Journal of Applied Mathematics
Volume 2013 (2013), Article ID 592738, 7 pages
Research Article

Truth Degrees Theory and Approximate Reasoning in 3-Valued Propositional Pre-Rough Logic

School of Science, Xi’an Polytechnic University, Xi’an 710048, China

Received 5 January 2013; Accepted 6 June 2013

Academic Editor: Francisco Chiclana

Copyright © 2013 Yingcang Ma et al. 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.


By means of the function induced by a logical formula , the concept of truth degree of the logical formula is introduced in the 3-valued pre-rough logic in this paper. Moreover, similarity degrees among formulas are proposed and a pseudometric is defined on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in 3-value logic pre-rough logic is established.