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

#### Muhammad Bilal KHAN [1] , Tahir BAKHAT [2] , Muhammad IFTİKHAR [3]

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.
Soft set, double framed soft set, lattice ordered double framed soft set, lattice ordered Boolean-algebra
• 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.
Primary Language en Mathematics Research Article Author: Muhammad Bilal KHAN Institution: International Islamic UniversityCountry: Pakistan Author: Tahir BAKHAT Institution: International Islamic UniversityCountry: Pakistan Author: Muhammad IFTİKHAR (Primary Author)Institution: International Islamic UniversityCountry: Pakistan Publication Date : December 30, 2019
 Bibtex @research article { jnt666707, journal = {Journal of New Theory}, issn = {2149-1402}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2019}, volume = {}, pages = {58 - 70}, doi = {}, title = {Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets}, key = {cite}, author = {KHAN, Muhammad and BAKHAT, Tahir and IFTİKHAR, Muhammad} } APA KHAN, M , BAKHAT, T , IFTİKHAR, M . (2019). Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets. Journal of New Theory , (29) , 58-70 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/51172/666707 MLA KHAN, M , BAKHAT, T , IFTİKHAR, M . "Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets". Journal of New Theory (2019 ): 58-70 Chicago KHAN, M , BAKHAT, T , IFTİKHAR, M . "Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets". Journal of New Theory (2019 ): 58-70 RIS TY - JOUR T1 - Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets AU - Muhammad Bilal KHAN , Tahir BAKHAT , Muhammad IFTİKHAR Y1 - 2019 PY - 2019 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 58 EP - 70 VL - IS - 29 SN - 2149-1402-2149-1402 M3 - UR - Y2 - 2019 ER - EndNote %0 Journal of New Theory Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets %A Muhammad Bilal KHAN , Tahir BAKHAT , Muhammad IFTİKHAR %T Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets %D 2019 %J Journal of New Theory %P 2149-1402-2149-1402 %V %N 29 %R %U ISNAD KHAN, Muhammad , BAKHAT, Tahir , IFTİKHAR, Muhammad . "Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets". Journal of New Theory / 29 (December 2020): 58-70 . AMA KHAN M , BAKHAT T , IFTİKHAR M . Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets. JNT. 2019; (29): 58-70. Vancouver KHAN M , BAKHAT T , IFTİKHAR M . Some Results on Lattice (Anti-Lattice) Ordered Double Framed Soft Sets. Journal of New Theory. 2019; (29): 70-58.