逻辑公式的模糊度-计算机科学与探索.PDFVIP

于 鹏.逻辑公式的模糊度[J].计算机科学与探索，2015 ，9（5）：635-640. ISSN 1673-9418 CODEN JKYTA8 E-mail: fcst@vip. 163.com Journal of Frontiers of Computer Science and Technology 1673-9418/2015/09(05)-0635-06 Tel: +86-10 doi: 10.3778/j.issn. 1673-9418.1406054 逻辑公式的模糊度* 于 鹏+ 陕西科技大学 理学院，西安 710021 Fuzzy Degree of Logical Formula YU Peng+ Faculty of Science, Shaanxi University of Science Technology, Xi ’an 710021, China + Corresponding author: E-mail: yupeng@ YU Peng. Fuzzy degree of logical formula. Journal of Frontiers of Computer Science and Technology, 2015, 9 (5) ：635-640. Abstract: From the view whether it is easy to judge a formula correctly or not, this paper proposes the concept of fuzzy degree of a given formula in classical two-valued logic, which uses the numbers of a propositional logic assign- ment 1 and 0. This paper gives the related properties of fuzzy degree, and points out the connections and differences between fuzzy degree and the definition of truth degree in quantitative logic. The following conclusions are got: (1) In a reasoning process, with the lower of the fuzzy degree of premise, the fuzzy degree of conclusion is also lower; (2) The set which constitutes of the same fuzzy degree proposition formulas is inconsistent; (3) If the distance of two formulas is closer, the fuzzy degree of two formulas is closer. Key words: quantitative logic; fuzzy degree; approximate reasoning; truth degree 摘 要：从判断一个命题正确与否的难易程度入手，在经典的二值逻辑系统中，利用一个命题公式赋值为1 与 赋值为0 的个数，引入了一个反映命题公式清晰程度的量——模糊度。给出了模糊度的相关性质，指出了模糊 度与计量逻辑学中真度定义之间的联系与区别，得到如下结论：（1）在一个推理中过程中，随着前提模糊度的 降低，结论的模糊度也随之降低；（2 ）具有相同模糊度的命题公式构成的命题集是一个不相容命题集；（3）两个 距离相近的命题公式，其模糊度也十分接近。 * The Natura