Aggregation Operators Research Articles

Neural net influenced magdm problem with modified choquet integral aggregation operators and correlation coefficient for triangular fuzzy intuitionistic fuzzy sets

Neural net influenced magdm problem with modified choquet integral aggregation operators and correlation coefficient for triangular fuzzy intuitionistic fuzzy sets

HQ-Net: A heatmap-based query backbone for point cloud understanding

With the advancement of sensor technology, including LiDAR and RGB-D cameras, tasks related to point cloud understanding have gained widespread application. The sampling and learning of feature points play a crucial role in point cloud understanding, representing a fundamental and essential aspect of 3D computer vision. In the realm of point cloud processing, traditional methods such as Farthest Point Sampling (FPS) are frequently employed to select feature points. These points are then used in conjunction with effective feature aggregation operators to facilitate reasoning. However, these traditional sampling methods primarily focus on the Euclidean distance between points, lacking a comprehensive consideration of point cloud features. To address this limitation, we introduce HQ-Net, a novel point cloud understanding model designed to optimize feature point sampling using a Heatmap-based Query Backbone. The Heatmap-based Query Backbone utilizes the Heatmap Module to select category-specific point features, effectively generating a heatmap tailored to the category features and automatically extracting features from the heatmap. Subsequently, the proposed Query Encoder is employed to facilitate the interaction between point features and query features, providing mutual guidance and enhancing the model’s ability to capture spatial structure and semantic information within point clouds. Additionally, we propose task-specific heads, such as classification and segmentation heads for different tasks, which can be seamlessly integrated with the backbone to achieve excellent performance. In various point cloud understanding tasks, including shape classification, part segmentation, and semantic segmentation, HQ-Net demonstrates excellent performance.

The fuzzy inference system based on axiomatic fuzzy sets using overlap functions as aggregation operators and its approximation properties

The fuzzy inference system based on axiomatic fuzzy sets using overlap functions as aggregation operators and its approximation properties

Distance and similarity measures on belief and plausibility under q-rung orthopair fuzzy sets with applications

Belief and plausibility functions based on evidence theory (ET) have been widely used in managing uncertainty. Various generalizations of ET to fuzzy sets (FSs) have been reported in the literature, but no generalization of ET to q-rung orthopair fuzzy sets (q-ROFSs) has been made yet. Therefore, this paper proposes a novel, simple, and intuitive approach to distance and similarity measures for q-ROFSs based on belief and plausibility functions within the framework of ET. This research addresses a significant research gap by introducing a comprehensive framework for handling uncertainty in q-ROFSs using ET. Furthermore, it acknowledges the limitations inherent in the current state of research, notably the absence of generalizations of ET to q-ROFSs and the challenges in extending belief and plausibility measures to certain aggregation operators and other generalizations including Hesitant fuzzy sets, Bipolar fuzzy sets, Fuzzy soft sets etc. Our contribution lies in the proposal of a novel approach to distance and similarity measures for q-ROFSs under ET, utilizing Orthopairian belief and plausibility intervals (OBPIs). We establish new similarity measures within the generalized ET framework and demonstrate the reasonability of our method through useful numerical examples. Additionally, we construct Orthopairian belief and plausibility GRA (OBP-GRA) for managing daily life complex issues, particularly in multicriteria decision-making scenarios. Numerical simulations and results confirm the usability and practical applicability of our proposed method in the framework of ET.

An infrared and visible image fusion using knowledge measures for intuitionistic fuzzy sets and Swin Transformer

