참고문헌
- U. Acar, K. Fatih and T. Bekir, Soft sets and soft rings, Computers and Mathematics with Applications, 59 (11) (2010), 3458-3463. https://doi.org/10.1016/j.camwa.2010.03.034
- A. U. Ahmed, S. Rahman and B. Davvaz, On intuitionistic fuzzy idempotent, prime, strongly irreducible and t-pure ideals of semirings, Journal of Intelligent & Fuzzy Systems, 33 (1) (2017), 433-443. https://doi.org/10.3233/JIFS-161747
- H. Aktas and N. Cagman, Soft sets and soft groups, Information Sciences, 177(13)(2007), 2726-2735. https://doi.org/10.1016/j.ins.2006.12.008
- M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications, 57 (9) (2009), 1547-1553. https://doi.org/10.1016/j.camwa.2008.11.009
- M. I. Ali, A note on soft sets, rough soft sets and fuzzy soft sets, Applied Soft Computing Journal, 11 (4) (2011), 3329-3332. https://doi.org/10.1016/j.asoc.2011.01.003
- M. I. Ali, M. Shabir and M. Naz, Algebraic structures of soft sets associated with new operations, Computers and Mathematics with Applications 61 (9) (2011), 2647-2654. https://doi.org/10.1016/j.camwa.2011.03.011
- K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1) (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
- J. N. Chaudhari, B. Davvaz and K. J. Ingale, Subtractive extension of ideals in semirings, Sarajevo Journal of Mathematics, 10 (22) (2014), 13-20. https://doi.org/10.5644/SJM.10.1.02
- D. Chen, E. C. Tsang, D. S. Yeung and X. Wang, The parameterization reduction of soft sets and its applications, Computers and Mathematics with Applications, 49 (5-6) (2005), 757-763. https://doi.org/10.1016/j.camwa.2004.10.036
- K. R. Chowdhury, A. Sultana, N. K. Mitra and K. Khan, Some structural properties of semirings, Annals of Pure and Applied Mathematics 5 (2) (2014), 158-167.
- F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Computers and Mathematics with Applications, 56 (10) (2008), 2621-2628. https://doi.org/10.1016/j.camwa.2008.05.011
- W. L. Gauand and D. J. Buehrer Vague sets, IEEE Transactions on Systems, Man and Cybernetics, 23 (2) (1993), 610-614. https://doi.org/10.1109/21.229476
- J. S. Golan, The theory of semirings with applications in mathematics and theoretical computer science, John Willy and Sons Inc., New York, 1999.
- M. B. Gorza lczany, A method of inference in approximate reasoning based on intervalvalued fuzzy sets, Fuzzy Sets and Systems, 21 (1) (1987), 1-17. https://doi.org/10.1016/0165-0114(87)90148-5
- J. M Howie, Fundamentals of semigroup theory, Oxford University Press Inc., New York, 1995.
- Y. B. Jun, Soft BCK/BCI-algebras, Computers and Mathematics with Applications, 56 (5) (2008), 1408-1413. https://doi.org/10.1016/j.camwa.2008.02.035
- S. Kar, S. Purkait and B. Davvaz, Fuzzy k-primary decomposition of fuzzy k-ideal in a semiring, Fuzzy Inf. Eng., 7 (2015), 405-422. https://doi.org/10.1016/j.fiae.2015.11.002
- W. A. Khan, B. Davvaz and A. Muhammad, (M, N)-soft intersection near semirings and (M, N)-α-inclusion along with its algebraic applications, Lobachevskii J. Math., 40 (1) (2019), 67-78. https://doi.org/10.1134/s1995080219010098
- X. P. Liu, D. J. Xiang and J. M. Zhan, Fuzzy isomorphism Theorems of soft rings, Neural Computing and Applications, 21 (2) (2012), 391-397. https://doi.org/10.1007/s00521-010-0439-8
- X. P. Liu, D. J. Xiang, J. M. Zhan and K. P. Shum, Isomorphism theorems for soft rings, Algebra Colloquium, 19 (2012), 649-656. https://doi.org/10.1142/S100538671200051X
- P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 44 (8-9) (2002), 1077-1083. https://doi.org/10.1016/S0898-1221(02)00216-X
- P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Computers and Mathematics with Applications, 45 (4-5) (2003), 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
- P. Majumdar and S. K. Samanta, On soft mappings, Computers and Mathematics with Applications, 60 (9) (2010), 2666-2672. https://doi.org/10.1016/j.camwa.2010.09.004
- D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37 (4-5) (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
- Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11 (5) (1982), 341-356. https://doi.org/10.1007/BF01001956
- Z. Pawlak and A. Skowron,Rudiments of rough sets, Information Sciences, 177 (1) (2007), 3-27. https://doi.org/10.1016/j.ins.2006.06.003
- B. Praba, A. Manimaran, V. M. Chandrasekaran and B. Davvaz, Cozero divisor graph of a commutative rough semiring, Advances in Algebra and Analysis, Trends in Mathematics, Springer Nature Switzerland AG, 2018 (2018), 67-75.
- A. Sezgin and A. O. Atagun, On operations of soft sets, Computers and Mathematics with Applications, 61 (5) (2011), 1457-1467. https://doi.org/10.1016/j.camwa.2011.01.018
- X. Xin and W. Li, Soft congruence relations over rings, Scientific World Journal, 2014 (2014), 1-9.
- S. Yamak, O. Kazanci and B. Davvaz, Soft hyperstructure, Computers and Mathematics with Applications, 62 (2) (2011), 797-803. https://doi.org/10.1016/j.camwa.2011.06.009
- L. A. Zadeh, Fuzzy sets, Information and Control, 8 (3) (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
- L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Information Sciences, 172 (1-2) (2005), 1-40. https://doi.org/10.1016/j.ins.2005.01.017
- J. Zhan and Y. B. Jun, Soft BL-algebras based on fuzzy sets, Computers and Mathematics with Applications, 59 (6) (2010), 2037-2046. https://doi.org/10.1016/j.camwa.2009.12.008