Molodtsov investigated the pioneer notion of soft set (S_fS) which provides a general framework for mathematical problems by affix parameterization tools during the analysis as compared to fuzzy set and q‐rung orthopair fuzzy set (q‐ROFS). The aim of this manuscript is to investigate the notion of q‐rung orthopair fuzzy soft set (q‐ROFS_fS), which provide a lay of foundation for those difficulties and complexities which the contemporary theories face during the study of uncertainty. Therefore, our main contribution in this manuscript is to investigate the q‐rung orthopair fuzzy soft weighted averaging, q‐rung orthopair fuzzy soft ordered weighted averaging and q‐rung orthopair fuzzy soft hybrid averaging operators in q‐ROF soft (q‐ROFS_f) environment. Further, the fundamental properties of these aggregation operators are studied. On the base of developed approach an algorithm for multicriteria decision making method is being presented. An application of medical diagnosis problems is solved on the proposed algorithm under the q‐ROFS_f environment. Finally, comparison between the developed operators with some existing operators are being presented showing the superiority and efficiency of the developed approach than the existing literature.

The primitive notions of rough sets and intuitionistic fuzzy set (IFS) are general mathematical tools having the ability to handle the uncertain and imprecise knowledge easily. EDA $\mathcal {S}$ (Evaluation based on distance from average solution) method has a significant role in decision making problems, especially when more conflicting criteria exist in multicriteria group decision making (MCGDM) problems. The aim of this manuscript is to present intuitionistic fuzzy rough- EDA $\mathcal {S}$ (IFR- EDA $\mathcal {S}$ ) method based on IF rough averaging and geometric aggregation operators. In addition, we put forward the concept of IF rough weighted averaging (IFRWA), IF rough ordered weighted averaging (IFROWA) and IF rough hybrid averaging (IFRHA) aggregation operators. Furthermore, the concepts of IF rough weighted geometric (IFRWG), IF rough ordered weighted geometric (IFROWG) and IF rough hybrid geometric (IFRHG) aggregation operators are investigated. The basic desirable characteristics of the investigated operator are given in detail. A new score and accuracy functions are defined for the proposed operators. Next, IFR-EDA $\mathcal {S}$ model for MCGDM and their stepwise algorithm are demonstrated by utilizing the proposed approach. Finally, a numerical example for the developed model is presented and a comparative study of the investigated models with some existing methods are expressed broadly which show that the investigated models are more effective and useful than the existing approaches.

In real life, human opinion cannot be limited to yes or no situations as shown in an ordinary fuzzy sets and intuitionistic fuzzy sets but it may be yes, abstain, no, and refusal as treated in Picture fuzzy sets or in Spherical fuzzy (SF) sets. In this article, we developed a comprehensive model to tackle decision-making problems, where strong points of view are in the favour; neutral; and against some projects, entities, or plans. Therefore, a new approach of covering-based spherical fuzzy rough set (CSFRS) models by means of spherical fuzzy $\beta$ -neighborhoods (SF $\beta$ -neighborhoods) is adopted to hybrid spherical fuzzy sets with notions of covering the rough set. Then, by using the principle of TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) to present the spherical fuzzy, the TOPSIS approach is presented through CSFRS models by means of SF $\beta$ -neighborhoods. Via the SF-TOPSIS methodology, a multi-attribute decision-making problem is developed in an SF environment. This model has stronger capabilities than intuitionistic fuzzy sets and picture fuzzy sets to manage the vague and uncertainty. Finally, the proposed method is demonstrated through an example of how the proposed method helps us in decision-making problems.

The objective of this paper is to present new interactive averaging aggregation operators by assigning associate probabilities for T-spherical fuzzy sets (T-SFSs). T-SFS is a generalization of several existing theories such as intuitionistic fuzzy sets and picture fuzzy sets to handle imprecise information. Under such an environment, we developed a series of averaging interactive aggregation operators under the features that each element is represented with T-spherical fuzzy numbers. Various properties of the proposed operators are also investigated. Further, to rank the different T-SFSs, we exhibit the new score functions and state their some properties. To demonstrate the presented algorithm, a decision-making process algorithm is presented with T-SFS features. To save non-renewable resources and to the protect environment, the use of renewable resources is important. Solar energy is one of the best renewable energy resources and is also environment-friendly and thus the selection of solar cells is typically a multi-attribute decision-making problem. Therefore, the applicability of the developed algorithm is demonstrated with a numerical example in the selection of the solar cells and comparison of their performance with the several existing approaches.

In this manuscript we develop a comprehensive model to tackle decision making problems where strong points of view are in the favor and against some projects, entities or plans. Therefore a new approach is adopted to hybrid q-rung orthopair fuzzy sets with notions of covering rough set and TOPSIS. This model has stronger capability than intuitionistic fuzzy set and Pythagorean fuzzy set to manage the uncertainty. Furthermore an example is given to demonstrate how the proposed method helps us in decision making problems.

This paper aims to originate two new notions that are soft rough Pythagorean fuzzy set and Pythagorean fuzzy soft rough set, and investigate some important properties of soft rough Pythagorean fuzzy set and Pythagorean fuzzy soft rough set in detail. Furthermore, classical representations of Pythagorean fuzzy soft rough approximation operators are presented. Then the proposed operators are applied on decision-making problem in which the experts provide their preferences in Pythagorean fuzzy soft rough environment. Finally through an illustrative example, it is shown that how the proposed operators work in decision-making problems.