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Picture fuzzy sets (PFSs), the generalization of intuitionistic fuzzy sets (IFSs), are more capable of dealing with vague data in real-life problems. Models based on PFSs may be suitable particularly in those circumstances where human perceptions become challenging as well as various kinds of reasoning, like yes, no, abstention, or denial. The aggregation operators (AOs) are essential components in information aggregation as they have the ability to aggregate a group of fuzzy numbers into a single fuzzy number of the same kind. A lot of aggregation operations for PFSs have been developed. Nevertheless, the existing aggregation operators for picture fuzzy information are inaccurate as they fail to aggregate a group of picture fuzzy numbers into a single picture fuzzy number (PFN). To cover the drawbacks of existing AOs, we developed some modified picture fuzzy aggregation operators (PFAOs) named as picture fuzzy modified weighted averaging (PFMWA), picture fuzzy modified ordered weighted averaging (PFMOWA) and picture fuzzy modified hybrid averaging (PFMHA) aggregation operator along with their distinctive features. These operators are essential in developing new multi-criteria decision-making (MCDM) techniques. This paper defines a number of stakeholder roles (or tactics), with an objective of overcoming the challenges to executing Education 4.0 (EDUC4) that have recently been highlighted in the literature. A MCDM problem provides the basis for the evaluation of the responsibilities of the stakeholders with respect to these constraints. Several management concerns are provided as stepping stones for the development of EDUC4 implementation. The purpose of this study is to identify the qualities that influence the degree of optimism for the adoption and implementation of the EDUC4 in Pakistan's education system while taking government policies into account. [ABSTRACT FROM AUTHOR]

Dombi t-norm (DTN) and t-conorm (TCN) are among the most effective triangular norms in fuzzy systems for aggregation purposes. The environment of interval-valued intuitionistic fuzzy (IVIF) set gives us precision in expressing uncertain information by using a membership grade (MG) and non-membership grade (NMG) in the form of closed subintervals of 0 ,   1 . The goal of this paper is to introduce DTN-based aggregation operators (AOs) for IVIF numbers (IVIFNs) and study their performance in the evaluation of the worth of energy recourses to be opted in Pakistan to deal with the energy crises situation. We first introduced some DTN and TCN-based operations for IVIFNs and developed two new AOs known as IVIF Dombi weighted averaging (IVIFDWA) and IVIF Dombi weighted geometric (IVIFDWG) operators. The validity and fitness of the proposed operators are tested. A case study is presented where the energy resources of Pakistan are discussed and the problem of the selection of sustainable energy resources in the context of Pakistan is investigated. The sensitivity analysis of the proposed IVIFDWA and IVIFDWG operators is studied and a comparative analysis of the current work with previous studies is established. [ABSTRACT FROM AUTHOR]

The harmful waste products, beverages, chemical agents that are discharged or emitted by industrial processes are categorized as industrial waste (IW). IW is one of the most severe problems facing governments around the world due to its environmental effect and severity. So the aim of this paper is to develop a method for selecting industrial waste management technique (IWMT) for industry. Dombi Norms were commonly referred to as Dombi operations, but their applications might be better expressed if they are presented with a new level of flexibility within the general parameter. Dombi operations have not yet been applied in non-linear Diophantine fuzzy sets (N-LDFSs) in a suitable form. Therefore we apply the Dombi operators on complex N-LDFS (CN-LDFS) and develop a generalized area of research in decision making problems (DMPs). The majority of decision-making challenges in the actual world contain a wide range of elements that must be taken into account. Making decision under such circumstances can frequently be challenging. To deal with such complicated issues, we require multi-attribute group decision-making (MAGDM) techniques. The aims to discuss MAGDM issues, this paper will introduce a new COmbinative Distance-based ASsessment (CODAS) methodology. In this paper, we put forward three novel aggregation operators (AOs): complex non-linear Diophantine fuzzy Dombi weighted averaging (CN-LDFDWA), complex non-linear Diophantine fuzzy Dombi order weighted averaging (CN-LDFDOWA), and complex non-linear Diophantine fuzzy Dombi hybrid weighted averaging (CN-LDFDHWA). These operators are used in the operational parameter to help a successful solution of the problem. Due to the growing energy and material shortages, as well as to comply with environmental laws and regulations and to take advantage of disposal economics in the current context, industrial waste (IW) should be taken into consideration as one of the potential resources in the steel industry. Further, the proposed decision support model applied to solve a case study regarding to IWMT for Pakistan steel mill corporation (PSMC) under complex N-LDF Dombi operators. The proposed method is more effective and reliable for decision making (DM) model, as compared to the existing method. • We developed aggregation operators (AOs) for CN-LDF Dombi Norms to solve MAGDM issue. • We developed CN-LDFDWA AOs based on CODAS method with all unknown information. • An example regarding to the selection of best IW technique for PSMC is provided. • Comparison provided the feasibility of our work and results are discussed based on ranking. [ABSTRACT FROM AUTHOR]

