Abstract
How to effectively deal with missing values in incomplete information systems (IISs) according to the research target is still a key issue for investigating IISs. If the missing values in IISs are not handled properly, they will destroy the internal connection of data and reduce the efficiency of data usage. In this paper, in order to establish effective methods for filling missing values, we propose a new information system, namely, a fuzzy set‐valued information system (FSvIS). By means of the similarity measures of fuzzy sets, we obtain several binary relations in FSvISs, and we investigate the relationship among them. This is a foundation for the researches on FSvISs in terms of rough set approach. Then, we provide an algorithm to fill the missing values in IISs with fuzzy set values. In fact, this algorithm can transform an IIS into an FSvIS. Furthermore, we also construct an algorithm to fill the missing values in IISs with set values (or real values). The effectiveness of these algorithms is analyzed. The results showed that the proposed algorithms achieve higher correct rate than traditional algorithms, and they have good stability. Finally, we discuss the importance of these algorithms for investigating IISs from the viewpoint of rough set theory.
Highlights
We review some basic concepts related to general binary relations and information systems [22,23,24]
(ii) When the missing values are less than 30%, the correct rates of Algorithm FMvRV are almost unchanged and close to 90%
Conclusion is paper established the fuzzy set-valued information system (FSvIS), which is an extension of the PSvIS
Summary
We review some basic concepts and notations in rough sets and fuzzy sets. A general binary relation on a nonempty set U is a subset of U × U. We call (U, R) a generalized approximation space, where R is a binary relation on a finite nonempty set U. Similarity measure is an important concept in fuzzy set theory, and it is defined as follows: Definition 4 (see [26]). Ere is a common method to construct binary relation in terms of similarity measure as follows: RSBλ (x, y) ∈ U × U | S(a(x), a(y)) ≥ λ, ∀a ∈ B, (8). E Uncertainty Measures of FSvISs. In Section 3.1, we establish three similarity relations in FSvISs. If we use the rough set approach to investigate FSvISs, we usually need to choose reasonable similarity relations according to the actual condition.
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