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.

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In the present manuscript, a novel concept of T -spherical fuzzy soft set is introduced with various important operations and properties. In the eld of information theory, an aggregation operator is a structured mathematical function that aggregates all the information received as input and provides a single output entity, found to be applicable for various important decision-making cases. Some averaging aggregation operators and geometric aggregation operators (weighted, ordered, and hybrid) for T -spherical fuzzy soft numbers have been proposed with their various properties. Further, utilizing the proposed aggregation operators of various types along with the properly de ned score function/accuracy function, an algorithm for solving a decision-making problem has been provided. The proposed methodology has also been well illustrated through a numerical example. Some comparative remarks and advantages of the introduced notion of Tspherical fuzzy soft set and the proposed methodology have been listed to ensure better motivation and readability.

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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.

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In the present communication, a new accuracy function is being provided to overcome the limitations of the existing score/accuracy functions for interval valued Pythagorean fuzzy sets. The proposed accuracy function has been validated and discussed in detail through the illustrative examples. Further, a new distance measure for interval valued Pythagorean fuzzy numbers has been proposed and used in context with the existing weighted averaging operators. Finally, in view of the proposed accuracy function, distance measure and weighted averaging operators, a numerical example of multi-criteria decision making process has been presented to validate the methodology.