Applications of Soft Intersection Sets in Hypernear Rings

Yıl 2020, Cilt: 3 Sayı: 1, 191 - 197, 15.12.2020

Mohammad Yahya Abbası , Sabahat Ali Khan , Ahmad Raza

Öz

In this paper, we introduce soft intersection hypernear-ring and shows how a soft set effects on a hypernear-ring structure by means of intersection and insertion of sets. Further, we explore some properties using hypernear-ring theoretic concepts for soft sets. Moreover, we have defined the cross product of two soft intersection hypernear-rings. We proved that the cross product of two soft intersection hypernear-rings is a soft intersection hypernear-ring and the cross product of two soft intersection hyperideals is a soft intersection hyperideal.

Anahtar Kelimeler

Hypernear-rings, Soft intersection sets, Soft intersection hyperideals

Kaynakça

• 1 A. Adeel, N. Yaqoob, M. Akram, W. Chammam, Detection and severity of tumor cells by graded decision-making methods under fuzzy N-soft model, Journal of Intelligent & Fuzzy Systems, 9 (1) (2020), 1303–1318.
• 2 M. Akram, N. Yaqoob, Intuitionistic fuzzy soft ordered ternary semigroups, International Journal of Pure and Applied Mathematics, 84(2) (2013), 93–107.
• 3 H. Aktas, N. Cagman, Soft sets and soft groups, Inform. Sci., 177 (2007), 2726–2735.
• 4 N.Cagman, S. Enginoglu, Soft set theory and uni-int decision making, Eur. J. Op. Res., 207 (2010), 848–855.
• 5 N. Cagman, F. Citak, H. Aktas, Soft int-group and its applications to group theory, Neural Comput. Appl., 21 (2012), 151–158.
• 6 P. Corsini, Prolegomena of hypergroup theory, Aviani editor, Second edition, (1993).
• 7 V. Dasic, Hypernear rings, Proceedings of the Fourth International Congress on A. H. A., Xanthi, Greece, World Scientific, (1990), 75–85.
• 8 B. Davvaz, V. L. Fotea, Hyperring Theory and Applications, International Academic Press, Palm Harber, Fla, USA (2007), 115.
• 9 V. M. Gontineac, On hypernear rings and H-hypergroups, Proceedings of the Fifth International Congress on A. H. A., Jasi Rumania, Hadronic Press, Inc., (1993), 171–179.
• 10 M. Gulistan, I. Beg, N. Yaqoob, A new approach in decision making problems under the environment of neutrosophic cubic soft matrices, Journal of Intelligent and Fuzzy Systems, 36(1) (2019), 295–307.
• 11 A. Khan, M. Farooq, N. Yaqoob, Uni-soft structures applied to ordered Γ-semihypergroups, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 90(3) (2020), 457–465.
• 12 J.G. Lee, K.H. Kim, On fuzzy subhypernear-rings of hypernear-rings with t-norms, Journal of the Chungcheong Mathematical Society, 23(2)(2010), 237–243.
• 13 F. Marty, Sur une generalization de la notion de group, 8th Congres Math. Scandinaves Stockholm, (1934), 45–49 .
• 14 D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19–31.
• 15 G. Pilz Near-rings, Noth-Holland, Publ Co., (1977).
• 16 A. Sezgin, A. O. Atagun, N. Cagman, Soft intersection near-rings with its applications, Neural Comput & Applic., 21 (2012), 221–229.
• 17 S. Yamak, O. Kazanci, B. Davvaz, Normal fuzzy hyperideals in hypernear-rings, Neural Comput & Applic., 20(2011), 25–30.
• 18 N. Yaqoob, M. Akram, M. Aslam, Intuitionistic fuzzy soft groups induced by (t,s)-norm, Indian Journal of Science and Technology, 6(4) (2013), 4282–4289.
• 19 J. Zhan, On properties of fuzzy hyperideals in hypernearrings with t-norms, J. Appl. Math. Comput., 20 (2006), 255–277.