Generalized fuzzy subhyperspaces based on fuzzy points

Year 2020, Volume: 69 Issue: 1, 782 - 793, 30.06.2020

Omid Reza Dehghan , M. Norouzı

https://doi.org/10.31801/cfsuasmas.606591

Abstract

We define (∈,∈∨q^{δ})-fuzzy subhyperspaces and (∈,∈∨q_{k}^{δ})-fuzzy subhyperspaces, as a generalization of fuzzy subhyperspaces, (∈,∈∨q)-fuzzy subhyperspaces and (∈,∈∨q_{k})-fuzzy subhyperspaces. In this way, we show that (∈,∈∨q_{k}^{δ})-fuzzy subhyperspaces are the largest family of generalized fuzzy subhyperspaces based on concepts of belongingness and quasi-coincidence. Moreover, we study some properties and investigate the difference of generalized fuzzy subhyperspaces, supported by examples.

Keywords

hypervector space, fuzzy subhyperspace, fuzzy point

References

• Ameri, R., Fuzzy hypervector spaces over valued fields, Iranian Journal of Fuzzy Systems, 2, (2005), 37--47.
• Ameri, R. and Dehghan, O. R., Fuzzy basis of fuzzy hypervector spaces, Iranian Journal of Fuzzy Systems, 7(3), (2010), 97--113.
• Ameri, R. and Dehghan, O. R., Dimension of fuzzy hypervector spaces, Iranian Journal of Fuzzy Systems, 8(5), (2011), 149--166.
• Bhakat, S. K. and Das, P., (∈,∈∨q)-fuzzy subgroup, Fuzzy Sets and Systems, 80, (1996), 359--368.
• Davvaz, B. and Corsini, P., Generalized fuzzy subhyperquasigroups of hyperquasigroups, Soft Computing, 10(11), (2006), 1109--1114.
• Davvaz, B. and Corsini, P., On (α,β)-fuzzy H_{v}-rings, Iranian Journal of Fuzzy Systems, 5(2), (2008), 35--47.
• Davvaz, B. and Corsini, P., Fuzzy (m,n)-ary subhypermodules (with thresholds), Journal of Intelligent and Fuzzy Systems, 23 (2012), 1--8.
• Davvaz, B. and Cristea, I., Fuzzy Algebraic Hyperstructures, Springer, 2015.
• Jun, Y. B., Generalizations of (∈,∈∨q)-fuzzy subalgebras in BCK/BCI-algebras, Computers and Mathematics with Applications, 58, (2009), 1383--1390.
• Jun, Y. B., Ozturk, M. A. and Muhiuddin, G., A generalization of (∈,∈∨q)-fuzzy subgroups, International Journal of Algebra and Statistics, 5(1), (2016), 7--18.
• Kazanci, O., Davvaz, B. and Yamak, S., Fuzzy n-ary polygroups related to fuzzy points, Computers and Mathematics with Applications, 58, (2009), 1466--1474.
• Kazanci, O., Davvaz, B. and Yamak, S., Fuzzy n-ary hypergroups related to fuzzy points, Neural Computing and Applications, 19, (2010), 649--655.
• Hila, K. and Naka, K., On fuzzy subhyperspaces of hypervector spaces, Iranian Journal of Science and Technology, Transaction A, Science, 37, (2013), 103--108.
• Marty, F., Sur une generalization de la notion de groupe, 8^{th} congres des Mathematiciens Scandinaves, Stockholm, (1934) 45-49.
• Mordeson, J. N. and Malik, D. S., Fuzzy Commutative Algebra, World Scientific, 1998.
• Mordeson, J. N. and Nair, S. P., Fuzzy Abstract Algebra, In: Fuzzy Mathematics, Studies in Fuzziness and Soft Computing, Physica, Heidelberg, 2001.
• Rosenfeld, A., Fuzzy groups, Journal of Mathematical Analysis and Applications, 35, (1971), 512--517.
• Scafatti-Tallini, M., Hypervector spaces, Fourth International Congress on Algebraic Hyperstructures and Applications, Xanthi, Greece, (1990) 167-174.
• Shabir, M. and Mahmood, T., Semihypergroups characterized by (∈,∈∨q_{k})-fuzzy hyperideals, Information Sciences Letters, 2(2), (2013), 101--121.
• Shabir, M. and Mahmood, T., Semihypergroups characterized by (∈_{γ},∈_{γ}∨q_{δ})-fuzzy hyperideals, Journal of Intelligent and Fuzzy Systems, 28, (2015), 2667--2678.
• Yin, Y., Zhan, J. and Davvaz, B., New types of fuzzy n-ary subhypergroups of an n-ary hypergroup, Iranian Journal of Fuzzy Systems, 9(5), (2012), 105--124.
• Yin, Y., Zhan, J. and Huang, X., Generalized fuzzy n-ary subhypergroups of a commutative n-ary hypergroup, Mathematica Slovaca, 62(2), (2012), 201--230.
• Zadeh, L. A., Fuzzy sets, Information and Control, 8, (1965), 338--353.
• Zhan, J., Davvaz, B. and Shum, K. P., A new view on fuzzy hypermodules, Acta Mathematica Sinica, English Series, 23(8), (2007), 1345--1356.