Zadeh's (min-max, standard) fuzzy logic and various other logics are commutative, but natural language has nuances suggesting the premises are not equal, with premises contributing to the conclusion according to their prominency. Therefore, we suggest variants of salience-based, noncommutative and non-associative fuzzy logic (prominence logic) that may better model natural language and reasoning when using linguistic variables. Noncommutative fuzzy logics have several theoretical and applicative motivations to be used as models for human inference and decision making processes. Among others, asymmetric relations in economy and management, such as buyer-seller, provider-user, and employer-employee are noncommutative relations and induce noncommutative logic operations between premises or conclusions. A class of noncommutative fuzzy logic operators is introduced and fuzzy logic systems based on the corresponding noncommutative logics are described and analyzed. The prominence of the operators in the noncommutative operations is conventionally assumed to be determined by their precedence. Specific versions of noncommutative logics in the class of the salience-based, noncommutative logics are discussed. We show how fuzzy logic systems may be built based on these types of logics. Compared with classic fuzzy systems, the noncommutative fuzzy logic systems have improved performances in modeling problems, including the modeling of economic and social processes, and offer more flexibility in approximation and control. Applications discussed include management and engineering problems and issues in the field of firms’ ethics or ethics of AI algorithms.

中文翻译：

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非交换逻辑系统及其在管理和工程中的应用

Zadeh的（最小-最大，标准）模糊逻辑和其他各种逻辑是可交换的，但是自然语言有细微差别，表明前提不相等，前提根据其突出程度对结论做出了贡献。因此，我们建议使用基于显着性，非交换性和非关联性的模糊逻辑（突出逻辑）的变体，这些变体在使用语言变量时可能会更好地建模自然语言和推理。非可交换模糊逻辑具有多种理论和应用动机，可用作人类推理和决策过程的模型。经济与管理中的不对称关系，例如买卖双方，提供者-用户和雇主-雇员之间的关系是非交换关系，并且会在前提或结论之间引发非交换逻辑运算。介绍了一类非交换模糊逻辑算子，并描述和分析了基于相应非交换逻辑的模糊逻辑系统。传统上假定非交换运算符中运算符的突出程度由其优先级确定。在基于显着性的非交换逻辑类中讨论了非交换逻辑的特定版本。我们展示了如何基于这些类型的逻辑构建模糊逻辑系统。与经典模糊系统相比，非交换模糊逻辑系统在建模问题（包括经济和社会过程的建模）方面具有改进的性能，并且在逼近和控制方面提供了更大的灵活性。讨论的应用程序包括公司伦理学或AI算法伦理学中的管理和工程问题。