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

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.