Prioritized Aggregation Operators Research Articles

Benchmarking of industrial wastewater treatment processes using a complex probabilistic hesitant fuzzy soft Schweizer–Sklar prioritized-based framework

The objective of this research work is to effectively handle the intricate and uncertain nature of decision-making in the context of industrial wastewater treatment. The prioritization of wastewater treatment is of utmost importance in order to save the environment, promote human health, ensure adherence to legal regulations, conserve resources, and foster overall sustainability. The demand for efficient and sustainable wastewater treatment processes is increasing globally, but selecting appropriate treatment technologies for industrial effluents is challenging due to its complex nature. Our study aims to provide a systematic framework for evaluating and selecting treatments based on efficacy, affordability, and environmental impact. Aggregation operators are one of the fundamental ideas in the framework of information fusion for addressing real-life problems. Numerous scholars have made significant contributions to the development of aggregation operators specifically designed for multi-parameter decision-making (MPDM) whenever circumstances are characterized by uncertainty. Regrettably, the current operators can only be employed within strict limits and constraints. Therefore, this research formulates novel prioritized aggregation operators that alleviate the restrictive constraints associated with the current operators. After this, we present a new methodology that combines the Schweizer–Sklar prioritized aggregation operators with a complex probabilistic hesitant fuzzy soft framework. For this purpose, we develop the averaging aggregation operators and geometric aggregation operators. Following that, we proceed to examine the theorems and properties associated with them by providing rigorous proofs. Then, we develop a novel decision-making technique with a numerical example based on the wastewater treatment process. Through this novel technique, the best process is the activated sludge process. We perform the validity tests to evaluate the feasibility and effectiveness of MPDM techniques.

Analysis of Digital Green Innovation Based on Schweizer–Sklar Prioritized Aggregation Operators for Interval-Valued Picture Fuzzy Supply Chain Management

Digital green innovation economics and management for Industry 5.0 was not widely recognized, and the commonly referenced industry paradigm was Industry 4.0. Furthermore, digital green innovation is part of the above information referring to the integration of digital technologies with environmentally sustainable practices to develop innovative solutions that evaluate ecological challenges. In this manuscript, we evaluate the Schweizer–Sklar operational laws based on interval-valued picture fuzzy (IVPF) values. Further, we investigate prioritized aggregation operators based on Schweizer–Sklar operational laws for IVPF information, called IVPF Schweizer–Sklar prioritized averaging operator, IVPF Schweizer–Sklar prioritized geometric operator, IVPF Schweizer–Sklar prioritized weighted averaging operator, and IVPF Schweizer–Sklar prioritized weighted geometric operator. Some properties for the above-initiated operators are also derived. Additionally, we analyze the digital green innovation with the help of multi-attribute decision-making technique for initiated operators to show the reliability and supremacy of the proposed theory. Finally, we demonstrate examples for addressing the comparison among the initiated theory and existing ideas to improve the worth of the derived theory.

Analysis of natural language processing in engineering documentations based on Schweizer-Sklar prioritized aggregation operators for bipolar complex hesitant fuzzy uncertainty

In the context of fuzzy relations, symmetry refers to a property where the relationship between two elements remains the same regardless of the order in which they are considered. Natural language processing (NLP) in engineering documentation discusses the application of computational methods or techniques to robotically investigate, analyze, and produce natural language information for manufacturing contents. The NLP plays an essential role in dealing with large amounts of textual data normally recovered in engineering documents. In this paper, we expose the idea of a bipolar complex hesitant fuzzy (BCHF) set by combining the bipolar fuzzy set (BFS) and the complex hesitant fuzzy set (CHFS). Further, we evaluate some algebraic and Schweizer-Sklar operational laws under the presence of BCHF numbers (BCHFNs). Additionally, using the above information as well as the idea of prioritized (PR) operators, we derive the idea of BCHF Schweizer-Sklar PR weighted averaging (BCHFSSPRWA) operator, BCHF Schweizer-Sklar PR ordered weighted averaging (BCHFSSPROWA) operator, BCHF Schweizer-Sklar PR weighted geometric (BCHFSSPRWG) operator, and BCHF Schweizer-Sklar PR ordered weighted geometric (BCHFSSPROWG) operator. Basic properties for the above operators are also discussed in detail, such as idempotency, monotonicity, and boundedness. Moreover, we evaluate the best way in which NLP can be applied to engineering documentations with the help of the proposed operators. Therefore, we illustrate the major technique of multi-attribute decision-making (MADM) problems based on these derived operators. Finally, we use some existing operators and try to compare their ranking results with our proposed ranking results to show the supremacy and validity of the investigated theory.

