Generalized Soft Intersectional Ideals in Ternary Semirings
DOI:
https://doi.org/10.53555/nnms.v1i4.558Keywords:
Ternary semirings, regular ternary semirings, weakly regular ternary semirings, soft intersectional ideals in ternary semiringsAbstract
In this paper we introduce the notions of soft intersectional ternary subsemirings and soft intersectional ideals in ternary semirings. We also discuss some basic results associated with these notions. In the last part of the paper we characterize regular and weakly regular ternary semirings by their soft intersectional ideals.
References
U. Acar, F. Koyuncu, B. Tanay, Soft sets and softrings, Computers and Mathematics with Applications, 59 (11) (2010) 3458-3463.
J. Ahsan, R. Latif, M. Shabir, Representations of weakly regular semirings by sections in a presheaf, Communications in Algebra, 21 (8) (1993) 2819-2835.
H. Aktas, N. Cagman, Soft sets and soft groups, Information sciences, 177 (13) (2007) 2726-2735.
M. I. Ali, M. Shabir, K. P. Shum, On soft ideals over semigroups, Southeast Asian Bulletin of Mathematics, 34 (2010) 595-610.
M. I. Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications, 57 (2009) 1547-1553.
M.I. Ali, M. Shabir, M. Naz, Algebraic structures of soft sets associated with new operations, Computational and Applied Mathematics with Applications, 61 (2011) 2647-2654.
S. K. Bhambri, M. K. Dubey, Anuradha, On Prime, Weakly Prime Left Ideals and Weakly Regular Ternary Semirings, South Asian Bulletin of Mathematics, 37 (2013) 801-811.
N. Cagman and S. Enginoglu, Soft matrix theory and its decision making, Computers and Mathematics with Applications, 59 (2010) 3308-3314.
N. Cagman and S. Enginoglu, Soft set theory and uni-int decision making, European Journal of Operational Research, 207 (2010) 848-855.
T. K. Dutta, S. Kar, On Regular Ternary Semirings, Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics, World Scientific, (2003) 343-355.
T. K. Dutta, S. Kar, A note on regular ternary semirings, Kyungpook Mathematics, 46 (2006) 357-365.
F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Computers and Mathematics with Applications, 56 (10) (2008) 2621-2628.
F. Feng, Y. B. Jun, X. Y. Liu, L. F. Li, An adjustable approach to fuzzy soft based decision making, Journal of Computational and Applied Mathematics, 234 (2010) 10-20.
F. Feng, M. I. Ali, M. Shabir, Soft relations applied to semigroups, Filomate, 27 (7) (2013) 1183-1196.
Y. B. Jun, Soft BCK/BCI-algebras, Computers and Mathematics with Applications, 56 (2008) 1408-1413.
Y. B. Jun, C. H. Park, Applications of soft sets in ideal theory of BCK / BCI-algebras, Information Sciences, 178 (2008) 2466-2475.
D. H. Lehmer, A ternary analogue of abelian groups, American Journal of Mathematics, 59 (1932) 329-338.
W. G. Lister, Ternary rings, Transaction ofAmerican Mathematical Society, 154 (1971), 37-55.
X. Ma and J. Zhan, SOFT INTERSECTION h-IDEALS OF HEMIRINGS AND ITS APPLICATIONS, International Journal of Pure and
Applied Mathematics, 32-2014 (301-308).
X. Ma, J. Zhan, Applications of a new soft set to h-hemiregular hemirings via (M,N)-SI-h-ideals, Journal of Intelligent and Fuzzy Systems, 26 (2014) 2515-2525.
T. Mahmood, U. Tariq, Generalized k-Ideals in Semirings using Soft Intersectional Sets, International Journal of Algebra and Statistics, 4 (1) (2015), 20-38.
P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 44 (2002) 1077-1083.
P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics with Applications, 45 (2003) 555-562.
D. Molodtsov, Soft set theory ----- first results, Computers and Mathematics with Applications, 37 (1999) 19-31.
Peng, Xindong, Y. Yang, Interval-valued Hesitant Fuzzy Soft Sets and their Application in Decision Making, Fundamenta Informaticae 141.1 (2015) 71-93.
A. Sezgin, A. O. Atagun, On operations of soft sets, Computers and Mathematics with Applications, 61 (2011) 1457-1467.
S. Z. Song, H. S. Kim, Y. B. Jun, Ideal theory in semigroups based on Intersectional Soft Sets, The Scientific World journal, 2014 (2014).
H. S. Vandiver, Note on a simple type of Algebra in which cancellation law of addition does not hold, Bulletin of the American Mathematical Society, 40 (1934) 914-920.
Y. Zou, Z. Xiao, Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems, 21 (2008) 941-945
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