In the study of group decision-making, the most important issue is how to coordinate opinions from different decision experts (DEs) to reach a consensus under uncertainty. To tackle uncertainties surrounding multi-attribute group decision-making (MAGDM) problems in real-life scenes, we introduce 2-tuple linguistic T-spherical fuzzy sets (2TLT-SFSs) which generalize T-spherical fuzzy sets by means of 2-tuple linguistic terms. The 2TLT-SFS model enables the degrees of membership, abstention, and non-membership to be expressed by linguistic terms. This makes it more flexible and descriptive to model the attitudes of DEs in MAGDM applications. Due to the fact that multi-input arguments are interconnected and DEs have a lot of options perception, we also define Muirhead mean (MM) aggregation operators (AOs) to facilitate the fusion of 2TLT-SF information. With the aid of 2TLT-SFSs and MM AOs, the main goal of this research is to present a general MAGDM framework by integrating the step-wise weight assessment ratio analysis (SWARA) with the complex proportional assessment (COPRAS). Firstly, the MM, weighted MM, dual MM, and weighted dual MM operators are adapted to the 2TLT-SF environment, which put forward several new notions such as the 2-tuple linguistic T-spherical fuzzy Muirhead mean (2TLT-SFMM), 2-tuple linguistic T-spherical fuzzy weighted Muirhead mean (2TLT-SFWMM), 2-tuple linguistic T-spherical fuzzy dual Muirhead mean (2TLT-SFDMM), and 2-tuple linguistic T-spherical fuzzy weighted dual Muirhead mean (2TLT-SFWDMM) operators. Meanwhile, some properties regarding idempotency, monotonicity, boundedness, and specializations of the proposed operators are analyzed. Secondly, an integrated 2TLT-SF-MAGDM framework is established. In the proposed decision framework, the 2TLT-SF-SWARA method is utilized to identify the subjective weights of decision attributes, and the 2TLT-SF-COPRAS approach is used to rank alternatives. Lastly, a case study concerning hydropower plants assessment is presented to demonstrate that the suggested scheme is feasible and effective. Furthermore, sensitivity and comparison analyses are conducted to show the robustness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In Pakistan, a hierarchical healthcare system is an efficient way of addressing the issue of limited and insufficient healthcare services. Identifying the various degrees of disease based on the doctor's diagnosis is an important step in developing the hierarchical healthcare treatment structure. This research presents a framework for dealing with the issue of diagnosis values presented as "picture fuzzy numbers (PFNs)". Specifically, the goal of this study is to establish some innovative operational laws and "aggregation operators" (AOs) in a picture fuzzy environment. In this regard, we proposed some new neutral or fair operational laws that incorporate the concept of proportional distribution in order to achieve a neutral or fair remedy to the positive, neutral and negative aspects of PFNs. Based on the developed operational laws, we proposed the "picture fuzzy fairly weighted average operator" and the "picture fuzzy fairly ordered weighted averaging operator". Compared to previous techniques, the proposed AOs provide more generalized and reliable. Furthermore, using proposed AOs with multiple decision-makers and partial weight information under PFNs, a "multi-criteria decision-making" algorithm is developed. Finally, we provide an example to show how the novel approach can aid hierarchical treatment systems. This is essential for merging the healthcare capabilities of the general public and optimizing the medical care system's service performance. [ABSTRACT FROM AUTHOR]

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