Bonferroni Mean Research Articles

Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM

In this article, we propose the generalized version of the extended, partitioned Bonferroni mean (EPBM) operator with a systematic investigation of its behavior and properties. It can aggregate data of various dimensions in one formulation by modeling mandatory conditions along with partitioned structure interrelationships amongst the criterion set. In addition, we generate the condition for weight vectors satisfied by the weighting triangle associated with the proposed extended aggregation operator. We employed the proposed operator to aggregate a dataset following a hierarchical structure. We found that by implementing the proposed operator one can even rank the alternatives more intuitively with respect to any intermediate perspective of the hierarchical system. Finally, we present an application of the proposed extended aggregation operator in a case-based example of a child’s home environment quality evaluation with detailed analysis.

Improved Bonferroni mean operator to apprehend graph based data interconnections with application to the Hacker Attack system

The Bonferroni mean (BM) operator has extended the class of interrelationship handling fusion functions by modeling homogeneous pairwise interactions among data entities. This operator has been further extended to diverse directions with the intention of capturing dissimilar association that exists within data sets of different real-world systems like, social network systems, biological systems, etc. It has been observed that some of the existing forms of the BM operator pre-assumes a specific model of association among data entities during its formulation, which may not be feasible in many systems. In this study, an effort has been made to develop the framework of the BM operator by generalizing the structure of relationship patterns among data entities. Classical graphs are considered as a prominent tool for describing pairwise relations among data entities. Such consideration prompted the proposal of a systematized framework of an improved version of the BM operator, denoted by the fGBM operator, where the unconventional association among data entities are portrayed through different graphical patterns. The fGBM operator has been formulated in a way that the knowledge of interactional information depicted through graphs is embedded into its processing system with the aim of capturing precise interconnections among entities. The generalized variation of the fGBM operator has also been proposed by substituting the sub-components of the fGBM operator with other precise forms of the aggregation functions to provide an illustrative alignment, which is quite expressible and interpretable, and also facilitates modeling mandatory prerequisites of the decision systems. For an applicatory aspect, the proposed operators have been utilized over the Hacker attack system and have been presented with a numerical example. A detailed comprehensive analysis has been presented to demonstrate the efficiency of the proposed operators.

Exploring factors affecting airport selection during the COVID-19 pandemic from air cargo carriers’ perspective through the triangular fuzzy Dombi-Bonferroni BWM methodology

The COVID-19 pandemic has created unexpected demand for air cargo in terms of rapid mobility of critical basic needs. Air cargo carriers aim to maximize their profits by taking advantage of the current demand and using their limited capacity in the right place. At this point, some of the qualifications of the airports in the places where demand plays a crucial role in this decision of the carriers. Thus, evaluating the factors considered in the airport selection for air cargo carriers during the COVID-19 period is curious. This study proposes a triangular fuzzy Dombi-Bonferroni best-worst method (BWM) framework with vast flexibility to establish the priority preferences of factors considered in selecting airports. The fuzzy BWM model becomes a superior decision support system by combining the Bonferroni mean operator's ability to consider interrelationships between attributes and the flexibility of the Dombi operator. In this sense, we highlight eighteen criteria based on five airport aspects: location, physical features, performance, costs, and reputation. Findings reveal that the foremost aspects are location and costs, whereas the most crucial factors are airport charges and handling charges. The study suggests that airports should follow a low-price policy for airport-related charges without compromising their sustainability to have a share of the increasing number of air cargo flights, especially during the COVID-19 period, when airline passenger flights are decreased. The study is crucial in deciding the strategy and policy of air cargo carriers and airports during the pandemic period.

Multicriteria decision-making methods and application on the basis of probabilistic uncertain trapezium cloud

Probabilistic Uncertain Linguistic Term Set (PULTS), as an emerging and effective linguistic expression tool, can appropriately describe the complex evaluation information of decision makers. The cloud model is powerful in handling complex cognitive linguistic information, based on which, this paper proposes two new Multicriteria Decision-Making (MCDM) Methods with PULTSs. Firstly, to avoid the problem of information loss in traditional linguistic conversion methods, Probabilistic Uncertainty Trapezium Cloud (PUTC) is proposed to quantify linguistic evaluation information. Secondly, the Probabilistic Uncertainty Trapezium Cloud Weighted Bonferroni mean (PUTCWBM) operator is defined, while presenting a new cloud score function and similarity measures. Additionally, two ranking methods are proposed, one on the basis of the similarity measures of PUTCs and ideal solutions, the other on the basis of the PUTCWBM operator and the cloud score function. Finally, the two methods are verified with an example of evaluation on masks, and the effectiveness and superiority of the methods are further illustrated through sensitivity analysis and method comparison.

