HESITANT FUZZY IDEAL EXTENSION IN PO-SEMIGROUPS

Year 2018, Volume: 8 Issue: 2 , 509 - 521 , 01.12.2018

M. Y. Abbasi A. F. Talee X. Y. Xie S. A. Khan

https://izlik.org/JA95HB94BB

Abstract

In this paper, the notions of extension of hesitant fuzzy ideals, hesitant fuzzy prime ideals, hesitant fuzzy semiprime ideals and hesitant 3-prime fuzzy ideals in po-semigroups are introduced with some of their properties are investigated. We discuss the relationship between between prime semi prime ideals and 3-prime ideals in po-semigroup by means of the extensions hesitant fuzzy ideals.

Keywords

Hesitant fuzzy ideal , hesitant fuzzy ideal extension , hesitant fuzzy prime , semiprime ideal , 3-prime hesitant fuzzy ideal

References

• [1] Abbasi, M. Y., Talee, A. F. and Basar, A., On properties of hesitant fuzzy ideals in semigroups (submitted).
• [2] Abbasi, M. Y., Talee, A. F. and Basar, A., Hesitant fuzzy ideals in po-semigroup (submitted).
• [3] Davvaz, B. and Khan, A., (2012), Generalized fuzzy filters in ordered semigroups, Iranian J. Sci. and Tech., A1, 77-86.
• [4] Jun, Y. B. and Song, S. Z., (2014), Hesitant fuzzy set theory applied to filters in MTL-algebras, Honam Math. J., 36 , 813-830.
• [5] Jun, Y. B., Lee, K. J. and Song, S. Z., (2015), Hesitant fuzzy bi-ideals in semigroups, Commun. Korean Math. Soc., 30 , 143-154.
• [6] Jun, Y. B., Ahn, S. S. and Muhiuddin, G., (2014), Hesitant Fuzzy Soft Subalgebras and Ideals in BCK/BCI-Algebras, the Scientific World Journal, 1-7.
• [7] Kehayopulu, N. and Tsingelis, M., (2004), Fuzzy bi-ideals in ordered semigroups, Inform. Sci., 171 , 13-28.
• [8] Kuroki, N., (1979), Fuzzy bi-ideals in semigroups, Comment. Math. Univ. St. Pauli, XXVIII-1 , 17-21.
• [9] Kuroki, N., (1991), On fuzzy semigroups, Inform. Sci., 53 , 203-236.
• [10] Mahmood, T., Khan, Q., and Jun Y, (2016), Vector Similarity Measures for Simplified Neutrosophic Hesitant Fuzzy Set and Their Applications, J. of Inequalities and Special Functions 7 , 176-194
• [11] Mahmood, T., Mehmood, F. and Khan, Q., (2016), Cubic Hesitant Fuzzy Sets and Their Applications to Multi Criteria Decision Making, International Journal of Algebra and Statistics, 5 , 19-51.
• [12] Mahmood, T., Mehmood, F. and Khan, Q., (2017), Some Generalized Aggregation Operators for Cubic Hesitant Fuzzy Sets and Their Applications to Multi Criteria Decision Making, Punjab University Journal of Mathematics, 49 , 31-49
• [13] Rosenfeld, A., (1971), Fuzzy groups, J. Math. Anal. Appl., 35 , 512-517.
• [14] Torra, V., (2010), Hesitant fuzzy sets, Int. J. Intell. Syst., 25 , 529-539.
• [15] Torra, V. and Narukawa,Y., (2009), On hesitant fuzzy sets and decision, in: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 1378-1382.
• [16] Xie, X. Y., (2001), Fuzzy ideals extensions of semigroups, Soochow journal of Mathematics, 27 , 125-138.
• [17] Xie, X. Y. and Yan, F., (2005), Fuzzy ideals extensions of ordered semigroups, Lobachevskii journal of Mathematics, 19 , 29-40.
• [18] Xie, X. Y. and Wu, M. F., (1996), On the ideal extensions in ordered semigroups, Semigroup Forum, 53 , 63-71.
• [19] Zadeh, L. A., (1965), Fuzzy sets, Information and Control, 8 , 338-353.