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基于粗糙商集的模糊隸屬度集值統計算法

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

  • 摘要: 模糊隸屬度無統一算法,定義存在分歧.根據模糊概念"內涵明確,外延不明確"的特點,定義隸屬度為不同外延對內涵的從屬程度.在信息系統中,概念的外延用對象表示,內涵由屬性表示,由此提出了求解隸屬度的新算法:由原始統計數據組成初始信息系統,用粗糙集理論求得其商集并構建集值信息系統;該集值信息系統對應的條件概率空間中的條件概率即為隸屬度.廣義上信息系統可分為信息系統(無決策屬性)和目標信息系統(有決策屬性)兩類.隸屬度也可分為兩類:第一類外延對象為內涵屬性本身值,如年齡對青年人的隸屬度(信息系統);第二類外延對象為不同于內涵屬性的另一屬性值,如邊坡工程安全系數對穩定狀態的隸屬度(目標信息系統).計算以上兩個實例,前者與已有結論作對比驗證,后者與函數選擇、經典統計方法及貝葉斯公理作對比驗證,可知結果可靠,算法可行.

     

    Abstract: 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.

     

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