8 (1975), 301–357. (Google Scholar)


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