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Interpolativity of at-least and at-most models of monotone fuzzy rule bases with multiple antecedent variables

机译：具有多个先验变量的单调模糊规则库的最少和最多模型的内插性

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摘要

Of the many desirable properties of fuzzy inference systems, not all are known to co-exist. For instance, a fuzzy inference system should be interpolative, i. e., if a fuzzy set equivalent to one of the antecedent fuzzy sets appears on the input of such a system, the inferred output should be equivalent to the respective consequent fuzzy set. Similarly, the defuzzified output obtained from a system based on a monotone fuzzy rule base should be monotone, i. e., if x, x' are crisp inputs to the system that are ordered x <= x', then, the corresponding defuzzified outputs from the system y, y' should also be ordered accordingly, i. e., y <= y'. However, the particular setting that ensures monotonicity need not simultaneously ensure interpolativity. Recently, Stepnicka and De Baets have investigated and demonstrated the co-existence of the above two properties in the case of fuzzy relational inference systems and single-input-single-output (SISO) rule bases. An extension of these results to the multiple-input-single-output (MISO) case is not straightforward due to the lack of a natural ordering in higher dimensions. In this work, we study the MISO case and show that similar results can be obtained when the monotone rule base is modeled based on at-most and at-least modifiers. (C) 2015 Elsevier B. V. All rights reserved.
机译：在模糊推理系统的许多理想特性中，并不是所有已知特性都是共存的。例如，模糊推理系统应该是内插的，即。例如，如果等效于其中一个模糊集之一的模糊集出现在这样的系统的输入上，则推断的输出应等效于相应的相应模糊集。类似地，从基于单调模糊规则库的系统获得的去模糊输出应为单调，即。例如，如果x，x'是系统的明文输入，且其排序为x <= x'，则来自系统y，y'的相应去模糊输出也应相应地进行排序，即i。例如，y <= y'。但是，确保单调性的特定设置无需同时确保内插性。最近，Stepnicka和De Baets在模糊关系推理系统和单输入单输出（SISO）规则库的情况下研究并证明了上述两个属性的共存。将这些结果扩展到多输入单输出（MISO）情况并非易事，因为在高维中缺少自然排序。在这项工作中，我们研究了MISO情况，并表明当基于最多和最少修饰符对单调规则库进行建模时，可以获得类似的结果。 （C）2015 Elsevier B. V.保留所有权利。

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