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Entropy measures and granularity measures for interval and set-valued information systems

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Abstract

In many practical situations, some of the attribute values for an object may be interval and set-valued. The interval and set-valued information systems have been introduced. According to the semantic relation of attribute values, interval and set-valued information systems can be classified into two categories, disjunctive (type 1) and conjunctive (type 2) systems. This paper mainly focuses on semantic interpretation of type 1. Then, a new fuzzy preference relation for interval and set-valued information systems is defined. Moreover, based on the new fuzzy preference relation, the concepts of fuzzy information entropy, fuzzy rough entropy, fuzzy knowledge granulation and fuzzy granularity measure are studied and relationships between entropy measures and granularity measures are investigated. Finally, an illustrative example to substantiate the theoretical arguments is given. These results may supply a further understanding of the essence of uncertainty in interval and set-valued information systems.

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Correspondence to Hong Wang.

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The authors declared that they have no conflicts of interest to this work.

Additional information

Communicated by A. Di Nola.

This study is supported by the Nature Science Foundation of Shanxi Province (No. 2008011012).

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Wang, H., Yue, HB. Entropy measures and granularity measures for interval and set-valued information systems. Soft Comput 20, 3489–3495 (2016). https://doi.org/10.1007/s00500-015-1954-4

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