Aggregation Operators Research Articles

Generalized picture fuzzy Frank aggregation operators and their applications

Picture fuzzy sets with four-dimensional features are widely used in decision-making as a mathematical tool because they can capture the uncertainty of data. However, the methods and techniques based on matrix theory are difficult to solve the decision problem involving high-dimensional data in a picture fuzzy setting. Therefore, operators that can identify high-dimensional data in a picture fuzzy environment are proposed to address this challenge. In this paper, firstly, by integrating the Frank operators into the picture fuzzy tensor, the generalized picture fuzzy Frank weighted arithmetic (GPFFWA) and generalized picture fuzzy Frank weighted geometric (GPFFWG) operators are defined. Their specific expressions are discussed, and the idempotency, order-preservation, boundedness, and commutativity of the proposed operators are also given. Then, combining the GPFFWA and GPFFWG operators, an algorithm is designed to solve the multi-criteria decision-making problem with high-dimensional data features in the picture fuzzy environment. Finally, a numerical example and related analysis demonstrate the effectiveness, superiority, and flexibility of the suggested technique. This work provides new theoretical and methodological support for developing and practicing the decision-making discipline.

Neutrality geometric aggregation operators based on cubic q-rung orthopair fuzzy sets and their applications in multiple attribute group decision-making problems

Cubic q-rung orthopair fuzzy set (Cq-ROFS) is a hybrid set that can hold much more information to handle data uncertainties. It provides more space for decision makers (DMs) to describe their opinion in the multi-attribute group decision-making (MAGDM). In order to involve neutral character to discuss the neutral values assigned by decision-makers, in this paper, some cubic q-rung orthopair fuzzy aggregation operators based on neutrality operation are proposed, such as the cubic q-rung orthopair fuzzy weighted neutrality geometric (Cq-ROFWNG) operator, the cubic q-rung orthopair fuzzy ordered weighted neutrality geometric (Cq-ROFOWNG) operator, the cubic q-rung orthopair fuzzy hybrid neutrality geometric (Cq-ROFHNG) operator. Meanwhile, some properties of these operators are discussed. Further, we develop a novel MAGDM approach based on the proposed operators in a cubic q-rung orthopair fuzzy environment. Finally, numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods.

Applications of Pythagorean Uncertainty weighted Average Aggregation operator to Multiple attribute group Decision Making

Applications of Pythagorean Uncertainty weighted Average Aggregation operator to Multiple attribute group Decision Making

Comprehensive evaluation of rural regional integrated clean energy systems considering multi-subject interest coordination with pythagorean fuzzy information

In the development of a comprehensive clean energy system in rural areas, how to evaluate it scientifically and effectively is an urgent problem to be solved. Artificial intelligence has already been widely applied in the field of energy technology, but its application in the comprehensive benefit evaluation is still insufficient. The purpose of this study is to conduct a comprehensive evaluation of the rural, regional integrated clean energy system with coordinated multi-subject interests. Firstly, the interest relationship between the subjects of the participating rural regional comprehensive clean energy system is analyzed. And, the comprehensive benefit evaluation index system is established based on farmers, rural grid, new energy investment operators, government and interest subject reciprocity partners. Secondly, Sugeno-Weber aggregation operators are more flexible and used to acquire smooth aggregated outcomes from a group of information in a single set. Moreover, an algorithm of the multi-attribute decision-making process also reveals the supremacy and reliability of the research work. A case study is established to evaluate the rural integrated clean energy system with coordinated multi-subject interests. The results are as follows. The index system reflects the characteristics of the comprehensive clean energy system in rural areas, such as environmental characteristics, economic characteristics, safety characteristics and clean energy characteristics. The advantages and validity of developed research work are proved by comparing the findings of pioneered approaches with existing mathematical operators. The ranking of suitable energy sources is Solar power > Biomass energy > Geothermal energy > Wind and hydropower based integrated clean energy system.

