Power Aggregation Operators Research Articles

Analysis of renewable energy resources based on frank power aggregation operators and EDAS method for circular bipolar complex fuzzy uncertainty

The model of circular bipolar complex fuzzy (Cir-BCF) sets computed based on the membership function, non-membership function, and radius among both functions for each value of the universal set. The technique of the Cir-BCF set is the modified or extended form of fuzzy sets, complex fuzzy sets, bipolar fuzzy sets, bipolar complex fuzzy sets, and simple circular bipolar fuzzy sets to cope with uncertain and vague information. In this manuscript, we describe the novel technique of frank operational laws based on Cir-BCF values for frank t-norm and frank t-conorm. Further, we simplify the model of Cir-BCF frank power averaging (Cir-BCFFPA), Cir-BCF frank power weighted averaging (Cir-BCFFPWA), Cir-BCF frank power geometric (Cir-BCFFPG), Cir-BCF frank power weighted geometric (Cir-BCFFPWG) operators, and highlighted their valuable properties, called idempotency, monotonicity, and boundedness. Moreover, analysis of renewable energy resources is very awkward and complicated, but it is natural sources of energy that are refilled constantly or relativeness quickly on a human timescale. Further, solar energy, hydroelectric energy, geothermal energy, biomass energy, and wind energy are five major sources of energy, but it is complex to find which one is the best and which one is worst. For evaluating the above problems, we construct the technique of evaluation based on the distance from the average solution (EDAS) method under the presence of the Cir-BCF numbers (Cir-BCFNs). At the end, we arrange the comparison between proposed and existing techniques based on some numerical examples to describe the validity and proficiency of the initiated information.

Analysis of Hamacher power aggregation operators for circular complex p, q-quasirung orthopair fuzzy 2-tuple linguistic sets and their application in green industry development

Green industry development focuses on balancing economic and financial growth with environmental stewardship and ensuring that companies and industries are contributing positively to both environmental sustainability and prosperity. This manuscript aims to develop the novel technique of circular complex p, q-quasirung orthopair fuzzy 2-tuple linguistic (CCp, q-QOF2-TL) set and their operational laws based on algebraic t-norms and Hamacher t-norms, where the algebraic t-norms and Einstein t-norms are the special cases of the Hamacher t-norms for parameter ϜℲs=l and ϜℲs=2. Further, we derive the Hamacher power aggregation operators based on any finite collection of CCp, q-QOF2-TL numbers (CCp, q-QOF2-TLNs), called CCp, q-QOF2-TL Hamacher power average (CCp, q-QOF2-TLHPA) operator, CCp, q-QOF2-TL Hamacher power weighted average (CCp, q-QOF2-TLHPWA) operator, CCp, q-QOF2-TL Hamacher power geometric (CCp, q-QOF2-TLHPG) operator, CCp, q-QOF2-TL Hamacher power weighted geometric (CCp, q-QOF2-TLHPWG) operator, and described their basic properties, called idempotency, monotonicity, and boundedness. Further, we demonstrate the technique of multi-attribute decision-making (MADM) problem based on the above operators to evaluate the major factor that will be playing in the development of the green industry. Finally, we compare the proposed ranking values with the obtained ranking values of existing techniques to show the supremacy and superiority of the initiated approaches.

EDAS method for circular pythagorean fuzzy with improved Dombi power aggregation operators and their application in policy analysis and decision support systems

A circular Pythagorean fuzzy set is a very dominant and reliable technique for coping with uncertain and vague information in genuine life problems because it contains the membership function, non-membership function, and radius between both grades with a condition that is the sum of the pair will be contained in the unit interval. The objective of this article is to define some improved Dombi operational laws based on circular improved Pythagorean fuzzy values. Moreover, we discuss some drawbacks of the existing Dombi aggregation operators based on circular improved Pythagorean fuzzy numbers. We also defined some improved Dombi averaging and geometric aggregation operators and their properties. Later on, a technique of evaluation based on distance from the average solution is stated by using the proposed operators. Additionally, we resolve the problem of policy analysis and decision support systems based on multi-attribute decision-making problems for initiated techniques to enhance the worth of the derived theory. Finally, we illustrate some examples for showing the supremacy and validity of the proposed theory with the help of comparative analysis between proposed ranking values and some existing ranking values.