Multi-Attribute Decision-Making for T-Spherical Fuzzy Information Utilizing Schweizer-Sklar Prioritized Aggregation Operators for Recycled Water

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.

Multi-attribute decision-making method based on complex T-spherical fuzzy frank prioritized aggregation operators

This article aims to introduce new aggregation operators (AOs) by assigning the positive real values known as priority degree among the strict priority levels. To Develop the complex T-spherical fuzzy (TSF) frank prioritized (CTSFFP) AOs, using the frank t-norm (FTN) and frank t-conorm (FTCN) operational laws, also explain sum, product, and power operations under complex TSF information. The TSF set framework has a superior structure for uncertain data handling than an existing intuitionistic fuzzy set (FS), Pythagorean FS (PyFS), q-rung orthopair FS (q-ROFS), picture FS (PFS), and spherical FS (SFS). Because the structure of the TSF set has the most generalized form of IFS, PyFS, q-ROFS, PFS, and SFS, it provides greater freedom to decision experts for handling information where these discussed sets fail to aggregate ambiguous details. Utilizing the idea of priority degree, proposed new AOs called CTSFFP weighted averaging (CTSFFPWA), CTSFFP ordered weighted averaging (CTSFFPOWA), CTSFFP hybrid weighted averaging (CTSFFPHWA), CTSFFP weighted geometric (CTSFFPWG), CTSFFP ordered weighted geometric (CTSFFPOWG), CTSFFP hybrid weighted geometric (CTSFFPHWG) operators. Some desirable properties of AOs, such as idempotency, monotonicity, and boundedness, are also discussed. To show the importance of proposed AOs, the real-life problem of multi-attribute decision-making (MADM) is solved with the help of developed CTSFFPWA and CTSFFPWG operators. To enhance the proposed AOs' superiority, compare the diagnosed theory with existing AOs and give conclusions.

Multi-Criteria Decision Making Model For Hotel Selection Problem Under Complex Dual Hesitant Fuzzy Information

ABSTRACT The notion of the “complex dual hesitant fuzzy set (CDHFS)” is the combination of the “dual hesitant fuzzy set (DHFS)” and the “complex fuzzy set (CFS).” It is characterized by two degrees, namely the membership and nonmembership, in the form of a finite subset on a unit disc in the complex plane. CDHFS is useful for dealing with real-world problems involving uncertain or hard-to-predict information. Also, to approximate smoothly, the Einstein operators are well-known aggregation operators, while prioritized operators are effective tools for prioritization among criteria. Therefore, the goal of this study is to develop some prioritized aggregation operators under the CDHFS environment; namely the complex dual hesitant fuzzy prioritized averaging (CDHFPA) operator, the complex dual hesitant fuzzy prioritized geometric (CDHFPG) operator, the complex dual hesitant fuzzy Einstein prioritized averaging (CDHFEPA) operator, and complex dual hesitant fuzzy Einstein prioritized geometric (CDHFEPG) operator. Some properties of the proposed operators are investigated in detail. In addition, a multi-criteria decision-making (MCDM) method based on the proposed operators with the complex dual hesitant fuzzy setting is developed. Moreover, a numerical example is given for the application and effectiveness of the developed MCDM approach. A comparison study is also done with existing methods to show that the proposed MCDM method is better and more reliable. The study finds that if the expert’s preference is used to choose the right aggregation operators, the decision maker will have access to a wide range of compromise solutions.

