Title :
T-Norm Based Cuts of Interval-Valued Fuzzy Sets
Author_Institution :
Sch. of Inf. Beijing, WUZI Univ., Beijing, China
Abstract :
We consider the system of interval-valued fuzzy sets (IVFS) in a universe X and study the cuts of an IVFS. Suppose a left continuous triangular norm is given. The t-norm Based cut (level set) of an IVFS is defined in a way that binds the membership lower bound and membership upper bound function via the triangular norm. This is an extension of usual cuts of IVFS. We show that the system of these cuts fulfills analogical properties as usual systems of cuts. However, it is not possible to reconstruct an IVFS from the system of t-norm Based cuts.
Keywords :
fuzzy set theory; probability; IVFS; continuous triangular norm; interval-valued fuzzy sets; membership lower bound function; membership upper bound function; t-norm-based cuts; universe X; Approximation methods; Artificial intelligence; Educational institutions; Fuzzy logic; Fuzzy sets; Level set; Upper bound; cut; interval valued fuzzy set; triangular norm;
Conference_Titel :
Intelligent Human-Machine Systems and Cybernetics (IHMSC), 2013 5th International Conference on
Conference_Location :
Hangzhou
Print_ISBN :
978-0-7695-5011-4
DOI :
10.1109/IHMSC.2013.186
