Research On Machine Learning With Ordered Pair Of Normalized Real Numbers

The ordered pair of normalized real numbers(OPNs)is a mathematical theory newly proposed in 2020.It combines two normalized real numbers into a single real number pair,and through a unique calculation method,compares,analyzes,and calculates the two real numbers in pairs.Compared to other mathematical theories such as complex numbers,intuitionistic fuzzy numbers,and Pythagorean fuzzy numbers,OPNs have fewer restrictions on the size relationship between real numbers and are more convenient for combination.Based on this advantage,this paper introduces OPNs into machine algorithms for the first time,and uses its mathematical advantages to improve existing machine learning algorithms,mainly including the following four research aspects:1.Multiple-similarity classification algorithm with OPNs.Due to the large impact of the selected similarity or distance metric on classification algorithms such as K-nearest neighbors(KNN),and the difficulty in selecting the optimal similarity or distance metric,the K-Nearest Neighbor Classification Algorithm with OPNs(OPNs-KNN)is proposed.The algorithm first converts ordinary data into OPNs using multiple similarity metrics,and then uses OPNs distance metrics to achieve OPNs classification.Compared with 6 improved algorithms such as distance-weighted K-nearest neighbor rules on datasets such as Iris and seeds,the experimental results show that the highest classification accuracy is improved by 15.28 percentage points.2.multiple similarity clustering algorithm with OPNs.Aiming at the problem that the clustering effect of the existing Fuzzy C-means clustering algorithm(FCM)is also greatly affected by the similarity or distance measurement method adopted,and it is difficult to choose the optimal similarity or distance measurement.The algorithm of Ordered pair of normalized real numbers clustering(OPNC)was proposed.Based on the distance measurement between OPNs proposed in OPNs-KNN algorithm,this algorithm expands the FCM algorithm,which makes the expanded OPNC algorithm can cluster OPNs.Since OPNs contain different similarity information,OPNC algorithm can further improve the clustering performance by combining different similarity measures.Experiments on multiple real data sets and comparison with other clustering algorithms verify that OPNC algorithm has excellent performance.3.Dimension reduction algorithm with OPNs.Currently,various dimensionality reduction algorithms have their own advantages and disadvantages,and their performance varies greatly on different datasets.This paper proposes a method to combine different dimensionality reduction algorithms through OPNs,to achieve complementary effects and further improve the accuracy of subsequent classification.Compared to existing work,this algorithm achieves the combination of different dimensionality reduction algorithms from a completely new perspective.By comparing the classification performance of the KNN algorithm on the new dataset after using a single algorithm for dimensionality reduction,the algorithm proposed in this paper has better classification performance.4.Fuzzy analytic hierarchy process with OPNs.Most analytic hierarchy processes(AHP)rely on expert judgments to determine priority levels and support decision-making.However,expert judgments may be subjective to some extent.We can also use machine learning algorithms to make objective decisions,but the judgments given by machine learning algorithms are closely related to the collected data and are not flexible enough.Therefore,this paper proposes a fuzzy analytic hierarchy process with the OPNs(OFAHP)using OPNs to combine expert judgments with machine learning algorithm judgments,and then make decisions through OPNs.This method retains decision flexibility while avoiding decisionmaking errors caused by expert biases.The case study verifies that this method can produce reasonable decision results,and when expert judgments are incorrect or invalid,the judgments of machine learning algorithms can correct expert opinions to obtain reasonable decision results.