Analysis of medical diagnosis based on fuzzy credibility dombi Bonferroni mean operator

Analysis of medical diagnosis based on fuzzy credibility dombi Bonferroni mean operator

Bonferroni Weighted Logarithmic Averaging Distance Operator Applied to Investment Selection Decision Making

Distance measures in ordered weighted averaging (OWA) operators allow the modelling of complex decision making problems where a set of ideal values or characteristics are required to be met. The objective of this paper is to introduce extended distance measures and logarithmic OWA-based decision making operators especially designed for the analysis of financial investment options. Based on the immediate weights, Bonferroni means and logarithmic averaging operators, in this paper we introduce the immediate weights logarithmic distance (IWLD), the immediate weights ordered weighted logarithmic averaging distance (IWOWLAD), the hybrid weighted logarithmic distance (HWLD), the Bonferroni ordered weighted logarithmic averaging distance (B-OWLAD) operator, the Bonferroni immediate weights ordered weighted logarithmic averaging distance (B-IWOWLAD) operator and the Bonferroni hybrid weighted logarithmic distance (HWLD). A financial decision making illustrative example is proposed, and the main benefits of the characteristic design of the introduced operators is shown, which include the analysis of the interrelation between the modelled arguments required from the decision makers and the stakeholders, and the comparison to an ideal set of characteristics that the possible companies in the example must portray. Moreover, some families, particular cases and brief examples of the proposed operators, are studied and presented. Finally, among the main advantages are the modeling of diverse perspectives, attitudinal characteristics and complex scenarios, through the interrelation and comparison between the elements with an ideal set of characteristics given by the decision makers and a set of options.

Selecting a Project Delivery System for Wastewater Treatment Plants With Related-Indicators Under a Pythagorean Fuzzy Environment

Identifying appropriate project delivery systems for wastewater treatment plants (PDSWTPs) plays an important role for wastewater industry decision makers. This study aims to develop a PDSWTP selection model to deal with the related-indicators case by combining the advantages of Pythagorean fuzzy sets and Bonferroni mean operators. The works of this study are as follows: 1) the case with related indicators is innovatively considered as specific to the water industry, and Bonferroni mean operator and Pythagorean fuzzy sets are introduced to PDSWTP selection, which can handle complexity and fuzziness for the actual application. 2) Pythagorean fuzzy weighted Bonferroni mean (PFWBM) and Pythagorean fuzzy weighted geometry Bonferroni mean (PFWGBM) operators are used to aggregate all related indicators in PDSWTP selection, and taking full advantage of PFWBM and PFWGBM operators, a selection framework for PDSWTPs is constructed. 3) To show the robustness, the PDSWTP selection results were given with different parameters in the proposed operators. Finally, a practice example is created, and the results shown are effective and applicable.

Power Bonferroni mean operators under complex pythagorean fuzzy settings and their applications in decision-making problems

Bonferroni means (BM) operator is the extended form of the arithmetic mean operator, used for simplifying non-dominant and non-feasible problems diagnosed in genuine life scenarios. A lot of aggregation operators are the specific parts of the BM operators under the consideration of different values of parameters which are the main parts of the BM operators. In the presence of the BM operator and a very well-known conception in the scenario of fuzzy set, called complex Pythagorean fuzzy (CPF) setting, the objective of this scenario is to diagnose the CPF power BM (CPFPBM) operator and utilize their beneficial results with important properties. Moreover, a multi-attribute decision-making (MADM) technique is evaluated in the presence of invented operators for CPF settings. In the last of this study, we diagnosed the superiority and efficiency of the invented works with the help of sensitive analysis and graphical illustrations to enhance the gap of the research works.

Decision-making strategy based on Archimedean Bonferroni mean operators under complex Pythagorean fuzzy information

Decision-making strategy based on Archimedean Bonferroni mean operators under complex Pythagorean fuzzy information

Generalized Intuitionistic Fuzzy Normalized Weighted Optimized Geometric Bonferroni Mean and Their Application to MADM

In an information age, people often need to face a lot of decision-making information when making decisions. Some indicators are on the high side and others are on the low side which is a common phenomenon in decision-making. So, it is difficult to make a correct and rational judgment. Long-term research has proved that information aggregation operator is an effective tool to solve this kind of problem. Bonferroni mean (BM) is an important information aggregation tool which has the main feature of capturing the interrelationships among aggregated arguments. Because the existing geometric Bonferroni mean (GBM) cannot reflect the two-layer average calculation and the weighted GBM do not feature reducibility, this paper develops the intuitionistic fuzzy normalized weighted optimized GBM (IFNWOGBM) and the generalized intuitionistic fuzzy normalized weighted optimized GBM (GIFNWOGBM) and also studies their desirable properties and special cases. In the end, based on the IFNWOGBM and GIFNWOGBM, a method to multiple attribute decision-making (MADM) problem is proposed. In order to verify the effectiveness of the method, it is used to select the location of the library.