Application of the Sugeno integral in Fuzzy Rule-Based Classification

Fuzzy Rule-Based Classification System (FRBCS) is a well-known technique to deal with classification problems. Recent studies have considered the usage of the Choquet integral and its generalizations (e.g.: CT-integral, CF-Integral and CC-integral) to enhance the performance of such systems. Such fuzzy integrals were applied to the Fuzzy Reasoning Method (FRM) to aggregate the fired fuzzy rules when classifying new data. However, the Sugeno integral, another well-known aggregation operator, obtained good results in other applications, such as brain–computer interfaces. These facts led to the present study, in which we consider the Sugeno integral in classification problems. That is, the Sugeno integral is applied in the FRM of a widely used FRBCS, and its performance is analyzed over 33 different datasets from the literature, also considering different fuzzy measures. To show the efficiency of this new approach, the results obtained are also compared with previous studies that involved the application of different aggregation functions. Finally, we perform a statistical analysis of the application.

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.

Some new types induced complex intuitionistic fuzzy Einstein geometric aggregation operators and their application to decision-making problem

Some new types induced complex intuitionistic fuzzy Einstein geometric aggregation operators and their application to decision-making problem

P,q-Quasirung orthopair fuzzy multi-criteria group decision-making algorithm based on generalized Dombi aggregation operators

p,q-Quasirung orthopair fuzzy multi-criteria group decision-making algorithm based on generalized Dombi aggregation operators

Assessment of learning management systems based on Schweizer–Sklar picture fuzzy Maclaurin symmetric mean aggregation operators

Assessment of learning management systems based on Schweizer–Sklar picture fuzzy Maclaurin symmetric mean aggregation operators

Multi-attribute group decision making based on p, q-quasirung orthopair fuzzy Yager prioritized weighted geometric aggregation operator of p, q-quasirung orthopair fuzzy numbers

Multi-attribute group decision making based on p, q-quasirung orthopair fuzzy Yager prioritized weighted geometric aggregation operator of p, q-quasirung orthopair fuzzy numbers

Selection of an Appropriate Global Partner for Companies Using the Innovative Extension of the TOPSIS Method with Intuitionistic Hesitant Fuzzy Rough Information

In this research, we introduce the intuitionistic hesitant fuzzy rough set by integrating the notions of an intuitionistic hesitant fuzzy set and rough set and present some intuitionistic hesitant fuzzy rough set theoretical operations. We compile a list of aggregation operators based on the intuitionistic hesitant fuzzy rough set, including the intuitionistic hesitant fuzzy rough Dombi weighted arithmetic averaging aggregation operator, the intuitionistic hesitant fuzzy rough Dombi ordered weighted arithmetic averaging aggregation operator, and the intuitionistic hesitant fuzzy rough Dombi hybrid weighted arithmetic averaging aggregation operator, and demonstrate several essential characteristics of the aforementioned aggregation operators. Furthermore, we provide a multi attribute decision-making approach and the technique of the suggested approach in the context of the intuitionistic hesitant fuzzy rough set. A real-world problem for selecting a suitable worldwide partner for companies is employed to demonstrate the effectiveness of the suggested approach. The sensitivity analysis of the decision-making results of the suggested aggregation operators are evaluated. The demonstrative analysis reveals that the outlined strategy has applicability and flexibility in aggregating intuitionistic hesitant fuzzy rough information and is feasible and insightful for dealing with multi attribute decision making issues based on the intuitionistic hesitant fuzzy rough set. In addition, we present a comparison study with the TOPSIS approach to illustrate the advantages and authenticity of the novel procedure. Furthermore, the characteristics and analytic comparison of the current technique to those outlined in the literature are addressed.

