A COMPREHENSION OF SOFT BINARY PIECEWISE GAMMA OPERATION: A NEW OPERATION FOR SOFT SETS
Bu makalenin ilk hali 15 Mayıs 2026 tarihinde yayımlandı. https://dergipark.org.tr/tr/pub/jamame/article/1537605
Düzeltme Notu
İmla hataları düzeltildi.
Öz
,Soft set theory gained popularity as a cutting-edge approach to handling uncertainty-related problems and modeling uncertainty after being introduced by Molodtsov in 1999. Numerous theoretical and practical applications have been conducting by make using of the theory. This paper presents a novel soft set operation, called the "soft binary piecewise gamma operation". Its basic algebraic characteristics are thoroughly examined. Furthermore, this operation's distributions over a number of soft set operations are investigated. We prove that given certain assumptions, the soft binary piecewise addition operation determines a commutative semigroup and a right-left system, and soft binary piecewise gamma operation, along with the some other types of soft sets, form many important algebraic structures, such as semirings and near-semirings in the collection of soft sets over the universe by considering the algebraic properties of the operation and its distribution rules together.
Anahtar Kelimeler
Soft sets, soft set operations, conditional complements, soft binary piecewise gamma operation
Kaynakça
- [2] MAJI, P.K, BISWAS, R. AND ROY, A.R. SOFT set theory. Computers and Mathematics with Applications, 45 (1): 555-562,2003.
- [3] PEI, D. AND MIAO, D. From soft sets to information systems. In: Proceedings of Granular Computing IEEE, 2: 617-621,2005.
- [4] ALI, M.I., FENG, F., LIU, X., MIN, W.K. AND SHABIR, M. On some new operations in soft set theory. Computers and Mathematics with Applications, 57(9): 1547-1553, 2009.
- [5] SEZGİN, A. AND ATAGÜN, A.O. On operations of soft sets. Computers and Mathematics with Applications, 61(5):1457-1467,2011
- [6] ALI, M.I, SHABIR, M., NAZ, M. Algebraic structures of soft sets associated with new operations, Computers and Mathematics with Applications, 61 2647–2654, 2011.
- [7] YANG, C.F. “A note on: “Soft set theory” [Computers & Mathematics with Applications 45 (2003), no. 4-5, 555–562],”, Computers & Mathematics with Applications, 56 (7), pp. 1899–1900, 2008
- [8] NEOG, I.J, SUT, D.K. A new approach to the theory of soft set, International Journal of Computer Applications, 32 (2), pp. 1-6, 2011
- [9] FU, L. Notes on soft set operations, ARPN Journal of Systems and Software, 1, pp. 205-208,2011.
- [10] GE, X., YANG, S. Investigations on some operations of soft sets, World academy of Science, Engineering and Technology, 75, pp. 1113-1116,2011.
- [11] SINGH, D. AND ONYEOZILI, I. A. Notes on Soft Matrices Operations. ARPN Journal of Science and Technology, 2(9), 861-869,2012.