In multi-attribute group decision-making (MAGDM) problems, prioritization is sometimes important. Several techniques and methods have been introduced in fuzzy systems to use prioritization. The main purpose of this paper is to propose prioritized aggregation operators (AOs) for intuitionistic fuzzy (IF) information. These AOs are symmetric in nature and are based on the novel Aczel–Alsina t-norm and t-conorm. Herein, we propose IF-prioritized Aczel–Alsina averaging (IFPAAA) and IF-prioritized Aczel–Alsina geometric (IFPAAG) operators. It is shown that these AOs satisfy the basic features of aggregation. Some additional results for these AOs are also investigated. These proposed operators can capture the prioritization phenomenon among the aggregated arguments, and the weights for prioritization are obtained from expert information. Finally, the proposed AOs are used in an MAGDM problem where a doctor is selected for a hospital. A comparison of the proposed prioritized AOs is also established with other well-known AOs to show the significance of the IFPAAA and IFPAAG operators.

This study introduces Interval-valued T-Spherical Fuzzy Dombi Hamy Mean (IVT-SPFDHM) Operators as a powerful tool for group decision-making. The IVT-SPFDHM operators allow for prioritization of fuzzy data, effectively managing uncertainty. Its framework is applied in diverse group decision-making contexts, presenting its adaptability and robustness in addressing complex real-world problems. This study examines the Multi-Attribute Decision-Making (MADM) issue in the IVT-SPFDHM environment where the qualifications and expertise are at varying levels of necessity. We regard the novel Aczel-Alsina aggregation operators (AOs) as the most recently created AOs, capable of handling considerable uncertainty. To propose some AOs, we investigated the Hamy mean (HM) operator in the following environment: Interval-valued T-Spherical Fuzzy weighted Dombi Hamy mean (IVT-SPWDHM) operator, stretch esteemed interval valued T-Spherical Dual Dombi Hamy Mean (IVT-SPFDDHM), and Interval-valued T-Spherical Fuzzy weighted Dual Dombi Hamy Mean (IVT-SPFWDDHM). The weights for prioritization are derived from the knowledge of experts, and the proposed operators can capture the phenomenon of prioritization among the aggregated arguments. The MADM models are then planned using the IVPWDHM and IVPWDDHM operators. Finally, we provided a sample example within the prioritized ones to select the best antiviral mask for fighting COVID.

To handle problematic and ambiguous data, Schweizer and Sklar added a parameter p in 1960, which helped to develop the theory of SS t-norm (SSTN) and t-conorm (SSTCN). The parameter p=-1.1 can be used to easily derive the information of the Hamacher and Lukasiewicz t-norms. Furthermore, prioritized aggregation operators (PAOs) choose which data will be collected into a singleton set. The main contribution of this work is the construction of new aggregation operators for T-spherical fuzzy (T-SF) information based on SS t-norm and t-conorm. Moreover, the fundamental characteristics of the operators are identified. Further, we developed MADM (Multi-Attribute Decision-Making) models and deduced several useful properties from the operators T-SFSSPA, T-SFSSWPA, T-SFSSPG, and T-SFSSWPG. Finally, using an actual case study, we were able to draw the conclusion that, in comparison to the ground-breaking and current methods to enhance the value and capability of the diagnosed operators, the proposed MADM algorithm performs noticeably better than the operators in place for resolving the water recycling problem in a way that is easy to understand.

The fusion of information is a very hectic process whenever we analyze the information. Several frameworks have been introduced to reduce the uncertainty while fusing the information. Among those techniques, the Pythagorean fuzzy rough set (PyFRS), which is based on approximations is a key idea for dealing with uncertainty when data is taken from real-world circumstances. Furthermore, the most adaptable and flexible operational laws based on the parameters for fuzzy frameworks are Aczel-Alsina t-norm (AATNM) and Aczel-Alsina t-conorm (AATCNM). The major goal of this work is to introduce some methods for the basic operations of the information in the shape of Pythagorean fuzzy rough (PyFR) values (PyFRVs). Consequently, the PyFR Aczel-Alsina weighted geometric (PyFRAAWG), PyFR Aczel-Alsina ordered weighted geometric (PyFRAAOWG), and PyFR Aczel-Alsina hybrid weighted geometric (PyFRAAHWG) operators are developed in this article based on AATNM and AATCNM. Further, some basic properties of the developed operators are observed and discussed. Further, the developed approaches are applied to the problem of multi-attribute group decision-making (MAGDM). The obtained results from the MAGDM problem are observed at various values of the parameters involved by AATNM and AATCNM. Moreover, the results are also compared with already existing techniques for the significance of the developed approach.

One significant benefit of the Maclaurin symmetric mean (MSM) is that it is a generalization of many extend operators and can consider the interrelationships among the multi-input arguments, such as multi-attributes or multi-experts in the multi-attribute group decision making (MAGDM). In the information fusion process, the Schweizer-Sklar T-norm (TN) and T-conorm (TCN), an important class of the TN and TCN, have more flexibility. We define SS operational rules of SFNs and extend SSTN, SSTCN to Spherical fuzzy values (SFVs) in order to fully utilize the advantages of SSTN, SSTCN, and MSM. Next, by combining the MSM with SS operational rules, we propose the spherical fuzzy Schweizer-Sklar weighted Maclaurin symmetric mean (SFSSWMSM) and spherical fuzzy Schweizer-Sklar Maclaurin symmetric mean (SFSSMSM) operators. This research examines their advantages and creates a novel approach based on these operators for particular MAGDM issues. Then, by comparing the suggested technique with current approaches in practical settings, its benefits and viability are demonstrated. Lastly, a few real-world examples are provided to demonstrate the applicability and benefits of the suggested approach in comparison to a few other approaches already in use.

The proposed study introduces innovative Maclaurin symmetrical mean aggregation operators (MSMAO) in picture fuzzy multiple-attribute group decision-making. These operators are built upon a newly developed Frank t-norm (FTN) and t-conorm (TCN). Utilizing these novel operators aims to enhance the effectiveness of decision-making processes in scenarios characterized by picture-fuzzy information. The study explores these aggregation operators' potential applications and advantages within the context of multiple-attribute group decision-making under uncertainty. As a novel method to handle MAGDM difficulties, we build these aggregation operators (AOs) on PFs in this paper by utilizing the FTN and TCN under PFs information. In addition, PF values (PFVs) and their fundamental operations are created and shown. Picture fuzzy Frank weighted Maclaurin symmetrical mean (MFFWMSM) and Picture fuzzy Frank Maclaurin symmetrical mean (MFFMSM) operators are two AOs introduced and studied based on these operations. The induction approach theoretically and quantitatively verifies the newly created AOs' accuracy and dependability. The problem of project evaluation utilizing these proposed operators is thoroughly examined to provide further applications and investigate the sensitivity of these PS Frank (PFF) operators. The outcomes of employing these PFF operators are contrasted with a few AOs of PFVs that were previously in existence. The suggested strategy is dependable and effective based on comparison outcomes.