Multiattribute decision‐making (MADM) approach is an effective method for handling ambiguous information in a practical situation. The process of the MADM technique has drawn a lot of interest from various academic and selection processes of extensive analysis. The aggregation operators (AOs) are the best mathematical tools and received a lot of attention from researchers. This article explored the theory of intuitionistic fuzzy IF sets (IFSs) and their certain fundamental operations. The theory of triangular norms also explores Aczel Alsina operations (AAOs) in advanced mathematical tools. The concepts of Heronian mean (HM) and geometric HM (GHM) operators are presented to define interrelationships among different opinions. We developed a list of certain AOs by utilizing AAOs under the system IF information, namely, IF Aczel Alsina HM (IFAAHM), IF Aczel Alsina weighted HM (IFAAWHM), IF Aczel Alsina GHM (IFAAGHM), and IF Aczel Alsina weighted GHM (IFAAWGHM) operators. Some particular characteristics of our invented methodologies are also presented. Solar energy is an effective, efficient resource to enhance electricity production and the country’s economic growth. Therefore, we studied an application of solar panel systems to solve real‐life problems under a robust technique of the MADM approach by utilizing our invented approaches of IFAAWHM and IFAAWGHM operators. A numerical example was also given to select more suitable solar panels under our proposed methodologies. To find the competitiveness and feasibility of discussed methodologies, we make an inclusive comparative study in which we contrast the results of existing AOs with the consequences of current approaches.

To cope with awkward and unreliable information in daily life issues, the theory of interval-valued picture fuzzy set (IVPFS) is a useful idea to manage unpredictable and vague information. An IVPFS contains the degree of truth, abstinence, and falsity in the finite subset of a unit interval with a rule that is the sum of the upper parts of all degrees is cannot exceed from unit interval. In this study, to find the interrelationships among any number of IVPFSs, we examined the interval-valued picture fuzzy frank averaging operator, interval-valued picture fuzzy frank weighted averaging operator, interval-valued picture fuzzy frank weighted geometric operator and discussed their properties. Moreover, some special cases of the presented operators based on IVPFSs are also discovered. The analytic hierarchy process (AHP) by using the IVPFSs is also explored and discussed in their different aspects. Finally, a multiattribute decision-making procedure is investigated by using proposed operators based on IVPFSs. We illustrated some numerical examples based on explored frank aggregation operators and AHP methods to examine the feasibility and validity of the presented approaches. The comparative analysis, geometrical representations, advantages of the investigated approaches are also discussed.

A pythagorean fuzzy set is a generalized fuzzy structure that copes with imprecisions of real life accurately and with a larger domain. The aim of this manuscript is to develop the notion of graph for newly established concept of interval-valued Pythagorean fuzzy set. We introduced the concept of interval-valued Pythagorean fuzzy graph (IVPyFG) and discussed its related ideas with the help of examples. The significance of using interval-valued fuzzy concepts over non-interval-valued fuzzy concepts are demonstrated numerically. Further, the advantages of using the new approach over the pre-existing ideas are demonstrated with the help of numerical examples. The main goal of this article is to study three types of decision-making problems using the framework of IVPyFGs. These three problems include the problem of selection of the best university in a network of universities, a supply chain management problem and the shortest path problem. The comparison of the new approach toward these problems with existing approaches is also established.