Utilizing serverless framework for dynamic visualization and operations in geospatial applications

ABSTRACT While substantial efforts have been invested in the development of Discrete Global Grid Systems (DGGS) spatial operations and their potential applications in the geospatial domain, it has become evident that there is a demand for an efficient and scalable system to handle the visualization of large-scale DGGS data. This study demonstrated the potential of DGGS in conjunction with the serverless framework for dynamic visualization at various resolutions, which is based on data storage and effective querying using PostgreSQL integrated into Amazon Aurora Serverless. The use of Amazon Web Services (AWS) Lambda for on-the-fly generation of hexagon geometries significantly reduced the storage requirements and improved the speed of the visualization process. In addition, we implemented on-the-fly spatial operations including point binning, thresholding, aggregation, and neighborhood operations in the DGGS, highlighting the capabilities of DGGS in vector and raster processing. The proposed system has shown promising results in terms of efficiency, scalability, and adaptability, making it a viable solution for large-scale geospatial data processing and visualization. Case studies using flood risk data and terrain data further illustrate the system’s practical applicability in on-the-fly spatial operations and rapid visualization.

Selection of AI Architecture for Autonomous Vehicles Using Complex Intuitionistic Fuzzy Rough Decision Making

The advancement of artificial intelligence (AI) has become a crucial element in autonomous cars. A well-designed AI architecture will be necessary to attain the full potential of autonomous vehicles and will significantly accelerate the development and deployment of autonomous cars in the transportation sector. Promising autonomous cars for innovating modern transportation systems are anticipated to address many long-standing transporting challenges related to congestion, safety, parking, and energy conservation. Choosing the optimal AI architecture for autonomous vehicles is a multi-attribute decision-making (MADM) dilemma, as it requires making a complicated decision while considering a number of attributes, and these attributes can have two-dimensional uncertainty as well as indiscernibility. Thus, in this framework, we developed a novel mathematical framework “complex intuitionistic fuzzy rough set” for tackling both two-dimensional uncertainties and indiscernibility. We also developed the elementary operations of the deduced complex intuitionistic fuzzy rough set. Moreover, we developed complex intuitionistic fuzzy rough (weighted averaging, ordered weighted averaging, weighted geometric, and ordered weighted geometric) aggregation operators. Afterward, we developed a method of MADM by employing the devised operators and investigated the case study “Selection of optimal AI architecture for autonomous vehicles” to reveal the practicability of the devised method of MADM. Finally, to reveal the dominance and supremacy of our proposed work, a benchmark dilemma was used for comparison with various prevailing techniques.

Climate Change Prediction Model using MCDM Technique based on Neutrosophic Soft Functions with Aggregate Operators

The increasing impact of climate change necessitates innovative approaches in modeling and prediction to mitigate its adverse effects. This paper introduces a novel methodology integrating Neutrosophic Soft Functions (NSFs) into climate change prediction frameworks. NSFs, a hybrid of Neutrosophic Set Theory and Soft Set Theory, provide a flexible framework for handling uncertain and imprecise information inherent in climate data. This study explores the application of NSFs in capturing the complex interplay of various climatic variables, including temperature, precipitation, humidity, and atmospheric pressure, thereby enhancing the accuracy and reliability of climate change predictions. By incorporating NSFs into existing predictive models, such as neural networks and fuzzy systems, this research demonstrates significant improvements in forecast precision, particularly in scenarios with limited or noisy data. Additionally, the paper discusses the integration of NSFs with advanced machine learning algorithms for climate pattern recognition and anomaly detection, enabling timely identification of climate change indicators and facilitating proactive measures for adaptation and mitigation. Through empirical validation using real-world climate datasets, this study underscores the efficacy of NSFs in enhancing the predictive capabilities of climate change models, thereby contributing to more informed decision-making in climate-related policies and strategies.

