Fuzzy vector spaces. (English) Zbl 0727.15002

The paper presents a new approach to the theory of fuzzy vector spaces [cf. G. C. Muganda, ibid. 38, No.3, 365-373 (1990; reviewed below) and D. S. Malik and J. N. Mordeson, Inf. Sci. 55, No.1-3, 271-281 (1991; reviewed above)]. The author defines a new fuzzy basis of a fuzzy vector space and examines its existence under diverse assumptions. He discusses also the existence of a common fuzzy basis for two fuzzy vector spaces on the same vector space. Some results concern the notion of the (real valued) dimension of a fuzzy vector space.


15A03 Vector spaces, linear dependence, rank, lineability
03E72 Theory of fuzzy sets, etc.
20N25 Fuzzy groups
Full Text: DOI


[1] De Luca, A.; Termini, S., A definition of non-probabilistic entropy in the setting of fuzzy sets theory, Inform. and control, 20, 301-312, (1970) · Zbl 0239.94028
[2] Dubois, D.; Prade, H., Fuzzy cardinality and the modeling of imprecise quantification, Fuzzy sets and systems, 16, 199-230, (1985) · Zbl 0601.03006
[3] Katsaras, A.K., Fuzzy topological vector spaces I, Fuzzy sets and systems, 6, 85-95, (1981) · Zbl 0463.46009
[4] Katsaras, A.K., Fuzzy topological vector spaces II, Fuzzy sets and systems, 12, 143-154, (1984) · Zbl 0555.46006
[5] Katsaras, A.K.; Liu, D.B., Fuzzy vector spaces and fuzzy topological vector spaces, J. math. anal. appl., 58, 135-146, (1977) · Zbl 0358.46011
[6] Lowen, R., Convex fuzzy sets, Fuzzy sets and systems, 3, 291-310, (1980) · Zbl 0439.52001
[7] Matloka, M., Finite fuzzy cone, Fuzzy sets and systems, 15, 209-211, (1985) · Zbl 0583.15002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.