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In this work, the classifications of, fuzzy vector planes of fuzzy 4-dimensional vector space and fuzzy projective lines of fuzzy 3-dimensional projective space from fuzzy 4-dimensional vector space are given. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we define the notion of a fuzzy spread of a fuzzy projective space. We classify the fuzzy line spreads of the smallest finite projective space, the Fano plane, and prove a general existence theorem for line spreads of arbitrary finite projective planes. We then extend the classical relation between designs and statistics to an application of the fuzzy spreads in statistics, by considering projective spaces as 2-designs. A fuzzy spread then gives a blueprint of how to make groups for test procedures where certain kinds of objects are mixed together and in each group one kind is over-represented. [Copyright &y& Elsevier]