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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.

Systematic assessment of insufficiencies and inexactness in the information along with parametrization of multi-sub attributes is one of the substantial features in the field of decision-making. In the present communication, a new way of defining Picture Fuzzy Hypersoft Set (PFHSS) has been presented which contains an additional capacity of accommodating the components of neutral membership (abstain) and refusal compared to intuitionistic fuzzy hypersoft set. The main objective of the present study is to establish the novelty of PFHSS with some of the basic operations and introduce various important aggregation operators. Some of the important properties and operational laws related to the introduced picture fuzzy hypersoft weighted average/ordered weighted average operator (PFHSWA/PFHSOWA) and weighted geometric/ordered weighted geometric operator (PFHSWG/PFHSOWG) have been proved in detail. On the basis of these aggregation operators and obtained results, a new algorithm for solving a decision-making problem, involving the multi-sub attributes and their parametrization in the shade of abstain and refusal feature, has been proposed. A numerical example of the selection process of employees for a company has been solved in order to suitably ensure and validate the implementation of the proposed methodology. Some of the advantageous features of the proposed notions and algorithm have been listed along with the comparative analysis in contrast with the existing literature. Finally, the efficacy of the proposed notion and methodology has been duly concluded with the scope for future work.