A pseudo metric on fuzzy sets based on the satisfaction function with viewpoint

Deciding a proper metric for crisp values are well established and the results are clear, but the operation on fuzzy values are inherently ambiguous because the fuzzy values include uncertainty. This paper deals with this distance metric on a set of crisp/fuzzy values with different viewpoints. A bounded pseudo-metric function (distance function) for a set of crisp/fuzzy values is proposed. The distance function is based on the satisfaction function on continuous domain with a viewpoint. The viewpoint was adopted to incorporate user´s preferences on the domain of discourse. The proposed distance function on a set of fuzzy values becomes a bounded metric function when the set of fuzzy values only contains crisp values. Then the role of viewpoints on the distance function is discussed. Finally, the relation between the proposed distance function and defuzzification is shown.