Koczy-Hirota模糊线性插值的分段线性度和基准研究
Investigating The Piece-Wise Linearity And Benchmark Related To Koczy-Hirota Fuzzy Linear Interpolation
摘要：
模糊规则插值（FRI）推理方法已被引入，以解决稀疏的模糊规则库和降低复杂性。第一个FRI方法是Koczy和Hirota（KH）提出的“线性插值”。此外，还提出了几个条件和准则，以统一FRI方法必须满足的共同要求。其中一个重要条件是，如果模糊规则的前件和后件在α-截集上保持分段线性（PWL），则结论的模糊集必须保持PWL。KH-FRI方法是不能满足这一条件的FRI方法之一。因此，本文的目标是研究与PWL性质相关的方程和符号，旨在突出KH FRI方法的问题性质，以证明其在PWL条件下的有效性。此外，本文的重点是构建基准的例子是一个基线，用于测试其他FRI方法的情况下，不满足KH FRI的线性条件。
英文摘要：
Fuzzy Rule Interpolation (FRI) reasoning methods have been introduced to address sparse fuzzy rule bases and reduce complexity. The first FRI method was the Koczy and Hirota (KH) proposed "Linear Interpolation". Besides, several conditions and criteria have been suggested for unifying the common requirements FRI methods have to satisfy. One of the most conditions is restricted the fuzzy set of the conclusion must preserve a Piece-Wise Linearity (PWL) if all antecedents and consequents of the fuzzy rules are preserving on PWL sets at α-cut levels. The KH FRI is one of FRI methods which cannot satisfy this condition. Therefore, the goal of this paper is to investigate equations and notations related to PWL property, which is aimed to highlight the problematic properties of the KH FRI method to prove its efficiency with PWL condition. In addition, this paper is focusing on constructing benchmark examples to be a baseline for testing other FRI methods against situations that are not satisfied with the linearity condition for KH FRI.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
