Set-valued statistical algorithm for fuzzy membership based on the rough quotient set

There is no uniform algorithm for fuzzy membership, and the definitions differ. According to the characteristic of the fuzzy concept"the meaning is clear and the extension is ambiguous", the membership is defined as the subordinate degree of different extensions to the connotation. In information systems, the extension of the theory of knowledge discovery is expressed by the object, and the meaning is expressed by its attributes. Based on the research results, a new algorithm for calculating the membership was proposed:the initial information systems are composed of original statistical data, and the set-valued information system is constructed by the quotient set which uses the rough set theory; in the set-valued information system, the conditional probability in the corresponding conditional probability space is the membership. In general, the information systems are divided into information systems without decision attributes and target information systems with decision-making attributes. The membership is also divided into two categories:firstly, the content of the extension object is the value of the property itself, such as young people to the age (information system); secondly, the extension object is different from the content attribute value of another property, such as engineering safety factor to stability (target information system). These two instances were calculated, the former is compared with the existing research results and the latter is verified by the function selection, classical statistical method and Bayesian formula; it is shown that the algorithm is feasible and the results are reliable.