A linear programming aggregation method based on generalized Zhenyuan integral in q-ROFN environment and the application of talent recruitment in universities

The reasonable ranking of binary pairs that characterize fuzzy information in many fuzzy decision problems is very important. To overcome some defects of the existing score functions for the q-rung orthopair fuzzy numbers (q-ROFNs), a novel score function and ranking criterion are proposed by the q-compression transformation and hesitation factor. The main motivation is to introduce the generalized Zhenyuan (GZ)-integral into the q-ROFN environment, and cleverly transform the aggregation operations into a linear programming problem through the arithmetic operations of q-ROFNs. The main contribution is to solve the aggregation problem of q-rung orthopair fuzzy generalized Zhenyuan integral ordered weighted average (q-ROFGZIOWA) operator through the optimization technique of linear programming, and a new decision making method is established by using the q-ROFGZIOWA operator and ranking criterion. The main innovation is to map all q-ROFNs to the unit triangle in the first quadrant (converted into intuitionistic fuzzy numbers, IFNs) according to the q-compression transformation in geometric significance, and the novel score function and its ranking criterion are proposed by combining hesitation factor, and then the aggregation operation based on generalized Z-integral is converted to an optimization problem in linear programming. Finally, the superiority of the proposed method are verified by comparing the aggregation results of two integral operators through an example, and apply the proposed method to the optimal decision-making of talent recruitment in universities. The proposed method can not only correct some flaws in the ranking of existing q-ROFNs, but also overcomes some defects of existing Choquet integral average (geometric) operators in a q-ROFN environment. These results are of great significance for further research on the widespread application of q-ROFNs.

Innovative player evaluation: Dual-possibility Pythagorean fuzzy hypersoft sets for accurate international football rankings

This study introduces an advanced approach for ranking international football players, addressing the inherent uncertainties in performance evaluations. By integrating dual possibility theory and Pythagorean fuzzy sets, the model accommodates varying degrees of ambiguity and imprecision in player attributes. Additionally, the use of hypersoft set theory enriches the analysis by capturing the multifaceted nature of player evaluations. The proposed aggregation operators refine the synthesis of diverse information sources, leading to a comprehensive and nuanced assessment. This research significantly enhances player evaluation methodologies, providing a more adaptable framework for a fair assessment of international football talent. A practical example illustrates the application of dual-possibility Pythagorean fuzzy hypersoft sets (DP-PFHSS). A numerical technique is proposed for solving multi-criteria decision-making (MCDM) challenges with known dual possibility information using the proposed aggregation operators. This decision-making algorithm effectively determines a football player's worth, contributing to the overall ranking and evaluation process. The approach aids in scouting and recruitment by facilitating talent identification and informed player signings. Graphical analysis, comparing existing and proposed methods using average and geometric operators, demonstrates the superiority of the proposed approach in the players evaluation, indicating that F1 is in the top ranking.

Complex Pythagorean neutrosophic normal interval-valued set with an aggregation operators using score values

The complex Pythagorean neutrosophic normal interval-valued set approach solves the multiple-attribute decision-making problem. We introduce the new concepts such as complex Pythagorean neutrosophic normal interval-valued weighted averaging, complex Pythagorean neutrosophic normal interval-valued weighted geometric, complex generalized Pythagorean neutrosophic normal interval-valued weighted averaging and complex generalized Pythagorean neutrosophic normal interval-valued weighted geometric operator. We demonstrate that complex Pythagorean neutrosophic normal interval-valued set satisfy algebraic structures such as associative, idempotent, bounded, commutative and monotonic properties. Additionally, we develop algorithm and flowchart that solve problems using these operators. Examples of using enhanced score values and accuracy values in real-world environments are provided in this paper. Artificial intelligence refers to the simulation or approximation of human intelligence in machines. Its goals include computer enhanced learning, reasoning and perception. Artificial intelligence is being used today across different industries, from finance to healthcare. Agricultural robots have been described as being highly dependent on computer and machine tool technology. Four factors can be used to evaluate the quality of a robotics system: the controller’s sophistication, the software efficiency, the maximum moment of inertia, and the manufacturer’s reliability. The best alternative can be determined by comparing expert opinions to the criteria. Therefore, the parameter ∇ has a very significant impact on the results of the model. This comparison aims to prove that the models under consideration are valid and valuable by comparing them with the available and proposed models. In conclusion, the value of ∇ significantly impacts the model performance. Based on the comparison and sensitivity analysis, we conclude that the proposed aggregation operation is superior and more reliable than the existing one. The criteria were compared to the most appropriate options based on expert assessments.

