Compensatory Fuzzy Logic is a transdisciplinary axiomatic theory, different from the Classical Norm and Conorm approach to improving interpretability by natural language. Archimedean Compensatory Fuzzy Logic (ACFL), introduced recently, uses different properties and interpretations of involved truth values. Membership functions involved are not studied explicitly in fuzzy theories, even though it is essential in solving problems. The definition of parameterized families of membership functions is not rare in fuzzy literature. However, according to our review, each of those families has the same shape except the recently introduced Continuous Linguistic Variables. That has been a limitation in the expressiveness of linguistic values. Besides, except for Dombi’s theory, these functions are often not related to logical operators. This paper aims to use ACFL to overcome each of these drawbacks. We generalize some fuzzy concepts, only using the ACFL generator function. A Generalized Sigmoidal Function and a Generalized Linguistic Modifier are s-shaped functions generated by it. Those elements define a parameterized family containing different shape functions like an increasing sigmoidal, decreasing sigmoidal and convex function; we call it a Generalized Continuous Linguistic Variable. This paper improves ACFL by unifying it into single theory elements like logic generator functions, linguistic modifiers, membership functions, and linguistic variables. The improved ACFL is not just a Pluralist Logic that makes compatible the classical approach of Norm and Conorm with CFL theory, but a contextual pluralist logic able to select a logic that better expresses specific contextual knowledge. This theory is valuable in Knowledge Discovery; because it creates new searching elements that allow selecting the `best logic´ for a particular dataset. We develop knowledge discovery cases for different databases to illustrate it and show its data sensitivity.

Compensatory Fuzzy Logic 是一种跨学科的公理化理论，不同于通过自然语言提高可解释性的 Classical Norm 和 Conorm 方法。最近推出的阿基米德补偿模糊逻辑 (ACFL) 使用不同的属性和对涉及的真值的解释。模糊理论中没有明确研究所涉及的隶属函数，尽管它在解决问题中是必不可少的。隶属函数的参数化族的定义在模糊文献中并不少见。然而，根据我们的评论，除了最近引入的连续语言变量之外，这些家族中的每一个都具有相同的形状。这是语言价值表达的一个限制。此外，除了 Dombi 的理论之外，这些函数通常与逻辑运算符无关。本文旨在使用 ACFL 来克服这些缺点中的每一个。我们概括了一些模糊概念，仅使用 ACFL 生成器函数。一广义 Sigmoidal 函数和广义语言修饰符是由它生成的 S 形函数。这些元素定义了一个包含不同形状函数的参数化族，如递增 sigmoidal、递减 sigmoidal 和凸函数；我们称之为广义连续语言变量. 本文通过将 ACFL 统一为逻辑生成器函数、语言修饰符、隶属函数和语言变量等单一理论元素来改进 ACFL。改进后的 ACFL 不仅是一种使 Norm 和 Conorm 的经典方法与 CFL 理论兼容的多元逻辑，而且是一种能够选择更好地表达特定上下文知识的逻辑的上下文多元逻辑。这个理论在知识发现中很有价值；因为它创建了新的搜索元素，允许为特定数据集选择“最佳逻辑”。我们为不同的数据库开发知识发现案例来说明它并展示它的数据敏感性。