Recently, a new extension of fuzzy sets, Pythagorean fuzzy sets (PFS), has attracted a lot of attention from scholars in various fields of research. Due to PFS’s powerfulness in modeling the imprecision of human perception in multicriteria decision‐making (MCDM) problems, this paper aims to extend the classical preference ranking organization method of enrichment evaluations (PROMETHEE) into the Pythagorean fuzzy environment. The proposed method takes not only the weights related to different criteria but also the preference relations as Pythagorean fuzzy numbers, therefore providing a broader range of choices for the decision‐maker to express their preferences. Five properties are put forward to regulate the designing of both intuitionistic and Pythagorean fuzzy PROMETHEE (PF‐PROMETHEE) preference functions. Furthermore two illustrative examples are given to demonstrate the detailed procedure of PF‐PROMETHEE, and comparisons are made to distinguish the differences among our proposed method, the classical PROMETHEE and intuitionistic PROMETHEE. The results show that PF‐PROMETHEE is effective, comprehensive, and applicable to a wide range of MCDM problems.
Machine learning applications have achieved impressive results in many areas and provided effective solution to deal with image recognition, automatic driven, voice processing etc. problems. As these applications are adopted by multiple critical areas, their reliability and robustness becomes more and more important. Software testing is a typical way to ensure the quality of applications. Approaches for testing machine learning applications are needed. This paper analyzes the characteristics of several machine learning algorithms and concludes the main challenges of testing machine learning applications. Then, multiple preliminary techniques are presented according to the challenges. Moreover, the paper demonstrates how these techniques can be used to solve the problems during the testing of machine learning applications.
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