For any country, the availability of electricity is crucial to the development of the national economy and society. As a result, decision-makers and policy-makers can improve the sustainability and security of the energy supply by implementing a variety of actions by using the evaluation of these factors as an early warning system. This research aims to provide a multi-criterion decision-making (MCDM) method for assessing the sustainability and security of the electrical supply. The weights of criteria, which indicate their relative relevance in the assessment of the sustainability and security of the energy supply, the MCDM method allow users to express their opinions. To overcome the impact of uncertainty and vagueness of expert opinion, we explore the notion of picture fuzzy theory, which is a more efficient and dominant mathematical model. Recently, the theory of Aczel-Alsina operations has attained a lot of attraction and has an extensive capability to acquire smooth approximated results during the aggregation process. However, Choquet integral operators are more flexible and are used to express correlation among different attributes. This article diagnoses an innovative theory of picture fuzzy set to derive robust mathematical methodologies of picture fuzzy Choquet Integral Aczel-Alsina aggregation operators. To prove the intensity and validity of invented approaches, some dominant properties and special cases are also discussed. An intelligent decision algorithm for the MCDM problem is designed to resolve complicated real-life applications under multiple conflicting criteria. Additionally, we discussed a numerical example to investigate a suitable electric transformer under consideration of different beneficial key criteria. A comparative study is established to capture the superiority and effectiveness of pioneered mathematical approaches with existing methodologies.

Disorders of the skin have been identified as skin diseases. These medical disorders may involve severe skin manifestations, including allergic reactions, frustration, and itching. Numerous skin disorders may be inherited, while other aspects may be caused by lifestyle. To diagnose the various skin disorders based on the symptoms of skin diseases, we introduce the novel idea of Interval-Valued T-Spherical Fuzzy Set (IV-TSFS) that significantly enhances the ability to handle vagueness and unpredictability in the data being gathered. The IV-TSFS takes the concept of T-SFS by incorporating Interval Values (IVs). This innovation greatly improves the capacity to represent and manage uncertainty because they offer a structured and flexible framework that captures real-world ambiguity, vagueness, and unpredictability as compared to other classical fuzzy models. In this article, we construct the extended conventional IV-TSF Evaluation based on Distance from Average Solution (EDAS) approach by using the conventional Evaluation based on Distance from Average Solution (EDAS) method and also identifying a wide range of possibilities and understanding the potential variability in outcomes, which is especially useful in Decision-Making (DM) scenarios. This method provides a balanced view of each alternative’s performance, helping decision-makers to rank and select the most suitable option effectively. It is the most powerful way to visualize and compare the performance of various alternatives in a structured and quantitative manner. Firstly, we briefly review the description of T-SFSs and IV-TSFSs and discuss the score function Ṩcr(₮), accuracy function Ἇcr(₮), and the basic Operational Laws (OLs) of IV-TSFVs. Next, we explain the extensive interventions of the extended conventional Interval-Valued T-Spherical Fuzzy (IV-TSF) EDAS method to cope with uncertain and unreliable information, which is especially useful in DM scenarios. Finally, a numerical example is provided to effectively diagnose the favorable skin disease based on the symptoms of skin diseases by using the IV-TSF EDAS approach, and several comparative results of our proposed model with other existing Aggregation Operators (AOs) are carried out to demonstrate the invaluable benefits associated with this strategy.

The following paper presents a new analytical framework for the optimization of player positioning, a methodology with significant practical implications. The method implements the multi-objective optimization by ratio analysis with full multiplicative form (MULTIMOORA) in a decision-making context in which several non-commensurable performance variables have to be combined. The application of Dombi operationalizes the framework by prioritizing weighted aggregation operators coupled with circular q-rung orthopair fuzzy sets (Cq-ROFSs). The Cq-ROFSs allow multidimensional representation of uncertainty, and allow dynamic actions upon the fuzzy parameter q, such that both intuitionistic fuzzy sets and Pythagorean fuzzy sets are subsets. Two Dombi prioritized operators on Cq-ROFSs are thereby devised a Cq-ROFSs Dombi prioritized weighted averaging operator (Cq-ROFSDPWA) and a Cq-ROFSs Dombi prioritized weighted geometric operator (Cq-ROFSDPWG). Results from empirical experiments are reported that demonstrate the performance of the resulting methodology, highlighting its practical relevance. The fundamental properties of these operators are also examined. The proposed aggregation operators are applied within the MULTIMOORA technique to assess their effectiveness. Numerical examples demonstrate that the methods yield logical and consistent results across different decision-making scenarios. Comparative analyses further highlight the advantages of the Cq-ROFSDPWA and Cq-ROFSDPWG operators over existing approaches.