Bonferroni Mean Operator Research Articles

Evaluating risk of IoT adoption in the food supply chain using an integrated interval-valued spherical fuzzy generalised TODIM method

The existing literature has shown that the Internet of Things (IoT) has proven to be beneficial for managing operations in the food supply chain. However, the potential failures resulting from these new technologies have not been thoroughly examined. Therefore, the aim of this study is to create a new framework for analyzing the risks associated with implementing IoT in the food supply chain. To achieve this, we introduce an extended failure mode and effect analysis framework using an integrated generalised Toma de Decisão Iterativa Multicritério (TODIM) method within the interval-valued spherical fuzzy setting. Initially, we developed a risk structure consisting of four dimensions and sixteen sub-factors to facilitate the implementation of IoT technology in the food supply chain. We then introduced an interval-valued spherical fuzzy-weighted Bonferroni mean operator to gather expert opinions and create a group risk matrix considering the interaction between the input risk data. Subsequently, we proposed a newly developed interval-valued spherical fuzzy TODIM method based on the Logarithmic percentage change-driven objective weighting (LOPCOW) method to evaluate and rank the risks associated with IoT application in the food supply chain. This method can capture the bounded rational decision behavior of experts and the uncertain preference of risk parameters. Based on the identified risk factors, we implemented a proposed risk analysis framework in line with the preferences of the experts. The results indicate that "human resource risk" and "uncertainty in technology adoption" are the most and least significant risks, respectively. We also conducted sensitivity and comparison studies to test the reliability and rationality of the proposed framework. The main findings can assist policymakers and managers in mitigating and minimizing the risks connected with IoT applications in the food supply chain. Additionally, these outcomes can aid stakeholders in making well-informed decisions about resource allocation for risk management.

A new multi-attribute group decision-making method based on Einstein Bonferroni operators under interval-valued Fermatean hesitant fuzzy environment

Faced with the increasing complexity and uncertainty of decision-making information, interval-valued Fermatean hesitant fuzzy sets (IVFHFSs) were presented as a novel mathematical model that handled uncertain data more effectively. However, existing multi-attribute group decision-making (MAGDM) methods based on IVFHFSs do not thoroughly investigate the operational laws. Also, these existing MAGDM methods do not take into account the connections between attributes and are less flexible. To address these issues, this paper proposes a new MAGDM method based on Einstein Bonferroni operators under IVFHFSs. First, we thoroughly examine the operational laws of Einstein t-norms under the IVFHFSs to further extend the study of the operational laws. Then, we introduce the interval-valued Fermatean hesitant fuzzy Einstein Bonferroni mean operator and the interval-valued Fermatean hesitant fuzzy Einstein weighted Bonferroni mean operator under Einstein t-norms. Our suggested aggregation operators consider the relationship between attributes and are far more flexible in comparison to the current approaches. Later, a novel MAGDM method based on Einstein Bonferroni operators under the IVFHFSs is given. Finally, the practicality and validity of the proposed method are demonstrated by a cardiovascular disease diagnosis application.

A Novel Method for Failure Mode and Effect Analysis Based on the Fermatean Fuzzy Set and Bonferroni Mean Operator

Failure mode and effects analysis (FMEA) helps to identify the weak points in the processing, manufacturing, and assembly of products and plays an important role in improving product reliability. To address the shortcomings of the existing FMEA methods in terms of the uncertainty treatment of information and not considering the weights and correlations between risk factors, we propose a new FMEA method. In this paper, the Fermatean fuzzy Z-number (FFZN) is proposed by fusing the Fermatean fuzzy number and Z-number. Extending it to the Bonferroni mean (BM) operator, the Fermatean fuzzy Z-number-weighted Bonferroni mean (FFZWBM) operator is proposed. A new FMEA method is proposed based on this operator. In order to overcome the factors not considered in the FMEA method, two new risk factors are proposed and added. The ability of experts to express fuzzy information is enhanced by introducing the FFS. The weights and correlations between the influencing factors can be handled by aggregating the evaluation information using the FFZWBM operator. Finally, the proposed method is applied to an arithmetic example and the accuracy of the proposed method is proved by teaming it with other methods.