Selection of Energy Trading Platform for Peer-to-Peer (P2P) Energy Trading by Using a Multi-Attribute Decision-Making Approach Based on Bipolar Fuzzy Aczel-Alsina Prioritized Aggregation Operators

Selection of Energy Trading Platform for Peer-to-Peer (P2P) Energy Trading by Using a Multi-Attribute Decision-Making Approach Based on Bipolar Fuzzy Aczel-Alsina Prioritized Aggregation Operators

Enhancing decision-making framework for talent cultivation quality evaluation using dual Hamy mean and prioritized aggregation operators

At present, the solidification of disciplines and majors in higher education, unclear training objectives, and the need to strengthen teacher information literacy are practical problems that constrain the optimization of the “artificial intelligence+” talent training model. Scientifically adjusting training objectives, upgrading the “artificial intelligence+” talent training model in higher education by integrating multi-disciplinary curriculum systems, strengthening school enterprise cooperation, industry education integration, establishing credit recognition mechanisms and diversified evaluation mechanisms. The quality evaluation of “Artificial Intelligence+” talent cultivation in higher education in the era of education informatization 2.0 is looked as the multiple-attribute decision-making (MADM) issue. In this paper, we extended the dual Hamy mean (DHM) operator and prioritized aggregation (PA) operator to 2-tuple linguistic neutrosophic sets (2TLNSs) to propose the 2-tuple linguistic neutrosophic prioritized DHM (2TLNPDHM) operator. Finally, a decision example for quality evaluation of “Artificial Intelligence+” talent cultivation in higher education in the era of education informatization 2.0 is employed to show the 2TLNPDHM operator. The main contributions of this study are summarized: (1) the 2TLNPDHM operator is built; (2) the 2TLNPDHM operator is designed to cope with the MADM with 2TLNNs; (3) an empirical real-life example for quality evaluation of “Artificial Intelligence+” talent cultivation in higher education in the era of education informatization 2.0 is supplied to proof the designed method; (4) some comparative decision studies are used to show the rationality of the 2TLNPDHM.

Evaluation of mental disorder with prioritization of its type by utilizing the bipolar complex fuzzy decision-making approach based on Schweizer-Sklar prioritized aggregation operators

A clinically important loss in a person’s understanding, emotive power, or conduct is a symptom of a mental disorder. It generally occurs for genetic, psychological, and/or cognitive reasons and is accompanied by discomfort or limitationin significant functional areas. It can be handled using techniques similar to those used to treat chronic conditions (i.e., precautions, examination, medication, and recovery). Mental diseases take a variety of forms. Mental disorder is also identified as mental illness. The latter is a more usual phrase that incorporates psychological problems, psychosocial disorders, and (other) states of mind linked to considerable discomfort, operational limitations, or danger of loss of sanity. To rank the most prevalent types of mental disorders is a multi-attribute decision-making issue and thus this article aims to analyze the artificial intelligence-based evaluation of mental disorders and rank the most prevalent types of mental disorders. For this purpose, here we invent certain aggregation operators under the environment of the bipolar complex fuzzy set such as bipolar complex fuzzy Schweizer-Sklar prioritized weighted averaging, bipolar complex fuzzy Schweizer-Sklar prioritized ordered weighted averaging, bipolar complex fuzzy Schweizer-Sklar prioritized weighted geometric, bipolar complex fuzzy Schweizer-Sklar prioritized ordered weighted geometric operators. After that, we devise a procedure of decision-making for bipolar complex fuzzy information by employing the introduced operators and then take artificial data in the model of bipolar complex fuzzy set to rank the most prevalent types of mental disorders. Additionally, this article contains a comparative study of the introduced work with a few current works for exhibiting the priority and superiority of the introduced work.

Linguistic q-rung orthopair fuzzy prioritized aggregation operators based on Hamacher t-norm and t-conorm and their applications to multicriteria group decision making

Linguistic q-rung orthopair fuzzy prioritized aggregation operators based on Hamacher t-norm and t-conorm and their applications to multicriteria group decision making

COMPLEX INTUITIONISTIC FUZZY DOMBI PRIORITIZED AGGREGATION OPERATORS AND THEIR APPLICATION FOR RESILIENT GREEN SUPPLIER SELECTION

One of the main problems faced by resilient supply chain management is how to solve the problem of supplier selection, which is a typical multi-attribute decision-making (MADM) problem. Given the complexity of the current decision-making environment, the primary influence of this paper is to propose the theory of Dombi operational laws based on complex intuitionistic fuzzy (CIF) information. Moreover, we examined the theory of CIF Dombi prioritized averaging (CIFDPA) and CIF weighted Dombi prioritized averaging (CIFWDPA), where these operators are the modified version of the prioritized aggregation operators and Dombi aggregation operators for fuzzy, intuitionistic fuzzy, complex fuzzy and complex intuitionistic fuzzy information. Some reliable properties for the above operators are also established. Furthermore, to state the art of the proposed operators, an application example in the presence of the invented operators is evaluated for managing resilient green supplier selection problems. Finally, through comparative analysis with mainstream technologies, we provide some mechanism explanations for the proposed method to show the supremacy and worth of the invented theory.

