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论文:2023,Vol:41,Issue(2):439-445 |
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引用本文： |
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王波, 惠小静, 鲁星. NM理论中积分真度的统一理论[J]. 西北工业大学学报 |
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WANG Bo, HUI Xiaojing, LU Xing. Unified theory of integral true degrees in NM theory[J]. Journal of Northwestern Polytechnical University |
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| NM理论中积分真度的统一理论 |
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| 王波, 惠小静, 鲁星 |
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| 延安大学 数学与计算机科学学院, 陕西 延安 716000 |
| 摘要: |
| 基于在幂零极小逻辑NM(nilpotent minimun)命题逻辑系统中,通过将公式诱导的函数进行积分的方法提出了公式的积分真度概念,利用积分不变性证明了积分真度MP规则、HS规则;在NM命题逻辑系统的全体公式之集上引入了积分相似度和积分伪距离,并且证明了关于相似度和伪距离的一些性质;通过发散度以及直径的概念,提出了NM命题模糊逻辑中反映理论相容程度新的隶属函数,利用隶属函数给出了相容度的概念,证明了不相容理论的相容度为0,完全相容理论的相容度为1。 |
| 关键词:
NM命题逻辑系统
积分真度
伪距离
相容度
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| Unified theory of integral true degrees in NM theory |
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| WANG Bo, HUI Xiaojing, LU Xing |
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| Mathematics and Computer Science College, Yan'an University, Yan'an 716000, China |
| Abstract: |
| Based on the NM propositional logic system of nilpotent minimum logic, the concept of the integral truth degree of the formula is firstly proposed by integrating the function induced by the formula, and the MP rule and HS rule of the integral truth degree are proved by means of the integral invariance. Secondly, in NM propositional logic the integral similarity and integral pseudo-distance are introduced into the set of general formulas of the system, and some good properties about the similarity and pseudo-distance are proved. Finally, in terms of the concept of divergence degrees and diameter, a new membership function for reflecting the consistency degrees of theories in NM propositional fuzzy logic is proposed, which is proved that of inconsistent theories are equal to 0 and that of completely consistent theories are equal to 1. |
| Key words:
NM propositional logic system
integral truth degree
pseudo-distance
consistency degree
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| 收稿日期: 2022-06-30
修回日期:
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| DOI: 10.1051/jnwpu/20234120439 |
| 基金项目: 国家自然科学基金(12261090)资助 |
| 通讯作者: 惠小静(1972-),延安大学教授,主要从事数理逻辑与不确定性推理研究。e-mail:xhmxiaojing@163.com
Email：xhmxiaojing@163.com |
| 作者简介: 王波(1997-),延安大学硕士研究生,主要从事数理逻辑与不确定性推理研究。
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| 作者相关文章 |
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| 王波 在本刊中的所有文章 |
| 惠小静 在本刊中的所有文章 |
| 鲁星 在本刊中的所有文章 |
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参考文献: |
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[1] ROSSER J B, TURQUETTE A R. Many-valued logic[M]. Amsterdamm:North-Holland, 1952:46-66
[2] PAVELKA J. On fuzzy logic Ⅰ,Ⅱ,Ⅲ[J]. Zeitschr f Math Logic and Grundlagen d Math, 1979, 25(1):45-52
[3] WANG Guojun, FU Li, SONG Jianshe. Theory of truth degrees of propositions in two-valued logic[J]. Science in China(Series A), 2002, 45(9):1106-1116
[4] 王国俊, 宋建设. 命题逻辑中的程度化方法[J]. 电子学报, 2006, 34(2):252-257 WANG Guojun, SONG Jianshe. Graded method in propositional logic[J]. Acta Electronica Sinica, 2006, 34(2):252-257 (in Chinesse)
[5] 惠小静. 基于真值的SBL_~公理化扩张系统的计量化[J]. 中国科学:信息科学,2014, 44(7):900-911 HUI Xiaojing. Quantification of truth-based SBL_~axomatic expansion systems[J]. Science in China:Information Science, 2014,44(7):900-911 (in Chinese)
[6] WANG Guojun, SHE Yehong. Topological description of divergency and consistency of two-valuedpropositionaltheories[J]. Acta Mathematical Sinica, Chinese Series, 2007, 50(4):841-850
[7] ZHOU Hongjun. Borel probabilistic and quantitative logic[J]. Science China Information Science, 2010, 53(2):1-12
[8] WANG Guojun, LEUNG Y. Integrated semantics and logic metricspaces[J]. Fuzzy Sets and Systems, 2003, 136(4):71-91
[9] WANG Guojun. A unified integrated method for evaluating goodness of propositions in several propositional logic systems and its applications[J]. Chinese Journal of Electronics, 2012, 21(2):195-201
[10] 李骏, 邓富喜. n值S-MTL命题逻辑系统中公式真度的统一理论[J]. 电子学报, 2011, 39(8):1864-1868 LI Jun, DENG Fuxi. Unified theory of truth degrees in n-valued S-MTL propositional logic[J]. Acta Electronica Sinica, 2011, 39(8):1864-1868 (in Chinese)
[11] 李骏, 姚锦涛. 命题逻辑系统SMTL中公式的积分真度理论[J]. 电子学报, 2013, 41(5):878-883 LI Jun, YAO Jintao. Integral truth degree theory of formulas in propositional logic system SMTL[J]. Journal of Electronics, 2013, 41(5):878-883 (in Chinese)
[12] ESTEVA F, GODO L. Monoidal t-norm based logic:towards a logic for left-continuous t-normas[J]. Fuzzy Sets and Systems, 2001, 124(4):271-288
[13] 裴道武. 基于三角模的模糊逻辑理论及其应用[M]. 北京:科学出版社, 2013 PEI Daowu. Fuzzy logic theory based on triangle mode and its application[M]. Beijing:Science Press, 2013 (in Chinese)
[14] 王国俊. 非经典数理逻辑与近似推理[M]. 北京:科学出版社, 2008 WANG Guojun. Non-classical mathematical logic and approximate reasoning[M]. Beijing:Science Press, 2008 (in Chinese)
[15] 王国俊. 数理逻辑引论与归结原理[M].2版. 北京:科学出版社, 2006 WANG Guojun. Introduction to mathematical logical and resolution principle[M]. 2nd ed. Beijing:Science Press, 2006 (in Chinese)
[16] WANG Guojun, ZHANG Wenxiu. Consistency degrees of finite theories in Lukasiewicz propositional fuzzy logic[J]. Fuzzy Sets and Systems, 2005, 149(2):275-284
[17] ZHOU Xiangnan, WANG Guojun. Consistency degrees of theories in some systems of propositional fuzzy logic[J]. Fuzzy Sets and Systems, 2005, 152(2):321-331
[18] ZHOU Hongjun, WANG Guojun. A new theory consistency index based on deduction theorems in several logic sysstem[J]. Fuzzy Sets and Systems, 2006, 157(3):327-443 |
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