A VIKOR Method Based on the Relative Closeness on Interval Linguistic Neutrosophic Uncertain Linguistic Numbers

In actual multi-attribute group decision-making problems, due to the complexity and uncertainty of objective things and the ambiguity of human thinking, decision-makers find it hard to give accurate evaluation information by crisp numbers. Even the weights of attribute values and decision-makers are ambiguous. At this time, we are more inclined to adopt the intuitive form of linguistic variables such as "excellent", "good" or "bad" to describe attribute values and weights. So in this paper, based on a neutrosophic set (NS), we further propose interval linguistic neutrosophic uncertain linguistic number (ILNULN). ILNULN combines interval linguistic neutrosophic and uncertain linguistic numbers, and it has the advantages of both. At the same time, due to the weighted arithmetic Bonferroni mean operator considering the interrelationship between aggregation parameters, therefore we combine the ILNULN and weighted arithmetic Bonferroni mean operator to propose the interval linguistic neutrosophic uncertain linguistic weighted arithmetic Bonferroni mean (ILNULWABM) operator. Finally, under the environment of interval linguistic neutrosophic and uncertain linguistic numbers, this article uses the linguistic weights and ILNULWABM operator to make VIKOR decision based on the relative closeness, and gives a practical example.

Bonferroni Mean Operator of Interval Linguistic Neutrosophic Uncertain Linguistic Number and its Application in Multi-Attribute Group Decision-Making

This paper proposes the concept of interval linguistic neutrosophic uncertain linguistic number (IL-NULN). As a new and effective way of NS expression, ILNULN combines interval linguistic neutrosophic numbers and uncertain linguistic numbers, which can better handle uncertain and inconsistent information. In the ILNULN, the first part “uncertain linguistic number” reflects the attitude of the decision maker (DM) towards the evaluation object, and the second part “interval linguistic neutrosophic number” reflects the subjective linguistic judgment of the DM on the given uncertain linguistic number. In addition, considering the weighted arithmetic Bonferroni mean (WABM) operator integrates the correlation of aggregation parameters, this paper combines the ILNULN and WABM operator to propose the interval linguistic neutrosophic uncertain linguistic weighted arithmetic Bonferroni mean (ILNUL-WABM) operator. Finally, under the environment of interval linguistic neutrosophic uncertain linguistic number, this paper uses the ILNULWABM operator to make VIKOR decision based on the relative closeness, and gives a practical example to solve multi-attribute group decision making (MAGDM) problems.

Supplier selection of complex equipment in a military-civilian collaborative two-tier supply network with uncertain preference: A matching perspective

Complex equipment refers to special equipment that differs from general equipment. The collaborative development work of complex equipment in the military-civilian integration context involves numerous suppliers. We consider a two-tier supply network composed of different suppliers that participate in the development work to assemble complex equipment that cooperate with a main-manufacturer regarding spare parts. However, in terms of spare parts, a substitution relationship exists in assembly work for complex equipment. Hence, selecting a suitable supplier from the matching process between suppliers and spare parts under a military-civilian integration background is essential. This study considers three main analyses to obtain a suitable supplier for the development work of complex equipment. First, we construct a two-stage model to acquire the necessary evaluation dimension for subsequent processes. Second, we examine the evaluated attributes for the matching process based on entropy-group-DEMATEL analysis. Third, we perform information aggregation for the uncertain preference information between spare parts and suppliers using a Bonferroni mean operator. Finally, an illustrative example is presented to demonstrate the whole efficiency. Through the aforementioned analysis, we can select a suitable supplier that could participate in complex equipment military-civilian collaborative development work.

