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.
Generalized fuzzy subhyperspaces based on fuzzy points
Year 2020,
Volume: 69 Issue: 1, 782 - 793, 30.06.2020
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.
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.
Dehghan, O. R., & Norouzı, M. (2020). Generalized fuzzy subhyperspaces based on fuzzy points. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 782-793. https://doi.org/10.31801/cfsuasmas.606591
AMA
Dehghan OR, Norouzı M. Generalized fuzzy subhyperspaces based on fuzzy points. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):782-793. doi:10.31801/cfsuasmas.606591
Chicago
Dehghan, Omid Reza, and M. Norouzı. “Generalized Fuzzy Subhyperspaces Based on Fuzzy Points”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 782-93. https://doi.org/10.31801/cfsuasmas.606591.
EndNote
Dehghan OR, Norouzı M (June 1, 2020) Generalized fuzzy subhyperspaces based on fuzzy points. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 782–793.
IEEE
O. R. Dehghan and M. Norouzı, “Generalized fuzzy subhyperspaces based on fuzzy points”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 782–793, 2020, doi: 10.31801/cfsuasmas.606591.
ISNAD
Dehghan, Omid Reza - Norouzı, M. “Generalized Fuzzy Subhyperspaces Based on Fuzzy Points”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 782-793. https://doi.org/10.31801/cfsuasmas.606591.
JAMA
Dehghan OR, Norouzı M. Generalized fuzzy subhyperspaces based on fuzzy points. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:782–793.
MLA
Dehghan, Omid Reza and M. Norouzı. “Generalized Fuzzy Subhyperspaces Based on Fuzzy Points”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 782-93, doi:10.31801/cfsuasmas.606591.
Vancouver
Dehghan OR, Norouzı M. Generalized fuzzy subhyperspaces based on fuzzy points. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):782-93.