Fuzzy homoclinic orbits and commuting fuzzifications

Authors:
Steven M. Pederson
Affiliations:
Department of Mathematics, Morehouse College, Atlanta, GA 30314, USA
Venue:
Fuzzy Sets and Systems
Year:
2005

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Abstract

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.