Development and application of a power Bonferroni mean operator based on the foreign fiber content grade evaluation method

Cubic q-rung orthogonal fuzzy sets (C q-ROFSs) are a sophisticated mathematical tool used to handle complex evaluation information in multi-attribute decision-making problems. In specific decision-making problems, the power Bonferroni mean (PBM) operator can reflect the correlation between different attributes and mitigate the impact of extreme evaluation information, thereby providing more practical value. This paper focuses on expanding the PBM operator into the C q-ROFS environment and deriving new PBM operators: the cubic q-rung orthogonal power Bonferroni averaging operator and weight cubic q-rung orthogonal PBM operator. The proposed operator shows strong flexibility and stability in the cubic q-rung orthogonal fuzzy environment. In the absence of weight information, there is a dearth of literature addressing the acceptable advantage and decision stability in the C q-ROFS environment; considering the regret behavior of decision information, a VIKOR method based on regret theory is proposed. The proposed method aggregates information using the proposed operator, determines the scheme and weights at two levels of attributes, and constructs a relative proximity decision matrix. Then, the VIKOR method calculates the group utility value and individual regret value based on the regret perception value to rank the alternatives. Finally, the method is applied to evaluate the cotton foreign fiber content, and its stability and effectiveness are verified through sensitivity analysis and comparison with existing methods.

A novel multi-attribute decision making method based on interval-valued fermatean fuzzy bonferroni mean operators

When handling complex uncertainty information for multi-attribute decision-making (MADM) problems, interval-valued Fermatean fuzzy sets (IVFFSs) are a novel and powerful tool with a wide range of prospective applications. However, existing MADM methods based on IVFFS ignore associations between attributes and are vulnerable to extreme values. Thus, this research proposes a novel MADM method based on IVFFSs. First, taking into consideration attribute relationships, we propose interval-valued Fermatean fuzzy Bonferroni mean (IVFFBM) operators and interval-valued Fermatean fuzzy weighted Bonferroni mean (IVFFWBM) operators based on IVFFSs. Further, interval-valued Fermatean fuzzy power Bonferroni mean (IVFFPBM) operator and interval-valued Fermatean fuzzy weighted power Bonferroni mean (IVFFWPBM) operator are suggested considering the impact of extreme values. Secondly, Attribute weights are a key component of MADM. A novel method for determining attribute weights based on fuzzy entropy is developed. Finally, a novel MADM approach is proposed based on the proposed operator and weight determination method. Experimental results on one real-life case demonstrate the superiority and effectiveness of our method.

Aczel-Alsina power bonferroni aggregation operators for picture fuzzy information and decision analysis

Picture fuzzy set (PFS) is an expedient mathematical approach for interpreting imprecise and nebulous information, and the power Bonferroni mean (PBM) operator is a crucial generalization of the power average (PA) operator, and the Bonferroni mean (BM) operator. Based on the Aczel-Alsina (AA), operational principles of PFS, we expand the PBM operator to integrate PFVs and develop a few AOs, namely PF Aczel-Alsina PBM (PFAAPBM) operator, weighted PF Aczel-Alsina PBM (WPFAAPBM) operator, PF Aczel-Alsina PGBM (PFAAPGBM) operator, and weighted geometric PF Aczel-Alsina PBM (WGPFAAPBM) operators respectively. These newly suggested PF Aczel-Alsina PBM operators can detect the connections between the membership, abstinence, and non-membership functions, which also maintain the important characteristics of the PBM operator. After that, we analyze a few enticing characteristics along with the particular applications of the suggested operators. Based on our suggested technique, we built an illustrated numerical example for the selection of competent research scientists to cope with MADM issues under the framework of PFVs. Finally, we contrast a few of our suggested methodologies with other prevailing methods to determine the feasibility and legitimacy of our suggested strategies.

