Information structures and entropy measurement for a fuzzy probabilistic information system

An information system (IS), an important model in the field of artificial intelligence, takes information structure as the basic structure. A fuzzy probabilistic information system (FPIS) is the combination of some fuzzy relations in the same universe that satisfy probability distribution. A FPIS as an IS with fuzzy relations includes three types of uncertainties (i.e., roughness, fuzziness and probability). This paper studies information structures in a FPIS from the perspective of granular computing (GrC). Firstly, two types of information structures in a FPIS are defined by set vectors. Then, equality, dependence and independence between information structures in a FPIS are proposed, and they are depicted by means of the inclusion degree. Next, information distance between information structures in a FPIS is presented. Finally, entropy measurement for a FPIS is investigated based on the proposed information structures. These results may be helpful for understanding the nature of structures and uncertainty in a FPIS.

Attribute significance based on inclusion degree for incomplete information systems and their applications to MADM problems

Attribute significance is very important in multiple-attribute decision-making (MADM) problems. In a MADM problem, the significance of attributes is often different. In order to overcome the shortcoming that attribute significance is usually given artificially. The purpose of this paper is to give attribute significance computation formulas based on inclusion degree. We note that in the real-world application, there is a lot of incomplete information due to the error of data measurement, the limitation of data understanding and data acquisition, etc. Firstly, we give a general description and the definition of incomplete information systems. We then establish the tolerance relation for incomplete linguistic information system, with the tolerance classes and inclusion degree, significance of attribute is proposed and the corresponding computation formula is obtained. Subsequently, for incomplete fuzzy information system and incomplete interval-valued fuzzy information system, the dominance relation and interval dominance relation is established, respectively. And the dominance class and interval dominance class of an element are got as well. With the help of inclusion degree, the computation formulas of attribute significance for incomplete fuzzy information system and incomplete interval-valued fuzzy information system are also obtained. At the same time, results show that the reduction of attribute set can be obtained by computing the significance of attributes in these incomplete information systems. Finally, as the applications of attribute significance, the attribute significance is viewed as attribute weights to solve MADM problems and the corresponding TOPSIS methods for three incomplete information systems are proposed. The numerical examples are also employed to illustrate the feasibility and effectiveness of the proposed approaches.

A three-way decision method based on hybrid data1

An information system as a database that represents relationships between objects and attributes is an important mathematical model in the field of artificial intelligence. Hybrid data means boolean, categorical, real-valued, set-valued data and missing data in this paper. A hybrid information system is an information system where its attribute is hybrid data. This paper proposes a three-way decision method based on hybrid data. First, the distance between two objects based on the conditional attribute set in a given hybrid information system is developed and Gaussian kernel based on this distance is acquired. Then, the fuzzy Tcos-equivalence relation, induced by this information system, is obtained by using Gaussian kernel. Next, the decision-theoretic rough set model in this hybrid information system is presented. Moreover, a three-way decision method is given by means of this decision-theoretic rough set model and inclusion degree between two fuzzy sets. Finally, an example is employed to illustrate the feasibility of the proposed method, which may provide an effective method for hybrid data analysis in real applications.