Fuzzy homoclinic orbits and commuting fuzzifications

Fuzzy homoclinic orbits and commuting fuzzifications are defined and studied. We study sufficient conditions, involving commuting fuzzifications, under which a crisp homoclinic orbit is preserved after fuzzification. We show the usual fuzzification is commuting and therefore preserves homoclinic orbits. Several examples are given regarding fuzzy homoclinic orbits and commuting fuzzifications.