Revolutionizing Multi-Criteria Decision Making with the Triangular Fuzzy Geometry Bonferroni Mean Operator (TFGBM)

This study investigates the Multi-Criteria Decision Making (MCDM) topic to address the complexities of decision processes involving ambiguous information. We introduce the Triangular Fuzzy Geometric Bonferroni Mean (TFGBM) operator, a novel aggregation technique inspired by the Geometric Bonferroni Mean (GBM) concept. This operator is intended to aggregate triangular fuzzy numbers within MCDM problems effectively. We thoroughly investigate the properties of TFGBM and its distinct forms to ensure its practical utility. We introduce the Triangular Fuzzy Geometric Weighted Bonferroni Mean (TFGWBM) operator to accommodate situations where input factors have variable degrees of significance. Based on this foundation, we present a comprehensive framework for decision-making involving multiple attributes in ambiguous triangular fuzzy environments. A relevant case study regarding selecting an optimal location for a Halal center demonstrates the efficacy and applicability of our methodology. We emphasize the tangibility and efficiency of the suggested methodology in improving decision-making processes by emphasizing this real-world application.

Decision methods based on Bonferroni mean operators and EDAS for the classifications of circular pythagorean fuzzy Meta-analysis

<p>Meta-analysis is a statistical technique used to process an overall summary estimation, and the technique of meta-analysis is mostly used in medicine, social science, and psychology. In this manuscript, we aimed to combine the techniques of the Bonferroni mean (BM) operator based on circular Pythagorean fuzzy (CPF) sets, called the CPF Bonferroni mean (CPFBM) operator, and CPF weighted Bonferroni mean (CPFWBM) operator and described their special cases with the help of two parameters, "s" and "t", and some describable properties of them are also proposed. Further, we present the evaluation technique based on distance from average solution (EDAS) technique and the proposed operators. Moreover, we use some examples to show the flexibility and dominance of the proposed operators by comparing the proposed methods with some existing techniques.</p>

A q-rung orthopair fuzzy decision-making framework considering experts trust relationships and psychological behavior: An application to green supplier selection

The selection of an optimal supplier is a critical and open challenge in supply chain management. While experts' assessments significantly influence the supplier selection process, their subjective interactions can introduce unpredictable uncertainty. Existing methods have limitations in effectively representing and handling this uncertainty. The paper aims to address these challenges by proposing a novel approach that leverages q-rung orthopair fuzzy sets (q-ROFSs). The novelty of the proposed approach lies in its ability to accurately capture experts' preferences through the use of q-ROFSs, which offer membership and non-membership degrees, providing a broader expression space compared to conventional fuzzy sets. Additionally, it incorporates social network analysis (SNA) to effectively consider the trust relationships among experts. The proposed approach is divided into three stages. The first stage, presents a novel method to determine experts' weights by combining SNA, the Bayesian formula, and the maximum entropy principle. This approach allows for a more precise representation of varying levels of expertise and influence among experts, addressing the uncertainty arising from subjective interactions. The second stage introduces a hybrid weight determination method to determine criteria weights within the context of q-ROFSs. Entropy plays a crucial role in capturing fuzziness and uncertainty in q-ROFSs, while the projection measure simultaneously provides information about the distance and angle between alternatives. By employing both objective weights estimated using entropy and normalized projection measure and subjective weights derived using an aggregation operator and a score function, the presented approach achieves a comprehensive assessment of criteria importance. To incorporate both subjective and objective weights effectively, game theory is applied which allows us to align decision-making with both quantitative and qualitative aspects, making the method more versatile and applicable. The third stage redefines the traditional Combined Compromise Solution (CoCoSo) method using Bonferroni mean operators which captures interrelationships among arguments to be aggregated. Furthermore, in recognition of the importance of an expert risk preferences and psychological behaviors, we apply regret theory, ensuring that the chosen solutions align more effectively with their underlying preferences and aspirations. The applicability and effectiveness of the proposed approach are demonstrated through a numerical example of green supplier selection. The comparative analysis illustrates the practicality and real-world relevance while the sensitivity analysis, confirms the stability and robustness of the proposed approach.

