Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets

Yıl 2019, Sayı: 29, 58 - 70, 30.12.2019

Muhammad Khan Tahir Bakhat Muhammad Iftikhar

Öz

In this article, we generalised the notion of the lattice (anti-lattice) ordered soft sets and introduced the notion of the lattice (anti-lattice) ordered double framed soft sets and proved some results by applying the basic operations like union, intersection, union-product and intersection-product, etc. Further, by applying the operations of restricted union and restricted intersection, we elaborated the applications of lattice ordered double framed soft sets in algebraic structure.

Anahtar Kelimeler

Soft set, double framed soft set, lattice ordered double framed soft set, lattice ordered Boolean-algebra

Kaynakça

• L. A. Zadeh, Fuzzy Sets, Information and Control 8(3) (1965) 338-353.
• K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20(1) (1986) 87-96.
• K. T. Atanassov, Operators over Interval Valued Intuitionistic fuzzy sets, Fuzzy Sets and Systems 64(2) (1994) 159-174.
• M. B. Gorzałczany, A Method of Inference in Approximate Reasoning Based on Interval-Valued Fuzzy Sets, Fuzzy Sets and Systems 21(1) (1987) 1-17.
• W. L. Gau, D. J. Buehrer, Vague Sets, IEEE Transactions on Systems, Man, and Cybernetics 23(2) (1993) 610-614.
• Z. Pawlak, Rough Sets, International Journal of Computer and Information Sciences 11(5), (1982) 341-356.
• D. Molodtsov, Soft Set Theory—First Results, Computers and Mathematics with Applications 37(4-5) (1999) 19-31.
• P. K. Maji, A. R. Roy, R. Biswas, An Application of Soft Sets in a Decision-Making Problem, Computers and Mathematics with Applications 44(8-9) (2002) 1077-1083.
• P. K. Maji, R. Biswas, A. Roy, Soft Set Theory, Computers and Mathematics with Applications 45(4-5) (2003) 555-562.
• H. Aktaş, N. Çağman, Soft sets and soft groups, Information Sciences 177(13) (2007) 2726-2735.
• M. I. Ali, T. Mahmood, M. M. U. Rehman, M. F. Aslam, On Lattice Ordered Soft Sets, Applied Soft Computing 36 (2015) 499-505.
• T. Mahmood, M. I. Ali, M. A. Malik, W. Ahmad, On Lattice Ordered Intuitionistic Fuzzy Soft Sets, International Journal of Algebra and Statistics 7 (2018) 46-61.
• T. Mahmood, Z. Rehman, A. Sezgin, Lattice Ordered Soft Near Rings, The Korean Journal of Mathematics 26(3) (2018) 503-517.
• Y. B. Jun, S. S. Ahn, Double Framed Soft Sets with Applications in BCK/BCI-Algebras, Journal of Applied Mathematics Volume (2012) Article ID 178159, 15 pages. http://dx.doi.org/10.1155/2012/178159
• B. Davvaz, Roughness in Rings, Information Sciences 164(1-4) (2004) 147-163.
• M. Naz, Some Studies on Algebraic Structure of Soft Sets, PhD dissertation Quaid-i-Azam University (2015) Islamabad, Pakistan.
• B. Davvaz, M. Mahdavipour, Roughness in Modules, Information Sciences, 176(24) (2006) 3658-3674.
• J. Zhan, Q. Liu, B. Davvaz, A New Rough Set Theory: Rough Soft Hemirings, Journal of Intelligent and Fuzzy Systems 28(4) (2015) 1687-1697.
• M. Shabir, S. Irshad, Roughness in Ordered Semigroups, World Applied Sciences Journal 22 (2013) 84-105.
• U. Acar, F. Koyuncu, B. Tanay, Soft Sets and Soft Rings, Computers and Mathematics with Applications 59(11) (2010) 3458-3463.
• A. S. Sezer, A. O. Atagün, A New Kind of Vector Space: Soft Vector Space, Southeast Asian Bulletin of Mathematics 40(5) (2016) 753-770.
• M. I. Ali, M. Shabir, F. Feng, Representation of Graphs Based on Neighborhoods and Soft Sets, International Journal of Machine Learning and Cybernetics 8(5) (2017) 1525-1535.
• M. Shabir, M. Naz, On Soft Topological Spaces, Computers and Mathematics with Applications 61(7) (2011) 1786-1799.
• M. Ullah, T. Mahmood, M. B. Khan, K. Ullah, On Twisted Soft Ideal of Soft Ordered Semigroups, Journal of Information Communication Technologies and Robotics Applications (JICTRA) (Formally known as NICE Research Journal of Computer Science) 8 (2017) 74-85.
• Y. B. Jun, K. J. Lee, A. Khan, Soft Ordered Semigroups, Mathematical Logic Quarterly 56(1) (2010) 42-50.
• M. I. Ali, M. Shabir, K. P. Shum, On Soft Ideals over Semigroups, Southeast Asian Bulletin of Mathematics 34(4) (2010) 595-610.
• M. Iftikhar, T. Mahmood, Some Results on Lattice Ordered Double Framed Soft Semirings, International Journal of Algebra and Statistics (IJAS) 7(1-2) (2018) 123-140.