Bonferroni Mean Operator Research Articles

Identifying native endemic plant species in Nilgiris using the interval type 2 q-rung orthopair fuzzy Bonferroni mean operator

Identifying native endemic plant species in Nilgiris using the interval type 2 q-rung orthopair fuzzy Bonferroni mean operator

An Approach to MADM Based on Aczel-Alsina Power Bonferroni Aggregation Operators for q-Rung Orthopair Fuzzy Sets

The power Bonferroni mean (PBM) is a combined networking system that can benefit both the power average (PA) operator, which might attenuate the effects of irrational data provided by the prejudiced decision-makers (DMs), and the BM operator, which may incorporate the interconnections between any two attributes. In this paper, we defined the aggregation operators (AOs), such as the power average (PA) operator and the power Bonferroni mean (PBM) operator, based on the Aczel-Alsina (AA) operational rules under the environment of the q-Rung Orthopair fuzzy set (q-ROFS), and provided their specific characteristics for the solution of numerical problems. We extend the power Bonferroni mean (PBM) operator under the framework of q-ROFVs to establish the q-Rung Orthopair Fuzzy Aczel-Alsina power Bonferroni mean (q-ROFAAPBM) operator and the q-Rung Orthopair Fuzzy Aczel-Alsina weighted power Bonferroni mean (q-ROFAAWPBM) operator and discuss a few of the most useful properties of these AOs. After that, the q-ROFAAWPBM operator is used to solve the multi-attribute decision-making steps for q-ROFVs. The disease is diagnosed with the MADM method, which shows its usefulness and effectiveness. Finally, the comparison of our developed approach has been demonstrated to be superior and more effective than the existing literature, and we can conclude the result.

Generalized triangular Pythagorean fuzzy weighted Bonferroni operators and their application in multi-attribute decision-making

<abstract><p>The consolidation of evaluations from various decision-makers within a group, concerning multiple attributes of limited schemes, seeks to unify or compromise collective preferences according to specific rules. The superior characteristics of Possibility Fuzzy Sets (PFS) in membership endow it with enhanced capabilities in depicting ambiguous information. The Bonferroni operator proficiently mitigates the influences of interrelations between attributes in decision-making dilemmas. To address the Multi-Attribute Decision Making (MADM) conundrum wherein attribute values are associative Triangular Pythagorean Fuzzy Numbers (TPFNs), a novel methodology leveraging the Generalized Triangular Pythagorean Fuzzy Weighted Bonferroni Mean (GTPFWBM) operator and the Generalized Triangular Pythagorean Fuzzy Weighted Bonferroni Geometric Mean (GTPFWBGM) operator is advanced. Initiating with the foundational Triangular Pythagorean Fuzzy Set and the Generalized Bonferroni Mean (GBM) operator, both the GTPFWBM and GTPFWBGM operators are delineated. Subsequent exploration dives into the intrinsic properties of these pioneering operators, encompassing facets like reducibility, permutation invariance, idempotency, monotonicity and boundedness. Building upon this foundation, a MADM methodology predicated on the GTPFWBM and GTPFWBGM operators is conceptualized. The culmination of this research underscores the method's rationality and practicality, illustrated through a venture capital investment exemplar.</p></abstract>

Dombi Bonferroni Mean Operators Under Bipolar Complex Fuzzy Environment and Their Applications in Internet World

Internet is almost a necessary facility and tool to solve daily life problems in every field life. Whether at the individual level or national and international level sale purchase of any kind of object has always been of much importance, especially after Corona Pandemic, when online business is at its peak. Because of the enhancement of online sales and purchases, various businessmen are looking for suitable internet websites for their businesses, and the selection of the most suitable internet websites is one of the multi-attribute decision-making (MADM) dilemmas. Thus, in this script, we take benefits of three various concepts that are Bonferroni mean (BM) operator which is a significant technique to catch the interrelatedness among any number of inputs, Dombi operations which are based on Dombi t-norm and t-conorm and the ability to create an aggregation procedure more flexible because of the parameter, bipolar complex fuzzy set (BCFS) which is an outstanding model for tackling two-dimensional information with negative aspect and interpret bipolar complex fuzzy (BCF) Dombi Bonferroni mean (BCFDBM), BCF weighted Dombi Bonferroni mean (BCFWDBM), BCF Dombi geometric Bonferroni mean (BCFDGBM), and BCF weighted Dombi geometric Bonferroni mean (BCFWDGBM) operators. After ward, in this script, for tackling MADM dilemmas in the setting of BCFS, we investigate a MADM procedure based on the investigated operators and solve a MADM dilemma (selection of a suitable internet website for businessmen). Further, to display the superiority and efficiency of our work, we compare our approach and operators with a few current approaches and operators.

Novel Fermatean Fuzzy Bonferroni Mean aggregation operators for selecting optimal health care waste treatment technology

Fermatean fuzzy set (FFS) is an expedient tool in today’s world for coping with uncertainty, ambiguity, and incompleteness that emerge in many decision-making processes. In light of the relevance of FFS, this work offers a Multi-Criteria Group Decision Making (MCGDM) method together with Bonferroni mean and weighted Bonferroni mean operators in FF environment. These operators consider the interdependencies between the parameters into account during aggregation process in group decision making. On the other hand, health care waste (HCW) is an unavoidable byproduct of healthcare institutions, and so HCW management is vital owing to its negative influence on public health and environment. In this study, the proposed FFMCGDM has been applied to determine the optimal HCW treatment technologies (TT) for assuring sustainable environmental development, considering six TTs as alternatives assessing against nine criteria. Moreover, the proposed approach has been illustrated through an empirical case study of many district hospitals in Tripura, India. The obtained results are compared to other two well-known MCDM techniques as well as existing Fermatean Fuzzy Aggregation Operators (FFAOs). A sensitivity analysis has also been carried out to examine the stability of the model. From the analysis, it has been found that the proposed technique is competitive to obtain the optimal HCW TT. For further validation of the proposed method, a well-known MCDM problem, namely Green Supplier Selection (GSS) has been modeled and solved.

