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On Cardinality of Fuzzy Sets

DOI: 10.5815/ijisa.2013.06.06

Keywords: Membership Value , Reference Function , Excluded Middle Laws , Fuzzy Cardinality of Fuzzy Sets

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Abstract:

In this article, we would like to revisit and comment on the widely used definition of cardinality of fuzzy sets. For this purpose we have given a brief description of the history of development of fuzzy cardinality. In the process, we can find that the existing definition fails to give a proper cardinality while dealing with complementation of fuzzy sets. So there arises the need of defining the cardinality in a different manner. Here a new definition of cardinality is proposed which is rooted in the definition of complementation of fuzzy sets on the basis of reference function. This definition of cardinality will inevitably play an important role in any problem area that involves complementation. Further, some important results are proven with the help of the proposed definition and it is found that these properties are somewhat analogus to those obtained with the help of the existing definition.

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