Intuitionistic Hesitant Fuzzy Subsemigroups of Semigroups
Abstract
The aim of this paper is to extend the hesitant fuzzy subsemigroups to intuitionistic hesitant fuzzy subsemigroups as well as extending of fuzzy subsemigroups to intuitionistic fuzzy subsemigroups by merging the concept of intuitionistic hesitant fuzzy set and subsemigroups. We define the definition of intuitionistic hesitant fuzzy sets on a semigroup and we characterize subsemigroups, left ideals, right ideals, ideals, bi-ideals, interior ideals and (1,2)-ideals in terms of intuitionistic hesitant fuzzy subsemigroups of semigroups. And relations between intuitionistic hesitant fuzzy subsemigroups and subsemigroups are obtained. Keywords : hesitant fuzzy set ; intuitionistic fuzzy set ; intuitionistic hesitant fuzzy subsemigroupReferences
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Howie, J. M. (1976). An Introduction to semigroup theory, Academic Press, 7, 257-264.
Jun, Y. B., Song, S. and Muhiuddin, G. (2016). Hesitant Fuzzy semigroup with a frontier, Journal of intelligent and fuzzy systems, 30, 1613-1618.
Kim, K. H. and Jun, Y. B. (2002). Intuitionistic fuzzy ideals of semigroups, Indian Journal of Pure and Applied Mathematics, 33(4), 443-449.
Kuroki, N. (1979). Fuzzy bi-ideals in semigroup, Commentarii mathematici Universitatis Sancti Pauli, 5, 128-132.
Kim, K. H. and Lee, J. G. (2005). On intuitionistic fuzzy bi-Ideals of semigroups, Turkish Journal of Mathematics, 29, 201-210.
Rosenfeld, A. (1971). Fuzzy groups, Journal of Mathematical Analysis and Applications, 35(3), 512-517.
Rodriguez, R. M., Martinez, L. and Herrera, F. (2012). Hesitant fuzzy linguistic term sets for decision making, Transactions on Fuzzy Systems, 20(1), 109-119.
Torra, V. (2010). Hesitant fuzzy sets, International Journal of Intelligent Systems, 25, 529-539.
Wei, G. (2012). Hesitant fuzzy prioritized operators and their application to multiple attribute decision making, Knowledge-Based Systems-Journal-Elsevier, 31, 176-182.
Wang, F. (2019). Intuitionistic fuzzy (1, 2)-ideals of semigroups. Journal of Physics: Conference Series, 1324(1),
012002.
Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338-353.
Beg, I.and Rashid, T. (2014). Group decision daking using intuitionistic hesitant fuzzy sets, International journal of Fuzzy Logic and Intelligent Systems, 14, 181-187.
Howie, J. M. (1976). An Introduction to semigroup theory, Academic Press, 7, 257-264.
Jun, Y. B., Song, S. and Muhiuddin, G. (2016). Hesitant Fuzzy semigroup with a frontier, Journal of intelligent and fuzzy systems, 30, 1613-1618.
Kim, K. H. and Jun, Y. B. (2002). Intuitionistic fuzzy ideals of semigroups, Indian Journal of Pure and Applied Mathematics, 33(4), 443-449.
Kuroki, N. (1979). Fuzzy bi-ideals in semigroup, Commentarii mathematici Universitatis Sancti Pauli, 5, 128-132.
Kim, K. H. and Lee, J. G. (2005). On intuitionistic fuzzy bi-Ideals of semigroups, Turkish Journal of Mathematics, 29, 201-210.
Rosenfeld, A. (1971). Fuzzy groups, Journal of Mathematical Analysis and Applications, 35(3), 512-517.
Rodriguez, R. M., Martinez, L. and Herrera, F. (2012). Hesitant fuzzy linguistic term sets for decision making, Transactions on Fuzzy Systems, 20(1), 109-119.
Torra, V. (2010). Hesitant fuzzy sets, International Journal of Intelligent Systems, 25, 529-539.
Wei, G. (2012). Hesitant fuzzy prioritized operators and their application to multiple attribute decision making, Knowledge-Based Systems-Journal-Elsevier, 31, 176-182.
Wang, F. (2019). Intuitionistic fuzzy (1, 2)-ideals of semigroups. Journal of Physics: Conference Series, 1324(1),
012002.
Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338-353.
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2021-05-21
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