International Journal of Mathematics and Mathematical SciencesVolume 2003, Issue 37, Pages 2349-2373http://dx.doi.org/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 Hindawi Publishing Corporation. 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 n, 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 allP,Qn}. Further, we extend the crisp vector into the fuzzy vector on fuzzy sets of n. Let D˜,E˜ be any two fuzzy sets on n and define the fuzzy vector E˜D˜=D˜E˜, then we have a pseudo-fuzzy vector space.