A New Pseudo-metric for Fuzzy Sets
作者： Laszlo Kovacs , Joel Ratsaby
DOI: 10.1007/978-3-319-07173-2_19
关键词: Mathematics 、 Fuzzy set 、 Triangle inequality 、 Membership function 、 Fuzzy number 、 Symmetric difference 、 Defuzzification 、 Type-2 fuzzy sets and systems 、 Metric (mathematics) 、 Discrete mathematics
摘要: A new distance function for fuzzy sets is introduced. It based on the descriptive complexity, that is, number of bits (on average) are needed to describe an element in symmetric difference two sets. The value gives amount additional information either one when other known. We prove a pseudo-metric, namely, it non-negative, symmetric, equals zero if identical and satisfies triangle inequality.
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