International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 37, Pages 2349-2373
doi:10.1155/S0161171203007932
Extension of n-dimensional Euclidean vector space En over ℝ to pseudo-fuzzy vector space over Fp1(1)
Department of Mathematics, National Taiwan University, Taipei, Taiwan
Received 17 July 2001
Copyright © 2003 Kweimei Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
For any two points P=(p(1),p(2),…,p(n)) and Q=(q(1),q(2),…,q(n)) of ℝn, we define the crisp
vector PQ⟶=(q(1)−p(1),q(2)−p(2),…,q(n)−p(n))=Q(−)P. Then we obtain an n-dimensional vector space En={PQ⟶| for all P,Q∈ℝn}. Further, we extend the crisp vector into the fuzzy vector on
fuzzy sets of ℝn. Let D˜,E˜ be any two fuzzy sets on ℝn and define the fuzzy vector E˜D˜⟶=D˜⊖E˜, then we have a pseudo-fuzzy vector space.