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A bipolar neutrosophic set (BNS) is designed to handle uncertain information by capturing both supportive and opposing aspects of data. In this paper, the pattern classification method is studied based on the proposed Hamming–Chebyshev hybrid distance measure (HCHDM). First, the HCHDM of the bipolar neutrosophic sets is proposed that not only captures discrete differences, but also reflects the maximum dimensional deviation in a more complex environment. Then, the axiomatic definition of the distance measure is proved and some examples are given to show it can better discriminate between the differences of BNSs. Based on the distance measure, an algorithm to solve the pattern classification problem is given. The numerical examples show that the proposed distance measure method is effective in solving pattern classification problems.

The picture fuzzy set (PFS) is a powerful tool to collect and handle large amounts of uncertain assess information in a new light. In this study, we explore some distance measures for the PFSs and propose Picture fuzzy ordered weighted distance measure and Picture fuzzy hybrid weighted distance measure. Some of their properties are also mathematically explored. Moreover, we introduce a model for the aforesaid distance measures to solve multiple attribute group decision making (MAGDM) method in an updated way. And at the end of our paper a practical application of investment alternatives selection is provided to illustrate the validity and applicability of the presented work.

In a wireless communication system, due to the presence of the surrounding objects, the amplitude of the received signal rapidly changes by reflection, diffraction, and scattering and noise is added to the received signal. This prompts multipath fading and interference, which affects the quality of communication. The proposed Adaptive Routing Scheme (ARS) considers the algorithm Reliable Routing (RR) using Average Bit Error Rate expressed in Nakagami-m fading channel (ABERN-m) to predict the quality of the link, the Energy Efficient Routing (EER) calculates Remaining Battery Energy (RBE) to extend the network lifetime. The Canberra Distance Measure (CDM) is used instead of Euclidean Distance Measure (EDM) to improve the accuracy of distance measurement in mobile nodes. The aim of the proposed scheme is to predict the best optimal path and maintain the consistent path to enhance the Quality of Service (QoS) in real-time communication to improve efficient traffic on the road. First published online 5 June 2020

Xu and Chen (J Syst Sci Syst Eng 17:432–445, 2008 ) introduced a type of ordered weighted distance measures called ordered weighted distance (OWD) measures whose fundamental aspect is the reordering step, which can be used in many actual fields, including group decision making, medical diagnosis, data mining, and pattern recognition, etc. The OWD measures are very suitable to deal with situations where the input data are expressed in exact numerical values. In this paper, we consider situations with linguistic, interval or fuzzy preference information, and develop some fuzzy ordered distance measures, such as linguistic ordered weighted distance measure, uncertain ordered weighted distance measure, linguistic hybrid weighted distance measure, and uncertain hybrid weighted distance measure, etc. After that, based on hybrid weighted distance measures, we establish a consensus reaching process of group decision making with linguistic, interval, triangular or trapezoidal fuzzy preference information.

The objective of this work is to present a novel multi-attribute decision making (MADM) method under interval-valued intuitionistic fuzzy (IVIF) set environment by integrating a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. Set pair analysis (SPA) theory is the modern uncertainty theory which is composed by the three components, namely “identity”, “discrepancy” and “contrary” degrees of the connection number (CN) and overlap with the various existing theories for handling the uncertainties in the data. Thus, motivated by this, in the present work, an attempt is made to enrich the theory of information measure by presented some exponential based distance measures using CNs of the IVIF sets. The supremacy of the proposed measure is also discussed. Afterward, a TOPSIS method based on the proposed distance measures is developed to solve MADM problem under IVIF environment where each of the element is characteristics by IVIF numbers. The utility, as well as supremacy of the approach, is confirmed through a real-life numerical example and validate it by comparing their results with the several existing approaches results.

The intuitionistic fuzzy set (IFS), as a generation of Zadeh’s fuzzy set, can express and process uncertainty much better. Similarity measures between IFSs are used to indicate the similarity degree between the information carried by IFSs. Although several similarity measures for IFSs have been proposed in previous studies, some of them cannot satisfy the axioms of similarity, or provide counterintuitive cases. In this paper, we first review several widely used similarity measures and then propose a new similarity measures. As the consistency of two IFSs, the proposed similarity measure is defined based on the direct operation on the membership function, non-membership function, hesitation function and the upper bound of membership function of two IFS, rather than based on the distance measure or the relationship of membership and non-membership functions. It proves that the proposed similarity measure satisfies the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns. Experiments on medical diagnosis and cluster analysis are carried out to illustrate the applicability of the proposed similarity measure in practice.

Connection number (CN) is one of the key features of a set pair analysis (SPA) theory to describe uncertainties in terms of three degrees, namely “identity”, “discrepancy” and “contrary”. In the present manuscript, the work has been done under environment of the intuitionistic fuzzy set, and some axioms of the distance measures based on Hamming, Euclidean, and Hausdorff metrics have been proposed whose preferences related to the attributes are made in the form of CN. Their desirable relations have also been investigated. Furthermore, based on these measures, an approach to investigating the decision-making problem has been presented. The effectiveness of the approach has been demonstrated through a case study. The comparative study as well as the advantages of the proposed measures over the existing measures has been presented.

The MULTIMOORA method is better than some of the existing decision making methods. However, it has not been improved to process Pythagorean fuzzy sets (PFSs). The decision results of the MULTIMOORA method greatly depend on the distance measure and score function. Although there are many studies focusing on proposing distance measures and score functions for PFSs, they still show some defects. In this paper, we propose two novel distance measures and a novel score function for PFSs for proposing a novel Pythagorean fuzzy MULTIMOORA method. To this end, two distance measures, Dice distance and Jaccard distance, are proposed for computing the deviation degree between two PFSs, and their general forms are also discussed. Afterward, a novel score function based on determinacy degree and indeterminacy degree is put forward for approximately representing PFSs. Then, the original MULTIMOORA method is extended by using the Dice distance and score function and it is used to solve the multicriteria decision making problems under the PFS information context. Finally, a real case for evaluating solid-state disk productions is handled using the proposed Pythagorean fuzzy MULTIMOORA method and another case for evaluating energy projects is given to verify the advantages of our studies by comparing them with the existing Pythagorean fuzzy distance measures, score functions, and decision making methods.

As a popular tool for modeling the qualitative assessment information, the hesitant fuzzy linguistic term sets (HFLTSs) can allow the decision makes or experts to give several possible linguistic terms to rate the objects with respect to the criterion. Although there exist many multi-criteria decision-making methods put forward for handling the HFLTSs, they were developed based on the assumption that the decision makers can always provide completely rational assessments and they do not take the decision makers’ psychological behaviors into consideration. In this paper, the traditional TODIM (an acronym in Portuguese for interactive multi-criteria decision making) method is extended to handle the HFLTSs based on the novel comparison function and distance measure. Firstly, we put forward a novel function for comparing two HFLTSs more effectively. After that, a novel hesitance degree function as well as some novel distance measures are given for HFLTSs. Then we apply them to extend the traditional TODIM method for solving the HFLTSs. Finally, a practical example concerning the evaluation and ranking of several satellite launching centers is provided to illustrate the validity and applicability of the proposed method.