A Multi-Criteria Group Decision-Making Approach For Robot Selection Using Interval-Valued Intuitionistic Fuzzy Information And Aczel-Alsina Bonferroni Means

The process of identifying the most appropriate robot for a particular industrial task has grown challenging and more difficult in the fast-paced environment. It is merely driven by the complex evolution and continuous integration of modern characteristics and advanced features by various suppliers. Industrial robots are now widely available in the marketplace, each possessing a distinctive collection of skills, attributes, and requirements. However, the selection of optimal robots is heavily influenced by factors such as the manufacturing environment, product design, production system, and overall cost considerations. These factors directly impact the decision-making process. The ultimate goal for the decision maker is to pinpoint and choose the most suitable robot, capable of delivering the desired output while minimizing costs and catering to the specific requirements of the industry. So, to consider it, in this paper, the hybrid structure of the Aczel-Alsina (AA) and Bonferroni mean (BM) operators for interval-valued intuitionistic fuzzy (IVIF) environment has been proposed, which can show the interrelationship between the multiple criteria and assist the expertise in decision-making (DM) process. Moreover, the algorithm and methodology for the multi-criteria group decision-making (MCGDM) problem have been defined which is further utilized by solving a real-world problem to demonstrate the effectiveness and validity of the proposed method. At last, the comparison analysis between prior and proposed studies has been displayed, and then followed by the conclusion of the result.

Corrections to “Some T-Spherical Hesitant Fuzzy Shapley Bonferroni Mean Operators and Their Applications”

Corrections to “Some T-Spherical Hesitant Fuzzy Shapley Bonferroni Mean Operators and Their Applications”

Some T-Spherical Hesitant Fuzzy Shapley Bonferroni Mean Operators and Their Applications

Some T-Spherical Hesitant Fuzzy Shapley Bonferroni Mean Operators and Their Applications

An intelligent decision methodology for triangular Pythagorean fuzzy MADM and applications to college English teaching quality evaluation

Abstract The development of contemporary college English teaching methods and practice should respect the subjective will of college students; fully tap their wisdom and potential; constantly innovate college English teaching methods, teaching practice activities, classroom teaching, and teaching evaluation models; create a good teaching atmosphere; and establish the concept of developmental evaluation. Through the innovation of teaching methods, college students’ actual language communication ability is cultivated, the teaching objectives and teaching methods of college English reading are innovated, and interactive, body language, role play, situational teaching, communicative teaching, and other teaching methods are used. The College English teaching quality evaluation is a classical multiple attribute decision making (MADM). In this article, the triangular Pythagorean fuzzy sets (TPFSs) are introduced, and the MADM problem is investigated under TPFSs. Based on the traditional dual generalized weighted Bonferroni mean operator and power average operator, the triangular Pythagorean fuzzy dual generalized power Bonferroni mean (TPFDGPBM) operator is proposed. Accordingly, the TPFDGPBM operator is employed to construct the triangular Pythagorean fuzzy MADM method. Finally, a numerical example for College English teaching quality evaluation is constructed to verify the TPFDGPBM technique.

Smart algorithmic solutions for neutrosophic multiple-attribute decision-making and applications to chair furniture comfort design evaluation

The activities in public places are becoming increasingly frequent, and public seats have become an important component of public space and an “auxiliary tool” for work, life, and leisure. The demand for such furniture in China is gradually increasing, but the design and research work of public seats is lagging behind the development status and speed of other civil and office furniture. Usually, public seats can be divided into two parts based on their usage: public indoor seats and public outdoor seats. How to understand the role and impact of public seats on the indoor environment, and how to establish a new design method for public seats in the context of the overall environmental system, are currently urgent issues to be solved. The chair furniture comfort design evaluation is a classical MADM issues. In such paper, the generalized weighted Bonferroni mean (WBM) operator and power average (PA) is constructed for MADM with single-valued neutrosophic sets (SVNSs). Then, the generalized single-valued neutrosophic number power WBM (GSVNNPWBM) operator is built and then the MADM decision methods are proposed based on the GSVNNPWBM operator. Finally, an example about chair furniture comfort design evaluation and some comparative analysis were given to demonstrate the GSVNNPWBM method.