T-Spherical Fuzzy Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

To deal with complicated decision problems with T-Spherical fuzzy values in the aggregation process, T-Spherical fuzzy Bonferroni mean operators are developed by extending the Bonferroni mean and Dombi mean to a T-Spherical fuzzy environment. The T-spherical fuzzy interaction Bonferroni mean operator and the T-spherical fuzzy interaction geometric Bonferroni mean operator are first defined. Then, the T-spherical fuzzy interaction weighted Bonferroni mean operator and the T-spherical fuzzy weighted interaction geometric Bonferroni mean operator are defined. Based on the Dombi mean and the Bonferroni mean operator, some T-Spherical fuzzy Dombi Bonferroni mean operators are proposed, including the T-spherical fuzzy Dombi Bonferroni mean operator, T-spherical fuzzy geometric Dombi Bonferroni mean operator, T-spherical fuzzy weighted Dombi Bonferroni mean operator and the T-spherical fuzzy weighted geometric Dombi Bonferroni mean operator. The properties of these proposed operators are studied. An attribute weight determining method based on the T-spherical fuzzy entropy and symmetric T-spherical fuzzy cross-entropy is developed. A new decision making method based on the proposed T-Spherical fuzzy Bonferroni mean operators is proposed for partly known or completely unknown attribute weight situations. The furniture procurement problem is presented to illustrate the new algorithm, and some comparisons are made.

A Novel Decision-Making Method for Selecting Superintendent Based on a Q-Rung Dual Hesitant Fuzzy Power Partitioned Bonferroni Mean Operator

The Q-rung dual hesitant fuzzy (q-RDHF) set is famous for expressing information composed of asymmetry evaluations, because it allows for several possible evaluations in both the membership degree and non-membership degree. Compared with some existing extended fuzzy theories, the q-RDHF set is more superior and flexible because it can handle asymmetric assessments. In order to assemble the evaluation information expressed by q-RDHF elements, this paper aims to propose new operators to integrate q-RDHF elements. The partitioned Bonferroni mean (PBM) operator is well-known for its advantages in coping with the inhomogeneous relationship between asymmetry input arguments. In this paper, we combine the PBM operator with the power average operator, and propose a family of q-RDHF power PBM operators. Some theorems and special cases for the new proposed operators are discussed. Furthermore, we provide a general framework for dealing with multiple attribute decision-making (MADM) problems using the novel proposed method. To better show the calculation details, a numerical case study of the application of the proposed method in a superintendent selection problem is introduced. In addition, we utilize the proposed method to compare it with some existing methods in order to show its flexibility and superiority. The results show that our method is much more advantageous when considering flexible actual situations. Finally, the conclusion is given. The main contributions of this study are to propose an appropriate method to solve unbalanced and asymmetry information in a q-RDHF environment, and to apply it into a realistic superintendent selection problem.

Analysis and Applications of Bonferroni Mean Operators and TOPSIS Method in Complete Cubic Intuitionistic Complex Fuzzy Information Systems

This article manages vagueness, asymmetric data, and risk demonstrated in awkward information. The ambiguity is handled with the help of possibility and strategic decision-making theory. A MADM (multi-attribute decision-making) tool, the sub-part of the strategic decision theory, plays an important role in the circumstances of fuzzy data. The major influence of this analysis is to initiate the mathematical ideology of cubic intuitionistic complex fuzzy (CICF) information and its well-known properties such as algebraic laws, score values, and accuracy values. It is also to determine various inequalities for finding the relation between any two CICF numbers (CICFNs). Further, we know that the Bonferroni mean (BM) operator is more generalized than the simple averaging/geometric aggregation operators due to parameters involved in the mathematical form of BM operators. Keeping the supremacy and consistency of BM operators, the idea of CICF Bonferroni mean (CICFBM) and CICF weighted BM (CICFWBM) operators are diagnosed. We try to describe their well-known results and properties such as idempotency, monotonicity, commutativity, and boundedness with various specific cases. Further, we investigate three different sorts of decision-making procedures such as MADM tool, TOPSIS (Technique for order of preference by similarity to ideal solution) method using similarity measures, and TOPSIS method using aggregation operators to enhance the quality of the decision-making process. This analysis expressed how to make decisions when there is asymmetric data about companies. Finally, we compute the comparative analysis of the diagnostic approaches with various existing theories to demonstrate the feasibility and flexibility of the exposed work to try to illustrate with the help of geometrical expressions.

