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首页> 外文期刊>International Journal Information Theories and Applications >Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets
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Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets

机译：定义两个模糊集之间矛盾程度的几何解释

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For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in [1] and [2], suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in [0,1] 2 . This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.
机译：在经典逻辑和模糊逻辑中，出于推理目的，信息本身都不应该相互矛盾，任何可用信息项也不应该相互矛盾。为了避免模糊逻辑中的这些麻烦，Trillas等人开始了对矛盾的研究。在[5]和[6]中。他们介绍了自相矛盾的模糊集和两个模糊集之间的矛盾的概念。而且，在[1]和[2]中指出不仅需要研究矛盾，而且需要研究这种矛盾的程度，并为此提出了一些措施。然而，矛盾本可以用其他方式来衡量。本文从几何角度着眼于研究两个模糊集之间的矛盾问题，从几何学的角度来看，这使我们找到了测量矛盾程度的新方法。为此，将两个模糊集解释为单位平方的子集，并确定所谓的矛盾区域。特别地，我们处理两个集合都表示[0,1] 2中的曲线的情况。这种新的几何方法使我们能够获得不同的功能来衡量整个距离的矛盾。而且，建立了这些矛盾量度函数的一些特性，并且在某些特定情况下，获得了这些不同函数之间的关系。

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