Fuzzy vector spaces. (English) Zbl 0727.15002

Lubczonok, P.

Fuzzy Sets Syst. 38, No. 3, 329-343 (1990).

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.

Reviewer: J.Drewniak (Katowice)

MSC:

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

Keywords:

fuzzy group; linear independence; fuzzy dimension; fuzzy vector spaces; fuzzy basis

Citations:

Zbl 0727.15001; Zbl 0727.15003

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