The objectives of infrared and visible image fusion are to generate a single image that includes significant objects and rich texture information. However, the current deep-learning methods ignore uncertainty in the decision-making process during the fusion phase. To address this issue, we propose a novel infrared and visible image fusion method using a Swin Transformer and knowledge measures of intuitionistic fuzzy sets (IFSs) named SWKIF-Fusion. This model employs a Swin Transformer-based pre-trained module for feature extraction, which is the most effective module for modeling long-range dependencies. The fusion process of SWKIF-Fusion integrates the proposed knowledge measure of IFSs. IFSs inherently possess a high capability to handle uncertainty, and the knowledge measure of IFSs provides uncertainty quantification. This integration in the fusion phase mitigates the uncertainty in the decision-making process. This fusion of IFSs, knowledge measures, and the Swin Transformer-based deep learning model enhances the overall performance, as demonstrated through experiments on the TNO, Roadscene, OTCBVS, M3FD, and MSRS datasets. This study also fills the gap in developing knowledge measures for IFSs by proposing novel general construction methods. It presents a theoretically sound framework for knowledge measures of IFSs using well-established mathematical concepts such as t-norms, t-conorms, automorphisms, and aggregation operators.

Innovative approaches to multi-attribute decision-making in brain carcinoma diagnosis: a complex q-rung orthopair trapezoidal fuzzy framework and aggregation operator analysis

Innovative approaches to multi-attribute decision-making in brain carcinoma diagnosis: a complex q-rung orthopair trapezoidal fuzzy framework and aggregation operator analysis

Real-Life Applications of New Type Spherical Fuzzy Sets and Its Extension Using Aggregation Operators

The purpose of this article is to present a novel approach to the multiple attribute decision-making problem (MADM) based on (l1, l2) spherical fuzzy sets (SFS). This is an extension of the SFS. As a result of this article, we will discuss the concept of spherical fuzzy weighted averaging (SFWA), spherical fuzzy weighted geometric (SFWG), generalized spherical fuzzy weighted averaging (GSFWA) and generalized spherical fuzzy weighted geometric (GSFWG). Here is a flowchart that shows how these operators are used in the algorithm we discussed. With the help of a numerical example, we illustrate the extended Euclidean and Hamming distance measures. Additionally, the SFN approach is characterized by idempotency, boundedness, commutativity, and monotonicity. These tools help you find the best option faster, simpler, and more conveniently. The result is a more precise conclusion and a more intimate relationship between (l1, l2). We compare some of the current models with those that have been proposed in order to demonstrate the dependability and utility of the models under investigation. The study also revealed fascinating and intriguing findings.

Ordering blockchain technology for multinational companies based on Yager aggregation operators under bipolar fuzzy information

Ordering blockchain technology for multinational companies based on Yager aggregation operators under bipolar fuzzy information

An Intelligent Decision Support System for Spherical Fuzzy Sugeno-Weber Aggregation Operators and Real-Life Applications

This article presents a novel approach to a decision support system for handling uncertainty and impreciseness in a large amount of human opinion. Sometimes, the aggregation of real-life applications is quite complex due to incomplete and redundant information about different preferences or alternatives. To handle such type of situations, a spherical fuzzy environment is a more effective and feasible framework with four components membership, abstinence, non-membership and refusal degree. We also formulate some flexible operations of Sugeno-Weber aggregation operators. Motivated by the theory of Sugeno-Weber t-norms, we constructed a family of mathematical methodologies, including Sugeno-Weber weighted average and weighted geometric operators in the light of spherical fuzzy information. An appropriate decision-making technique of the multi-attribute decision making (MADM) problem is also demonstrated to resolve complicated real-life applications. A numerical example is used to verify the compatibility and effectiveness of discussed mathematical approaches.

Analyzing risk factors of tuberculosis using type-2 interval-valued trapezoidal fuzzy numbers with Einstein aggregation operators extended to MCDM

The principal motive of this work is to evolve and initiate an extension from interval-valued fuzzy sets to type-2 interval-valued fuzzy sets (T2IVFS) related to weighted aggregation functions containing the Einstein operator. The chief reason for this extension is that the constancy of the terms can also be taken into data during the aggregation operation. The main goal of this article is to compose the aggregation operators and their characteristics such as the Type-2 interval-valued fuzzy Einstein weighted arithmetic aggregating operator (T2IVFEWA), Type-2 interval-valued fuzzy Einstein weighted geometric aggregating operator (T2IVFEWG), and the characteristics are expressed. At last, to intimate the effectiveness of the suggested approach and explicate the purpose of these operators, a hybrid multi-criteria decision-making problem (MCDM) to select the best risk factor for Tuberculosis (TB) is considered and the result is compared with the outcome of the existing operators and methods. Additionally, a sensitivity analysis was conducted to verify the robustness of the proposed decision-making process.