Prioritized aggregation operators based on Schweizer-Sklar t-norm for linear Diophantine fuzzy sets and their application in green sustainable chain

Schweizer and Sklar invented the idea of the Schweizer-Sklar t-norm and Schweizer-Sklar t-conorm in 1960. Additionally, prioritized aggregation operators were derived by Yager in 2008. Further, linear Diophantine fuzzy (LDF) information is a most recent generalization of q-rung orthopair, Pythagorean, and intuitionistic fuzzy sets. In this article, we invent the Schweizer-Sklar operational laws for LDF set based on the Schweizer-Sklar t-norm and t-conorm. Furthermore, we expose the LDF Schweizer-Sklar prioritized averaging (LDFSSPoA) operator, LDF Schweizer-Sklar weighted prioritized averaging (LDFSSWPoA) operator, LDF Schweizer-Sklar prioritized geometric (LDFSSPoG) operator, LDF Schweizer-Sklar weighted prioritized geometric (LDFSSWPoG) operator and evaluate their fundamental properties and results. Moreover, after evaluation of these operators, we evaluate the problem of the green sustainable chain to enhance the worth of the invented theory. Finally, we show the supremacy and accuracy of the proposed theory with the help of a comparative analysis between the proposed techniques with some existing techniques.

Retracted: Intuitionistic Fuzzy Prioritized Aggregation Operators Based on Priority Degrees with Application to Multicriteria Decision-Making

Retracted: Intuitionistic Fuzzy Prioritized Aggregation Operators Based on Priority Degrees with Application to Multicriteria Decision-Making

Intuitionistic uncertain linguistic prioritized aggregation operators and their application to multi-criteria decision making

The intuitionistic uncertain linguistic information aggregation problems considering different priority levels of criteria are investigated. Firstly, we extended the prioritized averaging (PA) operator to intuitionistic uncertain linguistic environment, defined two new prioritized aggregation operators called the intuitionistic uncertain linguistic prioritized weighted average (IULPWA) operator and the intuitionistic uncertain linguistic prioritized weighted geometric (IULPWG) operator, and established various desirable properties of the proposed operators. Secondly, we developed a multi-criteria decision making (MCDM) approach based on the IULPWA operator (or the IULPWG operator) to deal with the MCDM problems in which the criterion values take the form of intuitionistic uncertain linguistic numbers (IULNs) and the criteria are in different priority levels. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed method, and a comparison analysis is conducted to make clear the differences among the IULPWA operator, the IULPWG operator, the intuitionistic uncertain linguistic number weighted averaging (IULNWA) operator and the intuitionistic uncertain linguistic weighted geometric average (IULWGA) operator.

University’s recruitment process using Fermatean fuzzy Einstein prioritized aggregation operators

In comparison to intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), the Fermatean Fuzzy Set (FFS) is more efficacious in dealing ambiguous and imprecise data when making decisions. In this paper, we propose unique operations on Fermatean fuzzy information based on prioritized attributes, as well as Einstein’s operations based on adjusting the priority of characteristics in the Fermatean fuzzy environment. We use Einstein’s operations with prioritized attributes to propose new operations on Fermatean fuzzy numbers (FFNs), and then introduce basic aspects of these operations. Motivated by Einstein operations on FFNs, we develop Fermatean fuzzy Einstein prioritized arithmetic and geometric aggregation operators (AOs). In the first place, the concepts of a Fermatean fuzzy Einstein prioritized average (FFEPA), Fermatean fuzzy Einstein prioritized weighted average (FFEPWA), and Fermatean fuzzy Einstein prioritized ordered weighted average (FFEPOWA)-operators are introduced. Then, Fermatean fuzzy Einstein prioritized geometric (FFEPG) operator, Fermatean fuzzy Einstein prioritized weighted geometric (FFEPWG) operator, Fermatean fuzzy Einstein prioritized ordered weighted geometric (FFEPOWG) operator, and Fermatean fuzzy Einstein hybrid geometric (FFEHG) operator are given. We also go through some of the key characteristics of these operators. Moreover, using these operators, we establish algorithm for addressing a multiple attribute decision-making issue using Fermatean fuzzy data and attribute prioritizing. The case of university faculty selection is taken as a scenario to analyze and demonstrate the applicability of our suggested model. In addition, a comparison of the proposed and current operators is conducted, and the impact of attribute priority on the ranking order of alternatives is explored.