A group decision‐making algorithm considering interaction and feedback mechanisms for dynamic supplier selection under q‐ rung orthopair fuzzy information

Supplier selection is vital for enterprises to operate stably and achieve and sustain a competitive advantage. However, from the initial establishment to the gradual development and maturity of the enterprise, the supplier selection criteria change dynamically, and decision-makers are hardly in agreement in each stage, which creates challenges for enterprises when choosing suitable suppliers. As such, this paper proposes a multicriteria group decision-making method based on an interaction and feedback mechanism (IFM) and q-rung orthopair fuzzy sets theory. We introduce an IFM to achieve consensus among different decision-makers. We then develop the q-rung orthopair fuzzy weighted partitioned Bonferroni mean (q-ROFWPBM) operator to address the aggregation problem of dynamic multicriteria. A group decision-making algorithm combining the IFM and q-ROFWPBM operator is proposed to analyze the Hongxing Erke supplier selection. The results show that the proposed method can not only account for large differences of opinion among decision-makers during group decision-making but also consider the dynamic changes of supplier selection criteria in different stages of enterprise development and help enterprises choose suppliers suitable for their own development characteristics.

A multi-voter multi-commission nearest neighbor classifier

Many improved versions of k-nearest neighbor (KNN) have been proposed by minimizing total distances of multi k nearest neighbors (multi-voter) in each class instead of the majority voting, such as a local mean-based pseudo nearest neighbor (LMPNN) that give a better decision. In this paper, a new KNN variant called multi-voter multi-commission nearest neighbor (MVMCNN) is proposed to examine its benefits in enhancing the LMPNN. As the name suggests, MVMCNN uses some commissions: each calculates the total distance between the given query point (test pattern) and k pseudo nearest neighbors using the LMPNN scheme. The decision class is defined by minimizing those total distances. Hence, the decision in MVMCNN is obtained more locally than LMPNN. Examination based on 10-fold cross-validation shows that the proposed multi-commission scheme can enhance the original (single-commission) LMPNN. Compared with two single-voter models: KNN and Bonferroni Mean Fuzzy k-Nearest Neighbors (BM-FKNN), the proposed MVMCNN also gives lower mean error rates as well as higher Precision, Recall, and F1 Score, indicating that the multi-voter model provides a better decision than the single-voter ones.

BLeafNet: A Bonferroni mean operator based fusion of CNN models for plant identification using leaf image classification

Plants, the only natural source of oxygen, are the most important resources for every species in the world. A proper identification of plants is important for different fields. The observation of leaf characteristics is a popular method as leaves are easily available for examination. Researchers are increasingly applying image processing techniques for the identification of plants based on leaf images. In this paper, we have proposed a leaf image classification model, called BLeafNet, for plant identification, where the concept of deep learning is combined with Bonferroni fusion learning. Initially, we have designed five classification models, using ResNet-50 architecture, where five different inputs are separately used in the models. The inputs are the five variants of the leaf grayscale images, RGB, and three individual channels of RGB - red, green, and blue. For fusion of the five ResNet-50 outputs, we have used the Bonferroni mean operator as it expresses better connectivity among the confidence scores, and it also obtains better results than the individual models. We have also proposed a two-tier training method for properly training the end-to-end model. To evaluate the proposed model, we have used the Malayakew dataset, collected at the Royal Botanic Gardens in New England, which is a very challenging dataset as many leaves from different species have a very similar appearance. Besides, the proposed method is evaluated using the Leafsnap and the Flavia datasets. The obtained results on both the datasets confirm the superiority of the model as it outperforms the results achieved by many state-of-the-art models.

