Pythagorean fuzzy full implication multiple I method and corresponding applications
Pythagorean fuzzy full implication multiple I method and corresponding applications
复制标题
DOI：
10.3233/jifs-210527
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
TaiBen Nan;Haidong Zhang;Yanping He
中科院分区：
文献类型：
--
作者：
TaiBen Nan;Haidong Zhang;Yanping He
现有的结合毕达哥拉斯模糊集(PFS)的决策方法绝大多数都是基于聚集算子的，其逻辑基础不完善。因此，我们尝试建立两种基于毕达哥拉斯模糊多I方法的决策方法。本文致力于讨论基于PFS的全蕴涵多重I方法。我们首先提出了勾股t-范数、勾股t-余范、剩余勾股模糊蕴涵算子、勾股模糊双剩余以及基于勾股模糊双残数的模糊蕴涵算子之间的相似度等概念。此外，还建立了勾股模糊数学(PFMP)的全蕴涵多重I方法，并分析了PFMP全蕴涵多重I方法的可逆性和连续性。最后，通过一个实际问题的讨论，证明了勾股理论模糊全蕴涵多I方法在决策问题中的有效性。文中还解释了新方法相对于现有方法的优点。总体而言，所提出的方法都是基于逻辑推理的，因此能够更准确、完整地表达决策信息。
The overwhelming majority of existing decision-making methods combined with the Pythagorean fuzzy set (PFS) are based on aggregation operators, and their logical foundation is imperfect. Therefore, we attempt to establish two decision-making methods based on the Pythagorean fuzzy multiple I method. This paper is devoted to the discussion of the full implication multiple I method based on the PFS. We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO), Pythagorean fuzzy biresiduum, and the degree of similarity between PFSs based on the Pythagorean fuzzy biresiduum. In addition, the full implication multiple I method for Pythagorean fuzzy modus ponens (PFMP) is established, and the reversibility and continuity properties of the full implication multiple I method of PFMP are analyzed. Finally, a practical problem is discussed to demonstrate the effectiveness of the Pythagorean fuzzy full implication multiple I method in a decision-making problem. The advantages of the new method over existing methods are also explained. Overall, the proposed methods are based on logical reasoning, so they can more accurately and completely express decision information.