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| 基于支持度理论的广义Modus Ponens问题的最优解 |
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李骏1,2, 王国俊1
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1.陕西师范大学,数学与信息科学学院,陕西,西安,710062;2.兰州理工大学,理学院,甘肃,兰州,730050
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| 摘要: |
| 为了将模糊推理纳入逻辑的框架并从语构和语义两个方面为模糊推理奠定严格的逻辑基础,通过将模糊推理形式化的方法移植到经典命题逻辑系统中,把FMP(fuzzy modus ponens)问题转化为GMP(generalized modus ponens)问题,并基于公式的真度概念提出了公式之间的支持度,进一步利用支持度的思想引入了GMP问题以及CGMP(collective generalized modus ponens)问题的一种新型最优求解机制.证明了最优解的存在性,同时指出,在经典命题逻辑系统中存在着与模糊逻辑完全相似的推理机制.该方法是一种程度化的方法,这就使得求解过程从算法上实现成为可能,并对知识的程度化推理有所启示. |
| 关键词: GMP(generalized modus ponens)问题 CGMP(collective generalized modus ponens)问题 真度 支持度 最优解 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.10331010 (国家自然科学基金); the Innovation Foundation for Doctors of Shaanxi Normal University of China (陕西师范大学博士创新基金); the Outstanding Youth Foundation of Lanzhou University of Technology of China (兰州理工大学优秀青年基金) |
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| Optimal Solutions Based on Sustentation Degree for Problems of Generalized Modus Ponens |
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LI Jun,WANG Guo-Jun
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| Abstract: |
| In order to put fuzzy reasoning into the framework of logic and lays a solid logical foundation for fuzzy reasoning both syntactically and semantically,this paper transforms FMP(fuzzy modus ponens)into GMP (generalized modus ponens)by formalizing fuzzy reasoning and transplanting it into the classical propositional logic.Base on the concept of truth degrees of formulas,the sustentation degrees between formulas are put forward and a new kind of optimal solving mechanism is established for GMP and CGMP(collective generalized modus ponens).Existence theorems of optimal solutions are proved both for GMP and CGMP,and it is pointed out that there exists a completely similar reasoning mechanism between the classical propositional logic and the fuzzy logic. The graded method presented in this paper makes the algorithmic realization of solution procedure possible and serves as a guideline for the graded reasoning about knowledge. |
| Key words: GMP(generalized modus ponens)problem CGMP(collective generalized modus ponens)problem truth degree sustentation degree optimal solution |
