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Despite the significant advancements in fuzzy set theory, existing similarity measures for complex picture fuzzy sets (CPFSs) often result in impractical results in real-world scenarios. This presents a critical gap in accurately modeling and analyzing CPFSs, particularly in applications like pattern recognition and medical diagnosis. The present work addresses this problem by introducing various novel similarity measures for CPFSs, accompanied by rigorous axiomatic validation and a thorough discussion of their properties. Different sets of CPFSs have been empirically evaluated using both existing and proposed similarity measures, demonstrating the practical applicability and superiority of the latter. Based on the principle of maximum similarity, a comprehensive methodology involving these proposed measures has been illustrated, along with their implementation in solving different problems in pattern recognition and medical diagnosis. Additionally, a comparative analysis has been conducted to provide better clarity and understanding of the effectiveness of these measures. The results indicate that the proposed similarity measures offer significant advantages and improved accuracy for pattern recognition and medical diagnosis problems.

Numerous decision science processes involves the divergence measure is the most suitable information measure for dealing with the vagueness and impreciseness of the factors affecting the decision-making models. In this manuscript, a new kind of Hellinger information measure for a single-valued neutrosophic hypersoft set along with some important results have been presented and studied in detail. Also, we have presented the implementation of the proposed information measure to deal with the symptomatic detection of COVID-19 with a numerical illustration. In view of the existing methods related to divergence measures, some comparative results and remarks along with some important advantages have also been presented.

In this article, a new concept of the Complex Neutrosophic Matrix is introduced to solve different problems related to uncertainties. Based on the proposed matrix, we have provided various algebraic operations like addition, subtraction, union many others which will be of great help in establishing the fundamental concepts. The results obtained through the above operations will be consequently utilized in solving the higher-dimensional problems due to their matrix properties. This novel concept lays the foundation of various research solutions in the field of the complex neutrosophic matrix, which are yet to be considered by researchers. The matrix norm convergence of the proposed matrix has also been studied for the necessary foundation of the complex neutrosophic matrix. Also, the future studies of the proposed concept have been proposed.

In the last decades, different researchers have considerably incorporated the notion of neutrosophic sets, their properties and different measures for managing the uncertainty, impreciseness and vagueness in the information. It may be noted that neutrosophic set is a popular defined procedures for solving the classification problem and evaluation problem of decisionmaking. Numerical examples for the classification problem and the decision-making problem have also been presented and compared the obtained results with the well established existing approaches.

In the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a synchronized generalization of complex fuzzy sets and hesitant fuzzy sets in a systematic way. The novelty of the introduced notion lies in the selection of the best alternative among the available multiple favorable situations, where the possibility of its range is in the extended unit circle of the complex plane. We study the relationship between the CHFS and the complex intuitionistic fuzzy set (CIFS), along with validation of the obtained results. On the basis of the proposed notion, various properties, operations, and identities have been established with their necessary proof. The applications of CHFS in the process of filtering the signals for obtaining the reference signal using the necessary Fourier cosine transform or inverse Fourier cosine transform and identifying the maximum number of sunspots in a particular interval of solar activity have been suitably discussed with illustrative numerical examples. Some advantages of incorporating the proposed notion have also been tabulated for better understanding.

In various decision-making models the divergence measure is found to be a useful information measure in handling impreciseness and uncertainty among the qualitative and quantitative factors of the decision-making process. In the proposed work, a novel parametric divergence measure for neutrosophic sets has been proposed along with its various properties. On the basis of the proposed parametric divergence measure, we have outlined some methodologies along with its implementing procedural steps for classification problem (pattern recognition problem, medical diagnosis problem) and multi criteria decision making problem. Also, numerical examples for the application problems have been provided for illustration of the proposed methodologies. Comparative remarks along with necessary observations and advantages have also been presented in view of the existing appraoches.

The decision-making problems in which there are large numbers of qualitative and quantitative factors involved, the technique of dimensionality reduction plays an important role for simplicity and wider applicability. The impreciseness in the information about these factors are being considered in the neutrosophic perception with the parameters - degree of truth-membership, degree of indeterminacy (neutral) and degree of falsity for a better span of the information. In the present communication, we first propose a technique for finding the threshold value for the information provided in the form of neutrosophic soft matrix. Further, utilizing the proposed definitions of the object-oriented neutrosophic soft matrix and the parameter-oriented neutrosophic soft matrix, we present a new algorithm for the dimensionality reduction process. The proposed algorithm has also been applied in an illustrative example of decision-making problem. Further, a comparative analysis in contrast with the existing methodologies has been successfully presented with comparative remarks and additional advantages.

In the present communication, a parametric (R, S)-norm information measure for the Pythagorean fuzzy set has been proposed with the proof of its validity. The monotonic behavior and maximality feature of the proposed information measure have been studied and presented. Further, an algorithm for solving the multicriteria decision-making problem with the help of the proposed information measure has been provided keeping in view of the different cases for weight criteria, when weights are unknown and other when weights are partially known. Numerical examples for each of the case have been successfully illustrated. Finally, the work has been concluded by providing the scope for future work.

We introduce the concept of complex intuitionistic fuzzy soft sets which is parametric in nature. However, the theory of complex fuzzy sets and complex intuitionistic fuzzy sets are independent of the parametrization tools. Some real life problems, for example, multicriteria decision making problems, involve the parametrization tools. In order to get their new entropies, some important properties and operations on the complex intuitionistic fuzzy soft sets have also been discussed. On the basis of some well-known distance measures, some new distance measures for the complex intuitionistic fuzzy soft sets have also been obtained. Further, we have established correspondence between the proposed entropies and the distance measures of complex intuitionistic fuzzy soft sets.