Using fuzzy context-free grammars one can easily describe a finite number of ways to derive incorrect strings together with their degree of correctness. However, in general there is an infinite number of ways to perform a certain task wrongly. In this paper we introduce a generalization of fuzzy context-free grammars, the so-called fuzzy context-free $K$-grammars, to model the situation of making a finite choice out of an infinity of possible grammatical errors during each context-free derivation step. Under minor assumptions on the parameter $K$ this model happens to be a very general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism. Our first result characterizes the generating capacity of these fuzzy context-free $K$-grammars. As consequences we obtain: (i) bounds on modeling grammatical errors within the framework of fuzzy context-free grammars, and (ii) the fact that the family of languages generated by fuzzy context-free $K$-grammars shares closure properties very similar to those of the family of ordinary context-free languages.The second part of the paper is devoted to a few algorithms to recognize fuzzy context-free languages: viz. a variant of a functional version of Cocke-Younger- Kasami's algorithm and some recursive descent algorithms. These algorithms turn out to be robust in some very elementary sense and they can easily be extended to corresponding parsing algorithms.
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机译：使用模糊上下文无关文法，可以轻松地描述有限数量的方法来导出不正确的字符串及其正确程度。但是，通常有无数种错误执行某项任务的方法。在本文中，我们介绍了模糊上下文无关文法的泛化，即所谓的模糊上下文无关文法$ K $语法，以模拟在每次上下文无关过程中从无限可能的语法错误中进行有限选择的情况推导步骤。在参数$ K $的较小假设下，该模型恰好是一个非常通用的框架，可以通过单个生成机制正确描述以及错误地导出句子。我们的第一个结果表征了这些模糊的无上下文$ K $语法的生成能力。作为结果，我们得到：（i）在模糊上下文无关语法的框架内对语法错误进行建模的界限，以及（ii）由模糊上下文无关$ K $-语法生成的语言族具有非常相似的闭包特性本文的第二部分致力于识别模糊上下文无关语言的几种算法：即。 Cocke-Younger-Kasami算法的功能版本的变体和一些递归下降算法。这些算法在某些非常基本的意义上是可靠的，并且可以轻松地扩展为相应的解析算法。
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