Evaluating alternative low carbon fuel technologies using a stakeholder participation-based q-rung orthopair linguistic multi-criteria framework

It is widely believed that alternative low carbon fuels (ALCF) can be instrumental in achieving the transportation sector’s decarbonization goal. Unlike conventional fossil-based fuels, ALCF can be produced through a combination of different chemical processes and feedstocks. The inherent complexity of the problem justifies the multi-criteria decision-making (MCDM) approach to support decision-making in the presence of multiple criteria and data uncertainty. In this paper, we propose a novel stakeholder participation-based MCDM framework integrating experts' perspectives on ALCF production pathways using the analytics hierarchy process (AHP) and the q-rung orthopair linguistic partition Bonferroni mean (q-ROLPBM) operator. The key merit of our approach lies in treating criteria of different dimensions as heterogeneous indicators while considering the mutual influence between criteria within the same dimension. The proposed framework is applied to evaluate four ALCF production pathways against 13 criteria categorised under economic, environmental, technical, and social dimensions for the case of the United Kingdom (UK). Our analysis revealed the environmental and the economic dimensions to be the most important, followed by the social and technical evaluation dimensions. The e-fuel followed by the e-biofuel are found to be the two top-ranked production pathways that utilise the electrochemical reduction process and its combination with anaerobic digestion. These findings, along with our recommendations, provide decision-makers with guidelines on ALCF production pathway selection and formulate effective policies for investment.

The aggregation of Z-numbers based on overlap functions and grouping functions and its application on group decision-making

In this paper, we propose a series of novel aggregation techniques based on overlap and grouping functions for group decision-making (GDM) issues in the Z-number environment. Firstly, we introduce an optimization model to determine the underlying distribution for Z-numbers, meanwhile, the mean function of Z-numbers is revised to better reflect the three-dimensional structure of the Z-numbers. And then, a series of operations for Z-numbers using overlap and grouping function are defined, and their properties are also investigated. Subsequently, we construct the overlap function-based Z-number weighted Bonferroni mean (OZWBM) operator to integrate the information in the Z-number environment. Furthermore, to verify the efficiency of novel aggregation techniques, a new energy investment selection issue is addressed. Besides giving the rankings of alternatives, by analyzing the calculation results, we can also derive the degree of preference from investment experts in scoring each investment object. Finally, by comparing the existing methodologies, we confirm that the new approach is effective and reasonable for the multi-criteria group decision-making (MCGDM).

Analyzing the effect of different types of pollution with bipolar complex fuzzy power Bonferroni mean operators

When any amount of harmful materials (any substance or any type of energy) is introduced into the climate at a rate quicker than it very well may be scattered or securely put away, then pollution occurs. These harmful materials are known as pollutants which can be natural and can also be manmade such as trash generated by factories. These harmful materials harm the quality of land, air, and water and cause various types of pollution, which affects the environment. In this article, we analyze the effect of various types of pollution on the environment and evaluate the most harmful type of pollution through an illustrative example by employing power Bonferroni mean (BM) operators in the setting of the bipolar complex fuzzy set (BCFS), like bipolar complex fuzzy (BCF) power BM (BCFPBM), BCF weighted power BM (BCFWPBM), BCF power geometric BM (BCFPGBM), and BCF weighted power geometric BM (BCFWPGBM) operators and a decision-making (DM) procedure created on these operators in the environment of the BCFS which are introduced in this article. Furthermore, we illustrate that the introduced operators and a DM procedure in the environment of the BCFS are more effective and have a wide model and advantages than certain prevailing works.

Multiple Attribute Decision-Making Based on Bonferroni Mean Operators under Square Root Fuzzy Set Environment

The intuitionistic fuzzy set (IFS), which has a membership and non-membership degree, is a controlling and effective device for dealing with fuzziness and uncertainty. Recently,the square root fuzzy set which is one of the efficient generalizations of an IFS for dealing with uncertainty and haziness in information has beenintroduced. In this study, a novel method for multiple attribute decision-making (MADM) based on SR-fuzzy information isinvestigated. Since aggregation operators are significant in the decision-making (DM) process, to achievethis goal, the current paper suggests a variety of novel Bonferroni mean and weighted Bonferroni mean operators to aggregate the SR-fuzzy values for the various decision-maker preferences. To achieve this goal, the current paper suggests a variety of novel Bonferroni mean and weighted Bonferroni mean operators to aggregate the SR-fuzzy values for the various decision-maker preferences. SR-fuzzyBonferroni mean operator and weighted SR-fuzzy Bonferroni mean operator are established and their properties are described. Then, we constructed a MADM approach using the proposed operators for the SR-fuzzyinformation and proved the approach with a mathematical example. Inthe end, a comparative study ofthe developed and existing approaches has been discussed to evaluate the pertinency and practicality of the proposed DM technique.

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

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

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.