An Innovative Approach on Yao’s Three-Way Decision Model Using Intuitionistic Fuzzy Sets for Medical Diagnosis

In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a novel methodology to the three-way decision idea. Initially, we revamp the three-way decision model using rough set theory and incorporate interval-valued classes to handle intuitionistic fuzzy data. Secondly, we explore the use of intuitionistic fuzzy power weighted and intuitionistic fuzzy power weighted geometric aggregation operators to consolidate attribute values within the data system. Furthermore, we present a case study in the medical field to exhibit the validity and efficiency of our offered technique. This innovative method enables us to classify participants into three distinct zones based on their symptoms. The manuscript concludes with a summary of key points provided by the authors.

Interval-valued T-spherical fuzzy extended power aggregation operators and their application in multi-criteria decision-making

Abstract As an effective tool to show the fuzziness of qualitative information, the interval-valued T-spherical fuzzy set can utilize three kinds of information, namely, membership, abstinence, and non-membership, to show the opinions of decision-maker. Given this advantage, many interval-valued T-spherical fuzzy multi-criteria decision-making (IVTSF-MCDM) methods have been designed. However, most of the existing IVTSF-MCDM methods have a common limitation that the inability to effectively show the impacts of extreme data. To address this limitation, this study develops a novel MCDM method based on interval-valued T-spherical fuzzy extended power aggregation operator. First, interval-valued T-spherical fuzzy cross-entropy (CE) and interval-valued T-spherical fuzzy symmetrical CE are defined to measure the difference between two interval-valued T-spherical fuzzy numbers, which are used to determine criteria weights in MCDM. Second, interval-valued T-spherical fuzzy extended power average operator and interval-valued T-spherical fuzzy extended power geometric operator are proposed, and their properties are investigated. Moreover, in view of that criteria may be assigned to different weights, this study defines interval-valued T-spherical fuzzy extended power weighted average operator and interval-valued T-spherical fuzzy extended power weighted geometric operator to derive the order of alternatives. Finally, the applicability of the proposed method is validated by the case about investment country selection, while the sensitivity and comparison analyses are also conducted to further prove its advantages and effectiveness.

Multiple criteria decision-making based on linguistic spherical fuzzy copula extended power aggregation operators

Multiple criteria decision-making based on linguistic spherical fuzzy copula extended power aggregation operators

Implementation of Learning Management Systems (LMS) in higher education systems through bipolar complex hesitant fuzzy Aczel-Alsina power aggregation operators: A case review for China.

A learning management system (LMS) is a web-based application or software platform computed to facilitate the development, tracking, management, reporting, and delivery of education and training programs. Many valuable and dominant factors are working behind the Learning Management System (LMS), but no one can find which factor is most important and valuable for LMS during COVID-19 among the following five alternatives, called Improved Accessibility, Blended Learning, Collaboration and Communications, Assessment and Evaluation, and Administrative Efficiency. For this, first, we derive the techniques of bipolar complex hesitant fuzzy (BCHF) sets, and then we evaluate some flexible operational laws, called Algebraic operational laws and Aczel-Alsina operational laws. Secondly, using the above techniques, we elaborate the technique of BCHF Aczel-Alsina power averaging (BCHFAAPA), BCHF Aczel-Alsina power weighted averaging (BCHFAAPWA), BCHF Aczel-Alsina power geometric (BCHFAAPG), and BCHF Aczel-Alsina power weighted geometric (BCHFAAPWG) operators. Some basic properties are also investigated for each proposed operator. Further, to evaluate the problem concerning LMS, we compute the multi-attribute decision-making (MADM) techniques for invented operators. Finally, we select some prevailing operators and try to compare their ranking results with our proposed results to enhance the worth and capability of the invented theory.

Multiple-attribute group decision-making approach using power aggregation operators with CRITIC-WASPAS method under 2-dimensional linguistic intuitionistic fuzzy framework

