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In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similarity measure, weighted set-theoretic cosine similarity measure, grey similarity measure and weighted grey similarity measure. Then, we apply these similarity measures between picture fuzzy sets to building material recognition and minerals field recognition. Finally, two illustrative examples are given to demonstrate the efficiency of the similarity measures for building material recognition and minerals field recognition.

We extend to fuzzy similarity measures the study made for classical ones in a companion paper (Coletti and Bouchon-Meunier in Soft Comput 23:6827–6845, 2019). Using a classic method of measurement theory introduced by Tversky, we establish necessary and sufficient conditions for the existence of a particular class of fuzzy similarity measures, representing a binary relation among pairs of objects which expresses the idea of “no more similar than”. In this fuzzy context, the axioms are strictly dependent on the combination operators chosen to compute the union and the intersection.

The location of the electric vehicle charging station is deemed to be a multiple attribute group decision making (MAGDM) issue involving many experts and many conflicting attributes. In practical MAGDM issues, the information of uncertain and fuzzy cognitive decision is well-depicted by linguistic term sets (LTSs). These LTSs could be simply shifted into the probabilistic linguistic sets (PLTSs). In such paper, we design some novel probabilistic linguistic weighted Dice similarity measures (PLWDSM) and the probabilistic linguistic weighted generalized Dice similarity measures (PLWGDSM). Subsequently, the PLWGDSM-based MAGDM methods are presented under PLTSs. In the end, a practical case which concerns about the location planning of electric vehicle charging stations is offered to demonstrate the proposed PLWGDSM’s applicability and advantages.

Distance-based algorithms are widely used for data classification problems. The k-nearest neighbour classification (k-NN) is one of the most popular distance-based algorithms. This classification is based on measuring the distances between the test sample and the training samples to determine the final classification output. The traditional k-NN classifier works naturally with numerical data. The main objective of this paper is to investigate the performance of k-NN on heterogeneous datasets, where data can be described as a mixture of numerical and categorical features. For the sake of simplicity, this work considers only one type of categorical data, which is binary data. In this paper, several similarity measures have been defined based on a combination between well-known distances for both numerical and binary data, and to investigate k-NN performances for classifying such heterogeneous data sets. The experiments used six heterogeneous datasets from different domains and two categories of measures. Experimental results showed that the proposed measures performed better for heterogeneous data than Euclidean distance, and that the challenges raised by the nature of heterogeneous data need personalised similarity measures adapted to the data characteristics.

The location of the electric vehicle charging station (EVCS) is the important link in the construction of the EVCS. The optimal location of the electric vehicle directly affects the operating efficiency of the charging station and the satisfaction of the electric vehicle user, site selection play an important part throughout whole life cycle, which is deemed to be multiple attribute group decision making (MAGDM) issue involving many experts and many conflicting attributes. In practical MAGDM issues, the information of uncertain and fuzzy cognitive decision is well-depicted by uncertain linguistic term sets (ULTSs). These ULTSs could be simply shifted into the probabilistic uncertain linguistic sets (PULTSs). In such paper, we design some novel probabilistic uncertain linguistic weighted Dice similarity measures (PULWDSM) and the probabilistic uncertain linguistic weighted generalized Dice similarity measures (PULWGDSM). Subsequently, the PULWGDSM-based MAGDM methods are presented under PULTSs. In the end, a practical case which concerns about the location planning of electric vehicle charging stations is offered to demonstrate the proposed PULWGDSM’s applicability and advantages.

In this paper, we introduced some similarity measures for bipolar neutrosophic sets such as; Dice similarity measure, weighted Dice similarity measure, Hybrid vector similarity measure and weighted Hybrid vector similarity measure. Also we examine the propositions of the similarity measures. Furthermore, a multi-criteria decision-making method for bipolar neutrosophic set is developed based on these given similarity measures. Then, a practical example is shown to verify the feasibility of the new method. Finally, we compare the proposed method with the existing methods in order to demonstrate the practicality and effectiveness of the developed method in this paper.

In this article, we propose another form of ten similarity measures by considering the function of membership degree, non-membership degree, and indeterminacy membership degree between the q-ROFSs on the basis of the traditional cosine similarity measures and cotangent similarity measures. Then, we utilize our presented ten similarity measures and ten weighted similarity measures between q-ROFSs to deal with multiple attribute decision-making (MADM) problems including pattern recognition and scheme selection. Finally, two numerical examples are provided to illustrate the scientific and effective of the similarity measures for pattern recognition and scheme selection.

This paper contributes multivariate versions of seven commonly used elastic similarity and distance measures for time series data analytics. Elastic similarity and distance measures can compensate for misalignments in the time axis of time series data. We adapt two existing strategies used in a multivariate version of the well-known Dynamic Time Warping (DTW), namely, Independent and Dependent DTW, to these seven measures. While these measures can be applied to various time series analysis tasks, we demonstrate their utility on multivariate time series classification using the nearest neighbor classifier. On 23 well-known datasets, we demonstrate that each of the measures but one achieves the highest accuracy relative to others on at least one dataset, supporting the value of developing a suite of multivariate similarity and distance measures. We also demonstrate that there are datasets for which either the dependent versions of all measures are more accurate than their independent counterparts or vice versa. In addition, we also construct a nearest neighbor-based ensemble of the measures and show that it is competitive to other state-of-the-art single-strategy multivariate time series classifiers.

The most straightforward approaches to checking the degrees of similarity and differentiation between two sets are to use distance and cosine similarity metrics. The cosine of the angle between two n-dimensional vectors in n-dimensional space is called cosine similarity. Even though the two sides are dissimilar in size, cosine similarity may readily find commonalities since it deals with the angle in between. Cosine similarity is widely used because it is simple, ideal for usage with sparse data, and deals with the angle between two vectors rather than their magnitude. The distance function is an elegant and canonical quantitative tool to measure the similarity or difference between two sets. This work presents new metrics of distance and cosine similarity amongst Fermatean fuzzy sets. Initially, the definitions of the new measures based on Fermatean fuzzy sets were presented, and their properties were explored. Considering that the cosine measure does not satisfy the axiom of similarity measure, then we propose a method to construct other similarity measures between Fermatean fuzzy sets based on the proposed cosine similarity and Euclidean distance measures and it satisfies the axiom of the similarity measure. Furthermore, we obtain a cosine distance measure between Fermatean fuzzy sets by using the relationship between the similarity and distance measures, then we extend the technique for order of preference by similarity to the ideal solution method to the proposed cosine distance measure, which can deal with the related decision-making problems not only from the point of view of geometry but also from the point of view of algebra. Finally, we give a practical example to illustrate the reasonableness and effectiveness of the proposed method, which is also compared with other existing methods.

Set pair analysis (SPA) is an updated theory for dealing with the uncertainty, which overlaps with the other existing theories such as vague, fuzzy, intuitionistic fuzzy set (IFS). Keeping the advantages of it, in this paper, we propose some novel similarity measures to measure the relative strength of the different intuitionistic fuzzy sets (IFSs) after pointing out the weakness of the existing measures. For it, a connection number, the main component of SPA theory is formulated in the form of the degrees of identity, discrepancy, and contrary. Then, based on it some new similarity and weighted similarity measures between the connection number sets are defined. A comparative analysis of the proposed and existing measures are formulated in terms of the counter-intuitive cases for showing the validity of it. Finally, an illustrative example is provided to demonstrate it.