Title :
Homoclinic orbits in self-mappings of a space of fuzzy sets
Author :
Pederson, Steven M.
Author_Institution :
Dept. of Math., Morehouse Coll., Atlanta, GA, USA
Abstract :
This paper summarizes and gives new examples of the results in Pederson. Fuzzy homoclinic orbits are defined and studied for self-mappings of a particular metric space of fuzzy sets. Sufficient conditions are given, involving commuting fuzzifications, under which a crisp homoclinic orbit is preserved after fuzzification. It is noted that the usual fuzzification is commuting and therefore preserves homoclinic orbits. Several examples are given regarding fuzzy homoclinic orbits and commuting fuzzifications.
Keywords :
fuzzy set theory; commuting fuzzification; fuzzy homoclinic orbit; fuzzy set; self-mapping; Chaos; Differential equations; Educational institutions; Entropy; Extraterrestrial measurements; Fuzzy sets; Fuzzy systems; Orbits; State-space methods; Sufficient conditions;
Conference_Titel :
Fuzzy Information Processing Society, 2005. NAFIPS 2005. Annual Meeting of the North American
Print_ISBN :
0-7803-9187-X
DOI :
10.1109/NAFIPS.2005.1548637