Development of Aczel-Alsina t-norm based linear Diophantine fuzzy aggregation operators and their applications in multi-criteria decision-making with unknown weight information

Aczel-Alsina t-norm and t-conorm are intrinsically flexible and endow Aczel-Alsina aggregation operators with greater versatility and robustness in the aggregation process than operators rooted in other t-norms and t-conorm families. Moreover, the linear Diophantine fuzzy set (LD-FS) is one of the resilient extensions of the fuzzy sets (FSs), intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PyFSs), and q-rung orthopair fuzzy sets (q-ROFSs), which has acquired prominence in decision analysis due to its exceptional efficacy in resolving ambiguous data. Keeping in view the advantages of both LD-FSs and Aczel-Alsina aggregation operators, this article aims to establish Aczel-Alsina operation rules for LD-FSs, such as Aczel-Alsina sum, Aczel-Alsina product, Aczel-Alsina scalar multiplication, and Aczel-Alsina exponentiation. Based on these operation rules, we expose the linear Diophantine fuzzy Aczel-Alsina weighted average (LDFAAWA) operator, and linear Diophantine fuzzy Aczel-Alsina weighted geometric (LDFAAWG) operator and scrutinize their distinctive characteristics and results. Additionally, based on these aggregation operators (AOs), a multi-criteria decision-making (MCDM) approach is designed and tested with a practical case study related to forecasting weather under an LD-FS setting. The developed model undergoes a comparative analysis with several prevailing approaches to demonstrate the superiority and accuracy of the proposed model. Besides, the influence of the parameter Λ on the ranking order is successfully highlighted.

Divergence Measures and Aggregation Operators for Single-Valued Neutrosophic Sets with Applications in Decision-Making Problems

Divergence Measures and Aggregation Operators for Single-Valued Neutrosophic Sets with Applications in Decision-Making Problems

Multi-criteria decision-making model based on picture hesitant fuzzy soft set approach: An application of sustainable solar energy management

This study addresses the optimization of energy management within corporations to reduce expenditures and maximize profits. Focusing on proactive, coordinated, and systematic energy usage, the research emphasizes the importance of informed decisions through building management, energy audits, and equipment retrofits. The proposed concept of Picture Hesitant Fuzzy Soft Set (PHFSS) with Archimedean aggregation operators, featuring Einstein generators, is introduced. Various aggregation techniques, including PHFS weighted, weighted ordered, weighted geometric, ordered weighted geometric, and hybrid operators, are thoroughly examined. PHFSS is utilized to represent ambiguous information in decision-making processes. The study introduces a novel multi-criteria decision-making (MCDM) method to address the challenge of selecting optimal energy management sources, demonstrating its effectiveness through a large-scale numerical example. This approach surpasses the distance from average solution (EDAS) method in terms of effectiveness and reliability. The research contributes valuable insights into optimizing energy management, reducing costs, and mitigating environmental impact.

Application of Improved Class of Weighted Averaging Operators in Intuitionistic Fuzzy Ann Guided MAGDM E-Commerce Problems