Interval-valued dual hesitant fuzzy prioritized aggregation operators based on Archimedean t-conorm and t-norm and their applications to multi-criteria decision making

Interval-valued dual hesitant fuzzy prioritized aggregation operators based on Archimedean t-conorm and t-norm and their applications to multi-criteria decision making

Probabilistic hesitant bipolar fuzzy Hamacher prioritized aggregation operators and their application in multi-criteria group decision-making

Probabilistic hesitant bipolar fuzzy Hamacher prioritized aggregation operators and their application in multi-criteria group decision-making

Prioritized Aggregation Operators for Complex Intuitionistic Fuzzy Sets Based on Aczel-Alsina T-norm and T-conorm and Their Applications in Decision-Making

Prioritized Aggregation Operators for Complex Intuitionistic Fuzzy Sets Based on Aczel-Alsina T-norm and T-conorm and Their Applications in Decision-Making

Assessment of Structural Systems to Design Earthquake Resistance Buildings by Employing Multi-Attribute Decision-Making Method Based on the Bipolar Complex Fuzzy Dombi Prioritized Aggregation Operators

An earthquake is a natural phenomenon that occurs when two tectonic plates in the earth’s crust move against each other. This movement creates seismic waves that can cause the ground to shake, sometimes resulting in damage to buildings and infrastructure. It is important to be prepared for earthquakes, particularly if you live in an area that is at high risk for seismic activity. This includes having an emergency kit, knowing how to shut off utilities, having a plan in place for what to do in the event of an earthquake, and most importantly, constructing earthquake resistance buildings. The assessment and the ranking of structural systems to design earthquake resistance buildings is a MADM (multi-attribute decision-making) dilemma. Consequently, in this script, we initiate the method of MADM under the bipolar complex fuzzy (BCF) information. For this method, we devise BCF Dombi prioritized averaging (BCFDPA), BCF Dombi prioritized weighted averaging (BCFDPWA), BCF Dombi prioritized geometric (BCFDPG), and BCF Dombi prioritized weighted geometric (BCFDPPWG) operators by utilizing the Dombi aggregation operator (AO) with BCF information. After that, by using artificial data, we assess the structural systems to design earthquake resistance buildings with the assistance of the invented method of MADM. To exhibit the dominancy and supremacy of the elaborated work, the advantages, sensitive examination, graphical representation, and comparative study are described in this script.

Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making

Complex intuitionistic fuzzy (CIF) information covers the degree of membership and the degree of non-membership in the form of polar coordinates with a valuable and dominant characteristic where the sum of the real parts (the same rule for the imaginary parts) of the pair must be contained in the unit interval. In this paper, we first derive the Frank operational laws for CIF information and then examine the prioritized aggregation operators based on Frank operational laws for managing the theory of CIF information. These are the CIF Frank prioritized averaging (CIFFPA) operator, the CIF Frank prioritized ordered averaging (CIFFPOA) operator, the CIF Frank prioritized geometric (CIFFPG) operator, and the CIF Frank prioritized ordered geometric (CIFFPOG) operator with properties of idempotency, monotonicity, and boundedness. Furthermore, we derive the WASPAS (weighted aggregates sum product assessment) under the consideration or presence of the CIF information and try to justify it with the help of a suitable example. Additionally, we illustrate some numerical examples in the presence of the MADM (multi-attribute decision-making) procedures for evaluating the comparison between the proposed operators with some well-known existing operators to show the validity and worth of the proposed approaches.