Extension of n -dimensional Euclidean vector space E n over ℝ to pseudo-fuzzy vector space over F p 1 ( 1 )

Kweimei Wu

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-25

Abstract:

For any two points P = ( p ( 1 ) , p ( 2 ) , … , p ( n ) ) and Q = ( q ( 1 ) , q ( 2 ) , … , q ( n ) ) of ℝ n , we define the crisp vector P Q ⟶ = ( q ( 1 ) − p ( 1 ) , q ( 2 ) − p ( 2 ) , … , q ( n ) − p ( n ) ) = Q ( − ) P . Then we obtain an n -dimensional vector space E n = { P Q ⟶ | for all P , Q ∈ ℝ n } . Further, we extend the crisp vector into the fuzzy vector on fuzzy sets of ℝ n . Let D ˜ , E ˜ be any two fuzzy sets on ℝ n and define the fuzzy vector E ˜ D ˜ ⟶ = D ˜ ⊖ E ˜ , then we have a pseudo-fuzzy vector space.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:760372

DOI: 10.1155/S0161171203007932

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