Objectives: To propose a novel and improvised Artificial Neural Network (ANN) technique to solve Multiple Attribute Group Decision Making (MAGDM) problems and an improved class of Aggregation operators for combining Intuitionistic Fuzzy Set (IFS) matrices for the ANN algorithm. Methods: A novel class of improved aggregation operators namely the Improved Intuitionistic Fuzzy Weighted Arithmetic Averaging (IM-IFWAA) operator and the Improved Intuitionistic Fuzzy Ordered Weighted Averaging (IM-IFOWA) operator are proposed in this work. The proposed improved class of aggregation operators will aggregate the IFS matrix data sets appearing in the form of matrices and then the revised input vectors which is then fed into the ANN algorithm following Delta, Perceptron, and Hebb Learning Rule for the next phase. Findings: Aggregating the Intuitionistic Fuzzy set information or data in today’s digital world is a tedious task in the field of MAGDM problem-solving. In this work, two new classes of operators for aggregating the data sets are proposed namely the IM-IFWAA operator and the IM-IFOWA operator which will improve the performance of the ANN. Necessary theorems for the proposed operators are proved to provide consistency of the same. The input created using the aforementioned operators is then fed into the novel ANN algorithm for further computations. Varieties of learning rules are then engaged for ranking of the best alternative for the decision problem. The developed theory is supported by a numerical example which is computed using all the proposed techniques. Novelty: Most of the research done on Intuitionistic Fuzzy Artificial Neural Network models are based on learning rules or using some other calculations. The proposed methods of using novel and improvised aggregation operators for ANN are used to find the inputs for ANN where varieties of learning rules for ANN are employed for effective decision analysis. Keywords: ANN, Learning Rules, MAGDM, Intuitionistic Fuzzy Sets, Weighted Aggregation Operator

Research on group decision optimization and influence analysis in social network based on machine learning

With the rapid development of online social networks, the research on group decision-making in social networks has attracted extensive attention. Social networks facilitate interaction and behavior between individuals, businesses, and organizations. However, traditional group decision-making methods often ignore the social relationships between group members and fail to fully consider the impact of these relationships on subgroup division. In this work, we propose a novel model approach that combines graph neural networks and deep learning techniques to capture and analyze complex relational structures in social networks. The model uses node features and edge features to optimize the group decision-making process and effectively evaluate the influence between individuals through multi-layer network embedding and aggregation operations. Experimental analysis results show that the proposed method performs well in improving the accuracy and efficiency of decision-making, and significantly improves the quality of decision-making.

Utilizing aggregation operators based on q-rung orthopair neutrosophic soft sets and their applications in multi-attributes decision making problems

Neutrosophic sets provide greater versatility in dealing with a variety of uncertainties, including independent, partially independent, and entirely dependent scenarios, which q-ROF soft sets cannot handle. Indeterminacy, on the other hand, is ignored completely or partially by q-ROF soft sets. To address this issue, this study offers a unique novel concept as known as q-RONSS, which combines neutrosophic set with q-ROF soft set. This technique addresses vagueness using a set of truth, indeterminacy, and false membership degrees associated with the parametrization tool, with the condition that the sum of the qth power of the truth, indeterminacy, and false membership degrees be less than or equal to one. In addition, this study outlines operational laws for the suggested structure. The main purpose this article is to define some averaging and geometric operators based on the q-rung orthopair neutrosophic soft set. Furthermore, this article provides a step-by-step method and a mathematical model for the suggested techniques. To solve a MADM issue, this research article proposes a numerical example of people selection for a specific position in a real estate business based on a variety of criteria. Finally, to demonstrate the proposed model's superiority and authenticity, this article performs several analyses, including sensitivity analysis, to address the reliability and influence of various parameter "q" values on the alternatives and the ultimate ranking outcomes using the averaging and geometric operators. A comparison of the proposed operators to current operators demonstrates the validity of the proposed structure. Furthermore, a comparison of the proposed structure to current theories demonstrates its superiority by overcoming their limits and offering a more flexible and adaptable framework. Finally, this study reviews the findings and consequences of our research.

Using a fuzzy credibility neural network to select nanomaterials for nanosensors

Nanomaterials are the most important component of nanosensors, and the selection of the most desirable nanomaterial for nanosensors is a challenge for companies. The classical decision making procedure is very difficult and uncertain to select the desirable nanomaterial. Therefore, we develop a decision making model based on a fuzzy credibility neural network. In this article, we introduce a novel fuzzy credibility neural network using Dombi t-norms and co-norms and also using the score function of fuzzy credibility numbers. Further, the fuzzy credibility neural network applies to the decision making model for the selection of the best nanomaterial for nanosensors. In this approach or decision making model, we first collect data from three experts in the form of fuzzy credibility numbers and then use a neural network to aggregate the data with the help of Dombi t-norm and t-conorm. We consider the expert decision making criteria, which correspond to the input signals of the fuzzy credibility neural network, and calculate the weight of the input signal using distance measure techniques. Next, we compute the hidden layer information and the output layer information by using the fuzzy credibility neural network with the Dombi aggregation operator. The proposed approach is compared with other existing models of decision making and the results of the comparison show that the proposed technique is applicable and reliable for the decision support model.

