Theory of Γ-truth degree of formulas in continuous-valued Lukasiewicz system and its properties

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (13): 30-32.

• 研究、探讨 • Previous Articles Next Articles

Theory of Γ-truth degree of formulas in continuous-valued Lukasiewicz system and its properties

YANG Jinfeng1，CUI Yanli1，2，WU Hongbo2

1.Hanzhong Vocational and Technical College，Hanzhong，Shaanxi 723000，China
2.College of Mathematics & Information Science，Shaanxi Normal University，Xi’an 710062，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-05-01 Published:2011-05-01

连续值Luk系统中公式的Γ-真度及其性质

杨进峰1，崔艳丽1，2，吴洪博2

1.汉中职业技术学院，陕西汉中 723000
2.陕西师范大学数学与信息科学学院，西安 710062

Abstract

Abstract: The truth degree theory of Lukasiewicz system is further studied.Having combined the theory of [ΣΓ]-truth degree of formulas in n-valued Lukasiewicz system with the integrated truth degree theory in continuous-valued Lukasiewicz system，the concept of Γ-truth degree of formulas is introduced which is relative to the finite theory in continuous-valued Lukasiewicz system，and some essential properties are discussed.Simultaneously，the Γ-pseudo-metric onF(S)is established in Lukasiewicz system by employing the theory of Γ-truth degree.These results can broaden the scope of application of truth degree theory.

Key words: fuzzy logic, Lukasiewicz system, finite theory, integrated truth degree, Γ-truth degree, Γ-pseudo-metric

摘要： 对Lukasiewicz系统中的真度理论进行了进一步的研究。将n值Lukasiewicz系统中公式相对于有限理论的ΣΓ-真度理论与连续值Lukasiewicz系统中公式的积分真度相结合，在连续值Lukasiewicz系统中引入了公式相对于有限理论的Γ-真度理论，讨论了其中的主要性质；在公式集F(S)上引入了任意两公式相对于有限理论的Γ-伪距离，从而拓宽了真度理论的应用范围。

关键词: 模糊逻辑, Lukasiewicz系统, 有限理论, 积分真度, Γ-真度, Γ-伪距离

YANG Jinfeng1，CUI Yanli1，2，WU Hongbo2. Theory of Γ-truth degree of formulas in continuous-valued Lukasiewicz system and its properties[J]. Computer Engineering and Applications, 2011, 47(13): 30-32.

杨进峰1，崔艳丽1，2，吴洪博2. 连续值Luk系统中公式的Γ-真度及其性质[J]. 计算机工程与应用, 2011, 47(13): 30-32.

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Theory of Γ-truth degree of formulas in continuous-valued Lukasiewicz system and its properties

连续值Luk系统中公式的Γ-真度及其性质

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