Novel Aczel–Alsina operations-based hesitant fuzzy aggregation operators and their applications in cyclone disaster assessment

As a fuzzy set (FS) expansion, the hesitant fuzzy set (HFS) is successfully employed to demonstrate circumstances where it is admissible to ascertain a few potential membership degrees (MDs) of a component in a set because of the uncertainty between various values. Considering that there is still no research on Aczel–Alsina triangular norms and conorms in a hesitant fuzzy (HF) environment, in this article we introduce for the first time, Aczel–Alsina operations on HFSs. Then, based on these operations, we originate a few new aggregation operators for aggregating HF information namely HF Aczel–Alsina weighted averaging (HFAAWA) operator, HF Aczel–Alsina ordered weighted averaging (HFAAOWA) operator, HF Aczel–Alsina hybrid averaging (HFAAHA) operator, HF Aczel–Alsina weighted geometric (HFAAWG) operator, HF Aczel–Alsina ordered weighted geometric (HFAAOWG) operator, HF Aczel–Alsina hybrid geometric (HFAAHG) operator and HF Aczel–Alsina weighted Bonferroni mean (HFAAWBM) operator. Some essential characteristics of those suggested operators are shown, and the interrelatedness between them is displayed exhaustively. Then, we take advantage of those operators to produce a methodology to interpret the HF multiple attribute decision making (MADM) difficulties. We present a functional model for cyclone disaster assessment to certify the produced approaches and to establish their effectiveness and practicality. Further, we conduct comparison analysis for the legitimacy of our produced methodologies.

Covering-based compound mean operators arising from Heronian and Bonferroni mean operators in fuzzy and intuitionistic fuzzy environments

Both Heronian mean (HM) operators and Bonferroni mean (BM) operators can capture the interrelationship between input arguments and have been a hot research topic as a useful aggregation technique in fuzzy and intuitionistic fuzzy environments. In this paper, associated with the common characters of these operators we propose the covering-based compound mean operators in fuzzy environments to capture various interrelationships between input arguments, some desirable properties and special cases of the proposed mean operators are provided. Then, conditions under which these covering-based compound mean operators can be directly used to aggregate the membership degrees and nonmembership degrees of intuitionistic fuzzy information, are provided. In particular, novel intuitionistic fuzzy HM operators and intuitionistic fuzzy BM operators are directly derived from the classical ones. We list the detailed steps of multiple attribute decision making with the developed aggregation operators, and give a comparison of the new extensions of BM operators by this paper with the corresponding existing ones to prove the rationality and effectiveness of the proposed method.

An integrated qualitative group decision-making method for assessing health-care waste treatment technologies based on linguistic terms with weakened hedges

The assessment of the treatment technologies is a vital point for health care waste (HCW) management. The assessment process is regarded as a multi-attribute group decision-making problem. Considering individual knowledge backgrounds and psychological preferences, and various uncertainty factors which are difficult to describe numerical and precisely, experts often portray their individual assessments by employing qualitative expressions. Linguistic term with weakened hedge (LTWH) is an effective tool to quantify the qualitative information. Additionally, the Bonferroni mean (BM) can capture the interrelationship between input data and the combined compromise solution (CoCoSo) method could produce reliable outcomes. In this paper, we extend the BM operator into the LTWH environment and propose the linguistic term with weakened hedge BM (LTWHBM) operator and the weighted version, i.e., LTWHWBM, to depict the indeterminacy in the HCW management and cope with assessment of the treatment technology problems based on the developed novel operational rules of LTWHs. Various properties and special cases of these operators are investigated in detail. Furthermore, we design a LTWHWBM based CoCoSo group decision-making model, herein the LTWHWBM operator is employed to integrate individual experts’ preferences and the extend CoCoSo method is utilized to yield the ranking of alternatives. Ultimately, a case study concerning the assessment of the HCW treatment technologies is performed. The feasibility and favorable characteristics of the established model are justified by the comparisons with several prevailing methodologies and sensitivity analyses.

Performance Evaluation of Solar Energy Cells Using the Interval-Valued T-Spherical Fuzzy Bonferroni Mean Operators

To find the correspondence between every number of attributes, the Bonferroni mean (BM) operator is most widely used and proven to be a flexible approach. To express uncertain information, the frame of the interval-valued T-spherical fuzzy set (IVTSFS) is a recent development in fuzzy settings which discusses four aspects of uncertain information using closed sub-intervals of [0,1] and hence reduces the information loss greatly. In this research study, we introduced the principle of BM operators with IVTSFS to develop the principle of the inter-valued T-spherical fuzzy (IVTSF) BM (IVTSFBM) operator, the IVTSF-weighted BM (IVTSFWBM) operator, the IVTSF geometric BM (IVTSFGBM) operator, and the IVTSF-weighted geometric BM (IVTSFWGBM) operator. To see the significance of the proposed BM operators, we applied these BM operators to evaluate the performance of solar cells that play an important role in the field of energy storage. To do so, we developed a multi-attribute group decision-making (MAGDM) procedure based on IVTSF information and applied it to the problem of solar cells to evaluate their performance under uncertainty, where four aspects of opinion about solar cells were taken into consideration. We studied the results obtained using BM operators with some previous operators to see the significance of the proposed IVTSF BM operators.