Associated Probabilities’ Aggregations in Fuzzy Collaborative Filtering Recommender System Prediction

AbstractIn this article, the expert evaluations transformed in the multi-attribute decision-making (MADM) model are presented in the discrimination q-rung picture linguistic fuzzy numbers (q-RPLFNs). In the construction of a second-order additive fuzzy measure (TOAFM) the attributes’ interaction indexes and Shapley values are taken into account. The Shapley entropy maximum principle for identification of associated probabilities class (APC) of a TOAFM is constructed. Based on the APC of the TOAFM, a new aggregation operators’ class is constructed which represents some hybrid extensions of ordered weighted averaging (OWA), geometric (OWG), the Choquet integral averaging (CA) and geometric (CG) operators under discrimination q-rung orthopair fuzzy (q-ROF) and q-rung picture linguistic fuzzy (q-RPLF) information. These operators, constructed for the q-RPLF and q-ROF environments, take into account the overall pair interactions among attributes. Main properties on the correctness of extensions are proved: for the lower and upper capacities of order 2, all constructed operators consequently coincide with q-ROF and q-RPLF Choquet averaging and geometric operators, respectively. Constructed operators in the evaluation of prediction of fuzzy Collaborative Filtering Recommender Systems (CFRS) are used. New symmetric discrimination measures as some extensions of discrimination measures for the fuzzy CFRS are proposed. Users’ profile data by the constructed operators in the new similarity measure under q-rung picture linguistic environment are aggregated. The developed new approach is schematically described in such a way that it can be “embedded” in any existing CFRS model. An example is given to illustrate the results, for which the software designed to aggregate profile data for similarity comparison provides the use of new and well-known classical aggregation operators.

Development and experimental validation of analytical structures of some simplest fuzzy PI/PD controllers using Bounded Sum aggregation

In this work, utilization of Bounded Sum (BS) as an aggregation operator has been explored in the modeling of the simplest fuzzy two-term (PI/PD) controllers. Analytical structures of eight distinct fuzzy two-term controllers utilizing Larsen Product (LP) or Mamdani Minimum (MM) inference and Center of Area (CoA) defuzzification have been derived. In addition to modeling, analysis of controllers for their properties is conducted. Simulation studies are carried out on two nonlinear dynamic systems to show the effectiveness of the controllers proposed in this work. Apart from this, a real-time experimentation has also been conducted to test the applicability of the proposed controllers.

Aggregation operators based on Einstein averaging under q-spherical fuzzy rough sets and their applications in navigation systems for automatic cars

This study introduces innovative operational laws, Einstein operations, and novel aggregation algorithms tailored for handling q-spherical fuzzy rough data. The research article presents three newly designed arithmetic averaging operators: q-spherical fuzzy rough Einstein weighted averaging, q-spherical fuzzy rough Einstein ordered weighted averaging, and q-spherical fuzzy rough Einstein hybrid weighted averaging. These operators are meticulously crafted to enhance precision and accuracy in arithmetic averaging. By thoroughly examining their characteristics and interrelations with existing aggregate operators, the article uncovers their distinct advantages and innovative contributions to the field. Furthermore, the study illustrates the actual implementation of these newly constructed operators in a variety of attribute decision-making scenarios employing q-SFR data, yielding useful insights. Our suite of decision-making tools, including these operators, is specifically designed to address complex and uncertain data. To validate our approach, this study offers a numerical example showcasing the real-world applicability of the proposed operators. The results not only corroborate the efficacy of the proposed method but also underscore its potential significance in practical decision-making processes dealing with intricate and ambiguous data. Additionally, comparative and sensitivity analyses are presented to assess the effectiveness and robustness of our proposed work relative to other approaches. The acquired knowledge enriches the current understanding and opens new avenues for future research.