Fast assignment reduction in inconsistent incomplete decision systems

This paper focuses on fast algorithm for computing the assignment reduct in inconsistent incomplete decision systems. It is quite inconvenient to judge the assignment reduct directly ac-cording to its definition. We propose the judgment theorem for the assignment reduct in the inconsistent incomplete decision system, which greatly simplifies judging this type reduct. On such basis, we derive a novel attribute significance measure and construct the fast assignment reduction algorithm （F-ARA）, intended for com-puting the assignment reduct in inconsistent incomplete decision systems. Final y, we make a comparison between F-ARA and the discernibility matrix-based method by experiments on 13 Univer-sity of California at Irvine （UCI） datasets, and the experimental results prove that F-ARA is efficient and feasible.

Rough Integrals Generated by Function Rough Sets

The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.

Uncertainty and Reduction in Intuitionistic Fuzzy Covering Based Rough Sets

This paper proposes a novel pair of induced IF covering approximation operators in an IF covering approximation space,and discusses some basic properties about definable IFSs.A measure is defined to describe the uncertainty of IFSs in IF covering approximation spaces.Finally,we study the properties of reductions of an IF covering respectively based on induced IF covering approximation operators and IF covering approximation operators.

θ-improved limited tolerance relation model of incomplete information system for evaluation of water conservancy project management modernization

The modernization of water conservancy project management is a complicated engineering system involving a management system, a management method, management personnel, the exertion of social, economic, and ecological effects, and so on. However, indices for evaluating the modernization of water conservancy project management are usually unobtainable in practical applications. Conducting appropriate extension of the classical rough set theory and then applying it to an incomplete information system are the key to the application of the rough set theory Based on analysis of some extended rough set models in incomplete information systems, a rough set model based on the θ-improved limited tolerance relation is put forward. At the same time, upper approximation and lower approximation are defined under this improved relation. According to the evaluation index system and management practices, the threshold for θ is defined. An example study indicates the practicability and maneuverability of the model.

Uncertainty Representation of Ocean Fronts Based on Fuzzy-Rough Set Theory

Analysis of ocean fronts＇ uncertainties indicates that they result from indiscemibility of their spatial position and fuzziness of their intensity. In view of this, a flow hierarchy for uncertainty representation of ocean fronts is proposed on the basis of fuzzy-rough set theory. Firstly, raster scanning and blurring are carried out on an ocean front, and the upper and lower approximate sets, the indiscernible relation in fuzzy-rough theories and related operators in fuzzy set theories are adopted to represent its uncertainties, then they are classified into three sets： with members one hundred percent belonging to the ocean front, belonging to the ocean front＇s edge and definitely not belonging to the ocean front. Finally, the approximate precision and roughness degree are utilized to evaluate the ocean front＇s degree of uncertainties and the precision of the representation. It has been proven that the method is not only capable of representing ocean fronts＇ uncertainties, but also provides a new theory and method for uncertainty representation of other oceanic phenomena.

Rough Sets in Approximate Solution Space

As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and incomplete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set.A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.