An integrated CRITIC-MABAC model under 2-tuple linguistic cubic q-rung orthopair fuzzy information with advanced aggregation operators, designed for multiple attribute group decision-making

An integrated CRITIC-MABAC model under 2-tuple linguistic cubic q-rung orthopair fuzzy information with advanced aggregation operators, designed for multiple attribute group decision-making

Interval-valued fermatean fuzzy Aczel-Alsina geometric aggregation operators and their applications to group decision-making

Developing new aggregation operators on various classes of fuzzy sets and their generalizations is important in modelling real-life decision-making problems. Interval-valued Fermatean fuzzy sets (IVFFs) generalize the idea of interval-valued Pythagorean fuzzy sets (IVPFS) play a crucial role in modelling problems involving inadequate information. Decision-making problems modelled using IVFFNs require different score functions and aggregation operators on the set of IVFFNs. This study mainly focuses on establishing a few interval-valued Fermatean fuzzy (IVFF) aggregation operators by integrating the Aczel-Alsina (AA) operations to deal with group decision-making (GDM) problems. In this work, first, we discuss various Aczel-Alsina-based IVFF operations such as AA sum, AA product, and AA scalar multiplication for proposing a few new aggregation operators for the IVFF environment based on the new IVFF operations. Secondly, we introduce a few operators, including the interval-valued Fermatean fuzzy Aczel-Alsina (IVFFAA) weighted geometric operator, the IVFFAA ordered weighted geometric (IVFFAAOWG) operator, and the IVFFAA hybrid geometric (IVFFAAHG) operator. Various important properties such as idempotency, boundness, and monotonicity have also been studied. Thirdly, we establish multi-criteria group decision-making (MCGDM) method for solving real-life decision-making problems. Fourthly, we solve a model GDM problem to show the applicability and efficacy of our proposed MCGDM method, which utilizes the IVFFAAWG operator. Further, a sensitivity analysis is performed to ensure better performance, and finally, a comparative study of our method is done by comparing our proposed MCGDM approach with different existing methods.

Navigating ambiguity: A novel neutrosophic cubic shapley normalized weighted Bonferroni Mean aggregation operator with application in the investment environment

The Neutrosophic Cubic Shapley Normalized Bonferroni (NC-SNWBM) method represents a cutting-edge approach to decision making theory, combining three distinct mathematical frameworks the neutrosophic cubic sets (NCS), Shapley values, and the Bonferroni aggregation operator. This innovative method addresses the challenges posed by uncertainty, vagueness, and imprecision in decision-making (DM) processes, offering a comprehensive and versatile tool for handling complex and dynamic scenarios. Neutrosophic cubic sets offers a strong platform to handle ambiguous and vague data due to three components Membership Grade (MG), Non-Membership Grade (NMG) and Indeterminancy Grade (IG) in data. By adding Shapley Fuzzy Measures (SFM), which come from cooperative game theory, distribute values among cooperative agents equally and to account for each agent's contributions to all potential coalitions. The Bonferroni aggregation operator—a statistical aggregative tool that regulates the likelihood of many types in error in statistical tests and the interdependence of the input arguments by allowing different values to parameters involved. These values are further improved by normalization in the framework of the NC-SNWBM approach in order to consider the various degrees of impact that agents exert in various circumstances. This operator is smoothly combined with normalized Shapley values and neutrosophic cubic sets in the NC-SNWBM approach to enable the aggregation of data with different levels of imprecision and uncertainty from various sources using NCS. The MG, NMG and IG connected to NCS are important elements of the NC-SNWBM approach. To evaluate each element's contribution to the overall value distribution SFM are used, and the Bonferroni aggregation operator maintains a careful balance between conservatism and significance. Together, these components provide a thorough framework that successfully tackles the problems caused by ambiguity, imprecision, and uncertainty in scenarios involving decision-making. The NC-SNWBM operator is applied to a numerical problem as an application in investment environment and sensitive and comparative analysis are conducted. The recommendation based on sensitive and comparative analysis proposed.