中文摘要：

研究了类序关系下剩余型双极值fuzzy modus ponesns（FMP）问题的3I推理方法。通过引入类双极值诱导函数的概念,在单极算子和类双极值算子之间构建了一座桥梁。特别地给出了由单极剩余蕴涵构建类双极值剩余蕴涵的方法。在此基础上,给出了类序关系下剩余型双极值FMP问题的3I推理方法,并证明其解可以分解为两个相应的剩余型单极FMP问题的解。通过引入类双极值度量的概念,证明了本文提出的算法具有较好的鲁棒性,从而保证了其在实际控制系统中的应用。

英文摘要：

The aim of this paper is to research residual 3I method to bipolar-valued FMP problems under the bipolar category relation. By introducing the novel concept of the bipolar-valued category induced function, a bridge is constructed to connect bipolar-valued category operations with the corresponding unipolar operations, and the bipolar-valued category residual implicationinduced from unipolar residual implication is obtained. Based on the new defined implication, the residual 3I methods to bipolar-valued FMP problems under the bipolar category relationis put forth, together with the solutions, which are proved that can be degenerated to two corresponding unipolar 3I FMP solutions. The proposed method is proved to possess the virtue of robustness by introducing the concept of bipolar-valued category metric, which assures its application in the practical control system.