Almost bi-quasi-interior ideals and fuzzy almost bi-quasi-interior ideals of semigroups

Volume 26, Issue 2, pp 128--136 http://dx.doi.org/10.22436/jmcs.026.02.03

Publication Date: November 05, 2021 Submission Date: June 21, 2021 Revision Date: August 13, 2021 Accteptance Date: August 26, 2021

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Authors

R. Chinram - Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. W. Nakkhasen - Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand.

Abstract

The notion of bi-quasi-interior ideals of semigroups was introduced by Rao in 2018 which is a generalization of left ideals, right ideals, bi-ideals, quasi-ideals, interior ideals, bi-interior ideals and bi-quasi ideals of semigroups. In this paper, we introduce the concept of almost bi-quasi-interior ideals as a generalization of bi-quasi-interior ideals of semigroups and investigate their properties. Moreover, we define the notion of fuzzy almost bi-quasi-interior ideals of semigroups and consider some connection between almost bi-quasi-interior ideals and fuzzy almost bi-quasi-interior ideals of semigroups.

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Keywords

• Bi-quasi-interior ideal
• almost bi-quasi-interior ideal
• fuzzy almost bi-quasi-interior ideal.

MSC

•  03E72
•  20M12

References

• [1] S. Bogdanović, Semigroups in which some bi-ideal is a group, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat., 11 (1981), 261--266
  • View Article
  • MathSciNet


• [2] B. Davvaz, N. Firouzkouhi, Commutative rings derived from fuzzy hyperrings, Honam Math. J., 42 (2020), 219--234
  • View Article
  • MathSciNet
  • Google Scholar


• [3] O. Grošek, L. Satko, A new notion in the theory of semigroup, Semigroup Forum, 20 (1980), 233--240
  • View Article
  • MathSciNet
  • Google Scholar


• [4] L. Kamali Ardekani, B. Davvaz, On the number of fuzzy subgroups of dicyclic groups, Soft Comput., 24 (2020), 6183--6191
  • View Article
  • Google Scholar


• [5] N. Kaopusek, T. Kaewnoi, R. Chinram, On almost interior ideals and weakly almost interior ideals of semigroups, J. Discrete Math. Sci. Cryptogr., 23 (2020), 773--778
  • View Article
  • MathSciNet
  • Google Scholar


• [6] F. M. Khan, N. H. Sarmin, H. U. Khan, A novel approach toward fuzzy generalized bi-ideals in ordered semigroups, Scient. World J., 2014 (2014), 9 pages
  • View Article
  • Google Scholar


• [7] W. Krailoet, A. Simuen, R. Chinram, P. Petchkaew, A note on fuzzy almost interior ideals in semigroups, Int. J. Math. Comput. Sci., 16 (2021), 803--808
  • View Article
  • MathSciNet
  • Google Scholar


• [8] N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems, 5 (1981), 203--215
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] P. Muangdoo, T. Chuta, W. Nakkhasen, Almost bi-hyperideals and their fuzzification of semihypergroups, J. Math. Comput. Sci., 11 (2021), 2755--2767
  • View Article
  • Google Scholar


• [10] W. Nakkhasen, Intuitionistic fuzzy ideals of ternary near-rings, Int. J. Fuzzy Logic Intel. Syst., 20 (2020), 290--297
  • View Article
  • Google Scholar


• [11] S. Nawaz, M. Gulistan, N. Kausar, Salahuddin, M. Munir, On the left and right almost hyperideals of LA-semihypergroups, Int. J. Fuzzy Logic Intel. Syst., 21 (2021), 86--92
  • View Article
  • Google Scholar


• [12] P. Palakawong na Ayutthaya, B. Pibaljommee, Characterizations of ordered $k$-regularities on ordered semirings, Quasigroups Related Systems, 29 (2021), 107--121
  • View Article
  • MathSciNet
  • Google Scholar


• [13] P. M. Pu, Y. M. Liu, Fuzzy topology I. Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571--599
  • View Article
  • MathSciNet
  • Google Scholar


• [14] M. M. K. Rao, A study of a generalization of bi-ideal, quasi ideal and interior ideal of semigroup, Math. Morav., 22 (2018), 103--115
  • View Article
  • MathSciNet
  • Google Scholar


• [15] Y. S. Rao, S. Kosari, Z. Shao, M. Akhoundi, S. Omidi, A study on $A$-$I$-$\Gamma$-hyperideals and $(m, n)$-$\Gamma$-hyperfilters in ordered $\Gamma$-semihypergroups, Discrete Dyn. Nat. Soc., 2021 (2021), 10 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [16] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512--517
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] A. Simuen, S. Abdullah, W. Yonthanthum, R. Chinram, Almost bi-$\Gamma$-ideals and fuzzy almost bi-$\Gamma$-ideals of $\Gamma$-semigroups, Eur. J. Pure Appl. Math., 13 (2020), 620--630
  • View Article
  • MathSciNet
  • Google Scholar


• [18] A. Simuen, K. Wattanatripop, R. Chinram, Characterizing almost quasi-$\Gamma$-ideals and fuzzy almost quasi-$\Gamma$-ideals of $\Gamma$-semigroups, Commun. Math. Appl., 11 (2020), 233--240
  • View Article
  • Google Scholar


• [19] S. Suebsung, T. Kaewnoi, R. Chinram, A not on almost hyperideals in semihypergroups, Int. J. Math. Comput. Sci., 15 (2020), 127--133
  • View Article
  • Google Scholar


• [20] S. Suebsung, K. Wattanatripop, R. Chinram, A-ideals and fuzzy A-ideals of ternary semigroups, Songklanakarin J. Sci. Tech., 41 (2019), 299--304
  • View Article
  • Google Scholar


• [21] S. Suebsung, K. Wattanatripop, R. Chinram, On almost $(m, n)$-ideals and fuzzy almost $(m, n)$-ideals in semigroups, J. Taibah Univer. Sci., 13 (2019), 897--902
  • View Article
  • Google Scholar


• [22] S. Suebsung, W. Yonthanthum, K. Hila, R. Chinram, On almost quasi-hyperideals in semihypergroups, J. Discrete Math. Sci. Cryptogr., 24 (2021), 235--244
  • View Article
  • MathSciNet
  • Google Scholar


• [23] K. Wattanatripop, R. Chinram, T. Changphas, Fuzzy almost bi-ideals in semigroups, Int. J. Math. Comput. Sci., 13 (2018), 51--58
  • View Article
  • MathSciNet
  • Google Scholar


• [24] K. Wattanatripop, R. Chinram, T. Changphas, Quasi-$A$-ideals and fuzzy $A$-ideals in semigroups, J. Discrete Math. Sci. Cryptogr., 21 (2018), 1131--1138
  • View Article
  • MathSciNet
  • Google Scholar


• [25] L. A. Zadeh, Fuzzy set, Information and Control, 8 (1965), 338--353
  • View Article
  • MathSciNet
  • Google Scholar