To find the correspondence between every number of attributes, the Bonferroni mean (BM) operator is most widely used and proven to be a flexible approach. To express uncertain information, the frame of the interval-valued T-spherical fuzzy set (IVTSFS) is a recent development in fuzzy settings which discusses four aspects of uncertain information using closed sub-intervals of $\left[0,1\right]$ and hence reduces the information loss greatly. In this research study, we introduced the principle of BM operators with IVTSFS to develop the principle of the inter-valued T-spherical fuzzy (IVTSF) BM (IVTSFBM) operator, the IVTSF-weighted BM (IVTSFWBM) operator, the IVTSF geometric BM (IVTSFGBM) operator, and the IVTSF-weighted geometric BM (IVTSFWGBM) operator. To see the significance of the proposed BM operators, we applied these BM operators to evaluate the performance of solar cells that play an important role in the field of energy storage. To do so, we developed a multi-attribute group decision-making (MAGDM) procedure based on IVTSF information and applied it to the problem of solar cells to evaluate their performance under uncertainty, where four aspects of opinion about solar cells were taken into consideration. We studied the results obtained using BM operators with some previous operators to see the significance of the proposed IVTSF BM operators.

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.

To develop the theory of aggregation operators based on the Aczel-Alsina t-norm and t-conorm is a very challenging task for individuals, where the idea of Aczel-Alsina norms is the modified version of the algebraic norms. The main theme of this manuscript is to evaluate the Aczel-Alsina operational laws and Aczel-Alsina aggregation operators for complex single-valued neutrosophic (CSVN) information such as CSVN Aczel-Alsina weighted averaging (CSVNAAWA), CSVN Aczel-Alsina ordered weighted averaging (CSVNAAOWA), CSVN Aczel-Alsina hybrid averaging (CSVNAAHA), CSVN Aczel-Alsina weighted geometric (CSVNAAWG), CSVN Aczel-Alsina ordered weighted geometric (CSVNAAOWG), CSVN Aczel-Alsina hybrid geometric (CSVNAAHG) operators, idempotency, monotonicity, and boundedness. Additionally, in the presence of the above-derived operators, we illustrated a model of the MADM “multi-attribute decision-making” procedure for CSVN values. Finally, we employed various numerical examples to demonstrate the supremacy and efficiency of the discovered theory to compare it with various prevailing operators.

The impact of airborne pollutants present in the environment, entering the body through breathing, can cause significant risks of respiratory and heart-related health problems for individuals. For this, different air purifiers are commonly used to eliminate delicate particulate matter PM_2.5, and various studies have examined their effectiveness. This paper aims to analyze airborne pollutants and, by considering them, assess the performance of air purifiers in reducing the concentration of air pollutants in the environment. The aggregation operator (AO) plays a significant role in aggregating the multiple criteria and gives us a result in a singleton set, which assists us in decision-making (DM). So, considering this, the Heronian mean (HM) operator and its special cases such as averaging and geometric operators have been used in this paper. Moreover, circular intuitionistic fuzzy (C-IF) theory is more efficient and comprehensive than the intuitionistic fuzzy set (IFS), as the standard IFS cannot cope with the problems within a circular environment. So, the HM operator under the C-IF environment, such as circular intuitionistic fuzzy Heronian mean (C-IFHM) and it’s averaging and geometric operator, has been presented. Further, some prevalent and crucial properties and theorems have been defined. Then, an algorithm was developed to solve a multicriteria decision-making (MCDM) problem by using the proposed operators within the circular environment. To validate the effectiveness and priority, this paper presents a numerical example of MCDM, and a comparison analysis was conducted to verify the practicality of the proposed approach.

A single-valued Neutrosophic hesitant fuzzy set (SVNHFS) is a combination of a single-valued neutrosophic set (SVNS) and hesitant fuzzy set (HFS) that has been developed to address insufficient, unreliable, and vague environments in which each element has several possible options determined by the truthiness, indeterminacy and falsity value. By considering this, in this paper, we have proposed the Aczel-Alsina aggregation operator (AAAO) for SVNHFS, which is more flexible t-norm and t-conorm than the other and due to the flexible nature of parameters to solve Multi-Attribute decision making (MADM) problems. Further, the score function, accuracy function, and certainty function of SVNHFS have been defined. In this paper, we proposed the single-valued neutrosophic hesitant fuzzy Aczel-Alsina Weighted Averaging Operator (SVNHFAAWA), single-valued neutrosophic hesitant fuzzy Aczel-Alsina Weighted ordered Averaging Operator (SVNHFAAWOA), and single-valued neutrosophic hesitant fuzzy Aczel-Alsina hybrid averaging operator (SVNHFAAHA). To testify to the reliability and stability of the newly created aggregation operator (AO), an application of MADM has been discussed.

Many aggregation operators are studied to deal with multi-criteria group decision-making problems. Whenever information has two aspects, intuitionistic fuzzy sets and Pythagorean fuzzy sets are employed to handle the information. However, q-rung orthopair fuzzy sets are more flexible and suitable because they cover information widely. The current paper primarily focuses on the multi-criteria group decision-making technique based on prioritization and two robust aggregation operators based on Aczel–Alsina t-norm and t-conorm. This paper suggests two new aggregation operators based on q-rung orthopair fuzzy information and Aczel–Alsina t-norm and t-conorm, respectively. Firstly, novel q-rung orthopair fuzzy prioritized Aczel–Alsina averaging and q-rung orthopair fuzzy prioritized Aczel–Alsina geometric operators are proposed, involving priority weights of the information. Several related results of the proposed aggregation operators are investigated to see their diversity. A multi-criteria group decision-making algorithm based on newly established aggregation operators is developed, and a comprehensive numerical example for the selection of the most suitable energy resource is carried out. The proposed aggregation operators are compared with other operators to see some advantages of the proposed work. The proposed aggregation operators have a wider range for handling information, with priority degrees, and are based on novel Aczel–Alsina t-norm and t-conorm.