The 2-dimensional linguistic intuitionistic fuzzy variables (2DLIFVs) provide an efficient tool to model the cognitive information of experts in practical circumstances while considering the reliability of the evaluation results. It is a hybrid model representing qualitative information, which derives from integrating the 2-dimensional linguistic variables (2DLVs) with linguistic intuitionistic fuzzy numbers (LIFNs). In this work, we first define a novel score function to establish a proper ranking order among the 2DLIFVs. Next, we define a new distance measure under a 2-dimensional linguistic intuitionistic fuzzy framework to determine the difference between 2DLIFVs. Some mathematical properties and special cases of the defined distance measure are also discussed. The power average (PA) operators provide aggregation tools, allowing aggregated arguments to support each other in the aggregation process. Motivated by the notion of power average (PA) and power geometric (PG), we define four new aggregation operators (AOs) to aggregate 2DLIFVs by considering information correlation in terms of support degree during the aggregation process. Several mathematical properties of the proposed AOs are also investigated. In addition, a new integrated 2DLIF-CRITIC-WASPAS methodology is developed in the 2-dimensional linguistic intuitionistic fuzzy environment to deal with complex decision issues. In this method, a “Criteria Importance Through Intercriteria Correlation (CRITIC)” approach is used to obtain the associate weights of the attributes, and the “Weighted Aggregated Sum Product Assessment (WASPAS)” method is executed to establish a valid ranking order among the alternatives.Moreover, a real problem of venture capital investment related to renewable energy projects is considered to demonstrate the applicability of the proposed methodology. The evaluation process considers four aspects: the management team, service or product, finance, and the market, which are related to 14 attributes. A sensitivity analysis is carried out to explain the reliability of the obtained results. Comparing the proposed method with some extant methods establishes the strength and robustness of the formulated method in real-world situations.

Multi-attribute decision-making methods based on Aczel-Alsina power aggregation operators for English blended teaching quality evaluation under single-valued neutrosophic sets

As a new form of teaching, blended teaching can integrate the advantages of classroom teaching and online teaching and improve the overall quality and effectiveness of English teaching under the premise of changing the orientation of teachers and students. The English blended teaching quality evaluation is a multiple attribute decision making (MADM) issue. Aczel-Alsina t-norm and t-conorm operations have the true advantage of changeability by adjusting a decision parameter. power averaging (PA) operator allowed decision attributes to strengthen each other through weight information during fusion, thereby eliminating the influence of subjective weights on the decision results. Motivate through classical Aczel-Alsina operators, PA operator and the single-valued neutrosophic sets (SVNSs), in this paper, the single-valued neutrosophic number Aczel-Alsina power averaging (SVNNAAPA) operator and the single-valued neutrosophic number Aczel-Alsina power weighted averaging (SVNNAAPWA) operator are constructed under SVNSs. The SVNNAAPWA operator is built for MADM. Eventually, an example about English blended teaching quality evaluation and some selected comparative decision analysis is used to depict the SVNNAAPWA method.

Aczel–Alsina T-norm based group decision-making technique for the evaluation of electric cars using generalized orthopair fuzzy aggregation information with unknown weights

Data management and finding precise outcomes from large amounts of information are among the biggest challenges for scientists. The technique of multi-attribute group decision-making (MAGDM) is a valuable tool for investigating fuzzy data precisely. The key objective of the paper is to redefine the q-rung orthopair (q-RO) fuzzy set (FS) (q-ROFS) in the term of interval-valued and proposed new aggregation operators (AOs) based on the Aczel-Alsina (AA) t-norm (TN) and t-conorm (TCN) operations. The AA operational laws are a generalized form of existing TNs and TCNs and give more reliable results because they can fluctuate in their parametric values. The concept of interval-valued enlarges the space of membership degree (MD) and non-membership degree (NMD) for decision-makers. By taking qth power, the interval-valued q-ROFS (IV-q-ROFS) structure. The IV-q-ROFS can handle the uncertainty and vagueness in data, then interval-valued intuitionistic FS (IV-IFS) and interval-valued Pythagorean FS (PyFS) (IV-PyFS) and provide accurate results. The thought of power AOs (PAOs) makes the relationship between weight vectors and reduces the chances of uncertainty in aggregated results. By taking advantage of PAOs, this article is devoted to introducing the interval-valued q-ROF Aczel-Alsina power-weighted averaging (IV-q-ROFAAPWA) and interval-valued q-ROF Aczel-Alsina power-weighted geometric (IV-q-ROFAAPWG) operators. The fundamental axioms of AOs, idempotency, boundedness, and monotonicity, are also discussed. To illustrate the importance of suggested AOs, the real-life problem of electric car selection was solved by applying the MAGDM method using the proposed IV-q-ROFAAPWA and IV-q-ROFAAPWG operators. The comparison of proposed AOs with currently present AOs is also part of the article. We finally constructed solid conclusions.

