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Rarity-based similarity relations in a generalized fuzzy information system

A generalized fuzzy information system contains data about objects of interest characterized by some attributes. Every data in a domain attribute may be precise as well as imprecise data (fuzzy data). A more generalized representation of fuzzy information system may be regarded as a mapping to a possibility of fuzzy data in the corresponding domain attribute. In other words, a possibility of fuzzy data might be regarded as a level 2 fuzzy set. Similarity relation between two fuzzy data satisfies the properties of weak similarity relations in which similarity between two fuzzy data may not necessarily be symmetric or transitive. In the fuzzy information system, two objects are intuitively looked more similar if their similar values of attributes are rarer. Hence, this paper proposes a concept of calculating similarity between two objects by considering rare values of attributes in a generalized fuzzy information system.