Application of fermatean fuzzy weight operators and MCDM model DIBR-DIBR II-NWBM-BM for efficiency-based selection of a complex combat system

The use of complex automated combat systems is a basic feature of every modern combat operation, and all modern armies strive to implement such systems in their units. This paper investigates the choice of a complex combat system based on the efficiency criteria that condition it. The Defining Interrelationships Between Ranked criteria (DIBR) and the Defining Interrelationships Between Ranked criteria II (DIBR II) methods were used to determine the weight coefficients of the criteria, which proved to be effective in assessing the importance of each criterion in the context of making complex decisions. Aggregation of expert opinions, for each of the methods, was performed using the Normalized Weighted Bonferroni Mean (NWBM) operator. After the weight coefficients for both methods were obtained, the aggregation of the obtained values was performed using the Bonferroni Mean (BM) operator, which resulted in the final values of the weight coefficients of the criteria. In order to choose the optimal alternative, the Fermatean Fuzzy Weight Operators (FFWO) and BM operator were used. These operators contributed to the precise evaluation and ranking of alternatives, taking into account their characteristics and specificities. Furthermore, the paper analyzed the sensitivity of the output results to changes in the weight coefficients of the criteria. This is important in order to assess the stability of the Multiple Criteria Decision Making (MCDM) model and ensure its reliability in different scenarios. This work represents a significant contribution to the field of decision-making in this context and provides a useful framework for the selection of complex combat systems, and the combination of different methods and operators enables a comprehensive analysis and optimization of the research problem.

Dual Hesitant q-Rung Orthopair Fuzzy Interaction Partitioned Bonferroni Mean Operators and Their Applications

The purpose of this paper is to introduce interaction partitioned Bonferroni mean operators under dual hesitant q-rung orthopair fuzzy environment. Motivated by the idea of q-rung orthopair fuzzy interaction operational laws, partitioned Bonferroni mean, and dual hesitant q-rung orthopair fuzzy sets, for dual hesitant q-rung orthopair fuzzy numbers, we present dual hesitant q-rung orthopair fuzzy interaction operational rules and propose several dual hesitant q-rung orthopair fuzzy interaction partitioned Bonferroni mean aggregation operators, including the interaction partitioned Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers, the weighted interaction partitioned Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers, the interaction partitioned geometric Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers, and the weighted interaction partitioned geometric Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers. Moreover, some properties and special cases associated with these proposed operators are also analyzed. For dual hesitant q-rung orthopair fuzzy numbers, based on the proposed operators, a multicriteria group decision-making method is proposed. Finally, an example for missile purchase problem is illustrated to demonstrate the superiority and feasibility by comparing with other existing multicriteria group decision-making methods.

Evaluation of autonomous vehicle applications in smart airports using Dombi Bonferroni mean operator based CIVL-BWM-TODIM decision making methodology

Recent advancements on autonomous vehicles (AVs) have revolutionized the aviation industry, providing great potential to enhance sustainability for this fuel-intensive industry. Diverse operation types of AVs at airports have emerged (e.g., for baggage/passenger movement). This study aims to provide a guideline on how to switch from the traditional human-driving vehicle operations to AV operations, to help improve the smartness and sustainability of airport operations. Five alternative operation types are evaluated under ten criteria. We propose a new CIVL-BWM-TODIM with Dombi Bonferroni mean operator (DBM) decision framework. The combination of the Continuous Interval-Valued Linguistic tool (CIVL) and the Best Worst Method (BWM) improves the criterial evaluation consistency, and the integration of CIVL and TODIM increases the evaluation accuracy on human language and psychological feelings. Besides, the DBM operator helps effectively integrate information from different experts. Results suggest that applying AVs for both functional activities and scheduled people delivery is the best alternative to build smart and sustainable airports. Sensitivity analyses are conducted to examine the impacts of various parameters on decision making. Moreover, comparative analysis over existing decision-making methods are carried out to validate the merits of the proposed approach.