Schweizer-Sklar power aggregation operators based on complex intuitionistic fuzzy information and their application in decision-making

In 1960, Schweizer and Sklar introduced the novel Schweizer-Sklar t-norm and t-conorm which is used in the construction of aggregation operators. Schweizer-Sklar norms are more general than algebraic norms and Einstein norms. Additionally, computing the power operators based on the Schweizer-Sklar norms for complex Atanassov intuitionistic fuzzy (CA-IF) set is very awkward and complicated. In this manuscript, firstly, we propose the Schweizer-Sklar operational laws for CA-IF values, and secondly, we develop the CA-IF Schweizer-Sklar power averaging (CA-IFSSPA) operator, CA-IF Schweizer-Sklar power ordered averaging (CA-IFSSPOA) operator, CA-IF Schweizer-Sklar power geometric (CA-IFSSPG) operator, and CA-IF Schweizer-Sklar power ordered geometric (CA-IFSSPOG) operator. Some suitable and dominant properties for the above operators are also discussed. Furthermore, to simplify the above operators, we develop the procedure of decision-making technique, called multi-attribute decision-making (MADM) methods based on the proposed operators based on CA-IF values. Finally, we compare the proposed methods with some existing methods to describe the efficiency and capability of the discovered approaches by some examples.

Providing decision-making approaches for the assessment and selection of cloud computing using bipolar complex fuzzy Einstein power aggregation operators

In the last few years, cloud computing has become more popular. When someone refers to “the cloud,” which is where personal and professional documents are stored, they are moving away from more conventional software tools and apps and toward a more sophisticated use of the internet. A new technology known as “cloud computing” mainly refers to a centralized storage area made feasible by remote computers running software on the internet. Users will distribute services and resources throughout the network to enhance productivity. The selection and evaluation of cloud computing can be done by various approaches. In this manuscript, we analyze new approaches for the appraisal and selection of cloud computing. These approaches are based on the power Einstein AOs (PEAOs) which are also invented in this paper in the environment of bipolar complex fuzzy (BCF) information. Further, we do a comparative study of the devised work with several prevailing work from the literature to represent the advantages and dominance of the devised work.

A novel approach to decision making in rice quality management using interval-valued Pythagorean fuzzy Schweizer and Sklar power aggregation operators.

The Pythagorean fuzzy set and interval-valued intuitionistic fuzzy set are the basis of the interval-valued Pythagorean fuzzy set (IVPFS) which offers an effective approach to addressing the complex uncertainty in decision-analysis processes, making it applicable across a broad spectrum of applications. This paper introduces several aggregation operators within the IVPF framework, such as the interval-valued Pythagorean fuzzy SS power weighted average operator, and the interval-valued Pythagorean fuzzy SS power geometric operator using the notion of power aggregation operators through Schweizer and Sklar (SS) operations. The existence of SS t-norms and t-conorms in the IVPF framework for addressing multi-attribute decision-making problems gives the generated operator's ability to make the information aggregation approach more adaptable compared to other current ones. The application of the proposed approach holds the potential to enhance crop yield, optimize resource utilization, and contribute to the overall sustainability of agriculture. Additionally, sensitivity and comparative analyses are provided to clarify the stability and dependability of the results acquired through this approach.

A Systematic Analysis of EDAS Method and Power Aggregation Operators Based on Bipolar Complex Fuzzy Linguistic for Rural Energy Infrastructure Decision

A Systematic Analysis of EDAS Method and Power Aggregation Operators Based on Bipolar Complex Fuzzy Linguistic for Rural Energy Infrastructure Decision

Evaluation Based on Distance From Average Solution for Circular Pythagorean Fuzzy Schweizer-Sklar Power Aggregation Operators and Their Application in Transportation Problems for Linear Programming

Evaluation Based on Distance From Average Solution for Circular Pythagorean Fuzzy Schweizer-Sklar Power Aggregation Operators and Their Application in Transportation Problems for Linear Programming

Novel Aczel-Alsina Power Aggregation Operators for Circular Pythagorean Fuzzy Linguistics With Application to Waste Reduction and Recycling in Green Supply Chain Management

Novel Aczel-Alsina Power Aggregation Operators for Circular Pythagorean Fuzzy Linguistics With Application to Waste Reduction and Recycling in Green Supply Chain Management

Power aggregation operators based on hamacher t-norm and t-conorm for complex intuitionistic fuzzy information and their application in decision-making problems

Algebraic and Einstein are two different types of norms which are the special cases of the Hamacher norm. These norms are used for evaluating or constructing three different types of aggregation operators, such as averaging/geometric, Einstein averaging/geometric, and Hamacher averaging/geometric aggregation operators. Moreover, complex Atanassov intuitionistic fuzzy (CA-IF) information is a very famous and dominant technique or tool which is used for depicting unreliable and awkward information. In this manuscript, we present the Hamacher operational laws for CA-IF values. Furthermore, we derive the power aggregation operators (PAOs) for CA-IF values, called CA-IF power Hamacher averaging (CA-IFPHA), CA-IF power Hamacher ordered averaging (CA-IFPHOA), CA-IF power Hamacher geometric (CA-IFPHG), and CA-IF power Hamacher ordered geometric (CA-IFPHOG) operators. Some dominant and valuable properties are also stated. Moreover, the multi-attribute decision-making (MADM) methods are developed based on the invented operators for CA-IF information and the detailed decision steps are given. Many prevailing operators are selected as special cases of the invented theory. Finally, the derived technique will offer many choices to the expert to evaluate the best alternatives during comparative analysis.

