Muhammad FAROOQ, Asghar KHAN, Muhammad IZHAR, Bijan DAVVAZ

(M,N)-Int-Soft Generalized Bi-Hyperideals of Ordered Semihypergroups

Molodtsov introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper, we apply the notion of soft sets to the ordered semihypergroups and introduce the notion of (M , N )-int-soft generalized bi-hyperideals of ordered semihypergroups. Moreover their related properties are investigated. We prove that every int-soft generalized bi-hyperideal is an (M , N )-int-soft generalized bi-hyperideals of S over U but the converse is not true which is shown with help of an example. We present new characterization of ordered semihypergroups in terms of (M , N )-int-soft generalized bi-hyperideals.

Keywords:

Ordered semihypergroup, int-soft hyperideal int-soft generalized bi-hyperideal, (M, N )-int-soft hyperideal, N )-int-soft generalized bi-hyperideal,

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[1] H. Akta¸s and N. C¸ a˘gman, Soft sets and soft groups, Information Sciences, 177(13) (2007) 2726-2735.
[2] F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Computers and Mathematics with Applications, 56(10) (2008) 2621-2628.
[3] F. Feng, M. I. Ali and M. Shabir, Soft relations applied to semigroups, Filomat, 27(7) (2013) 1183-1196.
[4] F. Feng and Y. M. Li, Soft subsets and soft product operations, Information Sciences, 232 (2013) 44-57.
[5] Y. B. Jun, S. Z. Song and G. Muhiuddin, Concave soft sets, critical soft points, and union-soft ideals of ordered semigroups, The Scientific World Journal (2014) Article ID 467968, 11 pages.
[6] X. Ma and J. Zhan, Characterizations of three kinds of hemirings by fuzzy soft h-ideals, Journal of Intelligent and Fuzzy Systems 24 (2013) 535-548.
[7] D. Molodtsov, Soft set theory—first results, Computers and Mathematics with Applications, 37(4-5) (1999) 19–31.
[8] J. Zhan, N. C¸ a˘gman and A. S. Sezer, Applications of soft union sets to hemirings via SU-h-ideals, Journal of Intelligent and Fuzzy Systems 26 (2014) 1363-1370.
[9] F. Marty, Sur Une generalization de la notion de group, 8iemcongress, Mathematics Scandinaves Stockholm (1934) 45-49.
[10] S. Z. Song, H. S. Kim and Y. B. Jun, Ideal theory in semigroups based on intersectional soft sets, The Scientific World Journal, (2014) Article ID 136424, 8 pages.
[11] A. Khan, M. Farooq and B. Davvaz, A study on int-soft hyperideals in ordered semihypergroups, Submitted.
[12] S. Naz and M. Shabir, On soft semihypergroups, Journal of Intelligent and Fuzzy Systems 26 (2014) 2203-2213.
[13] S. Naz and M. Shabir, On prime soft bi-hyperideals of semihypergroups, Journal of Intelligent and Fuzzy Systems 26 (2014) 1539-1546.
[14] J. Tang, B. Davvaz and Y. F. Luo, A study on fuzzy interior hyperideals in ordered semihypergroups, Italian Journal of Pure and Applied Mathematics-N. 36 (2016) 125-146.
[15] J. Tang, A. Khan and Y. F. Luo, Characterization of semisimple ordered semihypergroups in terms of fuzzy hyperideals, Journal of Intelligent and Fuzzy Systems 30 (2016) 1735-1753.
[16] J. Tang, B. Davvaz, X. Y. Xie and N. Yaqoob, On fuzzy interior Γ-hyperideals in ordered Γ-semihypergroups, Journal of Intelligent and Fuzzy Systems 32 (2017) 2447-2460.
[17] M. Farooq, A. Khan and B. Davvaz, Characterizations of ordered semihypergroups by the properties of their intersectional-soft generalized bi-hyperideals, Soft Computing, 22(9), (2018) 3001-3010, DOI 10.1007/s00500-017-2550-6.
[18] A. Khan, M. Farooq and B. Davvaz, Int-soft interior-hyperideals of ordered semihypergroups, International Journal of Analysis and Applications, 14(2) (2017) 193-202.
[19] A. Khan, M. Farooq and B. Davvaz, On (M , N )-intersectional soft interior hyperideals of ordered semihypergroups, Journal of Intelligent and Fuzzy Systems, 33(6) (2017) 3895-3904.
[20] N. C¸ a˘gman and S. Engino˘glu, Soft set theory and uni-int decision making, European Journal of Operational Research, 207(2) (2010) 848-855.
[21] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965) 338-353.
[22] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1) (1986) 87–96 .
[23] P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Computers and Mathematics with Applications 45(5) (2003) 555–562.
[24] P.K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, The Journal of Fuzzy Mathematics 9(3) (2001) 589–602.
[25] F. Feng, Y. Li and N. C¸ a˘gman, Generalized uni-int decision making schemes based on choice value soft sets, European Journal of Operational Research, 220(1) (2012) 162–170.
[26] J. Mao, D. Yao and C. Wang, Group decision making methods based on intuitionistic fuzzy soft matrices, Applied Mathematical Modelling 37(9), (2013) 6425-6436.

Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2014
Yayıncı: Naim Çağman

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