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The Study on the (<i>L,M</i>)-Fuzzy Independent Set Systems
College of Biochemical Engineering, Beijing Union University, Beijing, China
College of Biochemical Engineering, Beijing Union University, Beijing, China
Mudanjiang Normal University, Mudanjiang, China
Mudanjiang Normal University, Mudanjiang, China
- 1 College of Biochemical Engineering, Beijing Union University, Beijing, China
- 2 College of Biochemical Engineering, Beijing Union University, Beijing, China
- 3 Mudanjiang Normal University, Mudanjiang, China
- 4 Mudanjiang Normal University, Mudanjiang, China
Advances in Pure Mathematics·Volume 06 (2016)·Pages 1057–1064·Published 12 December 2016·DOI10.4236/apm.2016.613078
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Abstract
Independent sets play an important role in matroid theory. In this paper, the definitions of pre-independent fuzzy set system and independent fuzzy set system in L -fuzzy setting are presented. Independent M -fuzzifying set system is introduced and some of its properties are discussed. Further independent ( L , M )-fuzzy set system is given and some of its properties are obtained. The relations of these independent set systems in the setting of fuzzy vector spaces and fuzzy graphs are showed .
KeywordsPre-Independent <i>L</i>-Fuzzy Set SystemIndependent <i>L</i>-Fuzzy Set SystemIndependent <i>M</i>-Fuzzifying Set SystemIndependent <i>(LM)</i>-Fuzzy Set System
- Goetschel, R. and Voxman, W. (1988) Fuzzy Matroids. Fuzzy Sets and Systems, 27, 291-302. https://doi.org/10.1016/0165-0114(88)90055-3
- Goetschel, R. and Voxman, W. (1989) Bases of Fuzzy Matroids. Fuzzy Sets and Systems, 31, 253-261. https://doi.org/10.1016/0165-0114(89)90007-9
- Goetschel, R. and Voxman, W. (1991) Fuzzy Rank Functions. Fuzzy Sets and Systems, 42, 245-258. https://doi.org/10.1016/0165-0114(91)90150-o
- Novak, L.A. (1997) On Fuzzy Independence Set Systems. Fuzzy Sets and Systems, 91, 365-374. https://doi.org/10.1016/s0165-0114(96)00147-9
- Novak, L.A. (2001) On Goetschel and Voxman Fuzzy Matroids. Fuzzy Sets and Systems, 117, 407-412. https://doi.org/10.1016/s0165-0114(98)00424-2
- Shi. F.-G. (2009) A New Approach to the Fuzzification of Matroids. Fuzzy Sets and Systems, 160, 696-705. https://doi.org/10.1016/j.fss.2008.05.007
- Shi, F.-G. (2000) L-Fuzzy Relation and L-Fuzzy Subgroup. Journal of Fuzzy Mathematics, 8, 491-499. (In Chinese)
- Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M. and Scott, D.S. (2003) Continuous Lattices and Domains, Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511542725
- Dwinger, P. (1982) Characterizations of the Complete Homomorphic Images of a Completely Distributive Complete Lattice I. Indagationes Mathematicae (Proceedings), 85, 403-414. https://doi.org/10.1016/1385-7258(82)90034-8
- Wang, G.-J. (1992) Theory of Topological Molecular Lattices. Fuzzy Sets and Systems, 47, 351-376. https://doi.org/10.1016/0165-0114(92)90301-J
- Huang, H.-L. and Shi, F.-G. (2008) -Fuzzy Numbers and Their Properties. Information Sciences, 178, 1141-1151. https://doi.org/10.1016/j.ins.2007.10.001
- Negoita, C.V. and Ralescu, D.A. (1975) Applications of Fuzzy Sets to Systems Analysis. Interdisciplinary Systems Research Series. Vol. 11, Birkhaeuser, Basel, Stuttgart and Halsted Press, New York. https://doi.org/10.1007/978-3-0348-5921-9
- F.-G. Shi. (2009) -Fuzzy Matroids. Fuzzy Sets and Systems, 160, 2387-2400. https://doi.org/10.1016/j.fss.2009.02.025