A sustainability evaluation framework for the urban energy Internet using the Fermatean fuzzy Aczel-Alsina hybrid MCDM method

The evaluation of urban energy internet (UEI) is crucial for the establishment of low-carbon cities. This paper aims to present a hybrid decision-making framework to address UEI evaluation problems from a sustainability perspective. First, the Fermatean fuzzy Aczel-Alsina power aggregation operators are proposed to aggregate evaluation information, and the remarkable properties of these operators are explored. Then, the combined weight of the criteria is determined through the decision-making trial and evaluation laboratory method and the Shannon entropy-based power weighted method within the Fermatean fuzzy circumstance. Moreover, the classic multiobjective optimization by ratio analysis plus the full multiplicative form method is extended using the proposed aggregation operators. Finally, an index system was constructed from a sustainability perspective, and the level of development of the four UEI projects is assessed using the proposed method. The experimental results demonstrate that the proposed method can provide beneficial guidelines for the construction and development of the UEI. Furthermore, the reliability and effectiveness of the proposed decision-making framework are validated through sensitivity analysis and a comparative study with existing MCDM methods.

Multi-attribute decision-making approach based on Aczel-Alsina power aggregation operators under bipolar fuzzy information & its application to quantum computing

The main aim of this paper is to present a new multi-attribute decision-making (MADM) approach for solving the problems under the uncertain and complex environment. The key challenges during any MADM problem are how to quantify the objective uncertainty information in the data and how to aggregate such collective information. To answer this, in this paper, we utilize the concept of the bipolar fuzzy information to mark the information in terms of the positive and negative support. To aggregate this different information, we propose some power aggregation operators based on the Aczel-Alsina operators (AAO). The AAOs are the generalized t-norm based operations with an additional parameter to analyze the influence of the expert preferences. Based on these AAO and bipolar fuzzy information, we stated bipolar fuzzy AA power weighted averaging and geometric operators and investigate their features. Later, based on these operators, we establish a MADM algorithm to solve the decision-making problems. The applicability of the stated algorithm is demonstrated through a case study related to quantum computing. The comparative studies and advantages of the study are also analyzed with the various prevailing theories.

A Novel Interval-Valued Decision Theoretic Rough Set Model with Intuitionistic Fuzzy Numbers Based on Power Aggregation Operators and Their Application in Medical Diagnosis

Intuitionistic fuzzy information is a potent tool for medical diagnosis applications as it can represent imprecise and uncertain data. However, making decisions based on this information can be challenging due to its inherent ambiguity. To overcome this, power aggregation operators can effectively combine various sources of information, including expert opinions and patient data, to arrive at a more accurate diagnosis. The timely and accurate diagnosis of medical conditions is crucial for determining the appropriate treatment plans and improving patient outcomes. In this paper, we developed a novel approach for the three-way decision model by utilizing decision-theoretic rough sets and power aggregation operators. The decision-theoretic rough set approach is essential in medical diagnosis as it can manage vague and uncertain data. The redesign of the model using interval-valued classes for intuitionistic fuzzy information further improved the accuracy of the diagnoses. The intuitionistic fuzzy power weighted average (IFPWA) and intuitionistic fuzzy power weighted geometric (IFPWG) aggregation operators are used to aggregate the attribute values of the information system. The established operators are used to combine information within the intuitionistic fuzzy information system. The outcomes of various alternatives are then transformed into interval-valued classes through discretization. Bayesian decision rules, incorporating expected loss factors, are subsequently generated based on this foundation. This approach helps in effectively combining various sources of information to arrive at more accurate diagnoses. The proposed approach is validated through a medical case study where the participants are classified into three different regions based on their symptoms. In conclusion, the decision-theoretic rough set approach, along with power aggregation operators, can effectively manage vague and uncertain information in medical diagnosis applications. The proposed approach can lead to timely and accurate diagnoses, thereby improving patient outcomes.