Bonferroni Mean Operator Research Articles

Someq-Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi-Attribute Group Decision Making

In the real multi-attribute group decision making (MAGDM), there will be a mutual relationship between different attributes. As we all know, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters. In addition, in describing uncertain information, the eminent characteristic of q-rung orthopair fuzzy sets (q-ROFs) is that the sum of the qth power of the membership degree and the qth power of the degrees of non-membership is equal to or less than 1, so the space of uncertain information they can describe is broader. In this paper, we combine the BM operator with q-rung orthopair fuzzy numbers (q-ROFNs) to propose the q-rung orthopair fuzzy BM (q-ROFBM) operator, the q-rung orthopair fuzzy weighted BM (q-ROFWBM) operator, the q-rung orthopair fuzzy geometric BM (q-ROFGBM) operator, and the q-rung orthopair fuzzy weighted geometric BM (q-ROFWGBM) operator, then the MAGDM methods are developed based on these operators. Finally, we use an example to illustrate the MAGDM process of the proposed methods. The proposed methods based on q-ROFWBM and q-ROFWGBM operators are very useful to deal with MAGDM problems.

2-Dimension Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean and Its Application in Multiple Attribute Decision Making

2-dimension uncertain linguistic variables (2DULVs) are a powerful tool to express the fuzzy or uncertain information, and the weighted Bonferroni mean can not only take the attribute importance into account but also capture the interrelationship between the attributes. However, the traditional Bonferroni mean can only deal with the crisp numbers. In this paper, Bonferroni mean was extended to process the 2DULVs. Firstly, we proposed the normalized weighted geometric Bonferroni mean (NWGBM) operator and the generalized normalized weighted geometric Bonferroni mean (GNWGBM) operator, which have the characteristics of reducibility and also consider the interrelationships between two attributes. Then we introduced the computation rules, characteristics, the expected value and comparison method of the 2DULVs. Further, we developed the 2-dimension uncertain linguistic normalized weighted geometric Bonferroni mean (2DULNWGBM) and the 2-dimension uncertain linguistic generalized normalized weighted geometric Bonferroni mean (2DULGNWGBM), and explored some properties and discussed some special cases of them. Finally, we developed a new decision making method based on these operators, and an example is given to compare with the existing methods.

Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods

Linguistic neutrosophic numbers (LNN) is presented by Fang and Ye in 2017, which can describe the truth, falsity, and indeterminacy linguistic information independently. In this paper, the LNN and the Bonferroni mean operator are merged together to propose a LNN normalized weighted Bonferroni mean (LNNNWBM) operator and a LNN normalized weighted geometric Bonferroni mean (LNNNWGBM) operator and the properties of these two operators are proved. Further, multi-attribute group decision methods are introduced based on the proposed LNNNWBM and LNNNWGBM operators, and then an example is provided to demonstrate the application and validity of the proposed methods. In addition, in order to consider the effect of the parameters p and q on the decision results, different pairs of parameter values are employed to verify the decision results.

Grey Relational Analysis Method for Probabilistic Linguistic Multi-criteria Group Decision-Making Based on Geometric Bonferroni Mean

In practical decision-making problems, probabilistic linguistic term sets (PLTSs) are a very useful and flexible way to represent the qualitative judgments of experts. The PLTSs also have strong ability to express the information vagueness and uncertainty in the real-world applications. Considering the interrelationship among the input arguments of PLTSs, we extend the geometric Bonferroni mean to the probabilistic linguistic environment and design an approach for the application of multi-criteria group decision-making with PLTSs. First, we develop the probabilistic linguistic geometric Bonferroni mean and the weighted probabilistic linguistic geometric Bonferroni mean (WPLGBM) operators. The properties of these aggregation operators are investigated. Second, we utilize the WPLGBM operators to fuse the information in the probabilistic linguistic multi-criteria group decision-making (PLMCGDM) problem, which can obtain much more information in the process of group decision-making. By introducing the grey relational analysis method, we present its extension and further design a new approach for the PLMCGDM. Finally, an example is given to elaborate our proposed algorithm and successfully validate its performance.

Frank Choquet Bonferroni Mean Operators of Bipolar Neutrosophic Sets and Their Application to Multi-criteria Decision-Making Problems

In this study, comprehensive multi-criteria decision-making (MCDM) methods are investigated under bipolar neutrosophic environment. First, the operations of BNNs are redefined based on the Frank operations considering the extant operations of bipolar neutrosophic numbers (BNNs) lack flexibility and robustness. Subsequently, the Frank bipolar neutrosophic Choquet weighted Bonferroni mean operator and the Frank bipolar neutrosophic Choquet geometric Bonferroni mean operator are proposed based on the Frank operations of BNNs. The proposed operators simultaneously consider the interactions and interrelationships among the criteria by combining the Choquet integral operator and Bonferroni mean operators. Furthermore, MCDM methods are developed based on the proposed aggregation operators. A numerical example of plant location selection is conducted to explain the application of the proposed methods, and the influences of parameters are also discussed. Finally, the proposed methods are compared with several extant methods to verify their feasibility.

Extended Bonferroni Mean Under Intuitionistic Fuzzy Environment Based on a Strict t-Conorm

The Bonferroni mean (BM) operator, originally introduced by Bonferroni, assumes homogeneous relationship among the input arguments. Recently, extended BM (EBM) operator is developed to capture heterogeneous relationship among real arguments and linguistic 2-tuple data. In this paper, we investigate the EBM operator with Atanassov’s intuitionistic fuzzy sets (AIFSs) by using additive generators of strict t-conorms in the operations of AIFSs. This new operator is referred to as AIF-EBM operator. We also define weighted AIF-EBM (WAIF-EBM) operator by using the said operations. Moreover, we investigate several desirable properties of the proposed operators and we prove that some known specific intuitionistic fuzzy aggregation operators are special cases of the proposed AIF-EBM and WAIF-EBM operators. Subsequently, by utilizing the proposed operators, we develop a new approach for determining criteria weights, where criteria are heterogeneously interrelated. The contribution ends by introducing a numerical example with a comparative analysis of the proposed approach and the existing processes. The results of the numerical example are also analyzed with parameterized strict t-conorms.

Some intuitionistic linguistic dependent Bonferroni mean operators and application in group decision-making

Some intuitionistic linguistic dependent Bonferroni mean operators and application in group decision-making

Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators

The partitioned Bonferroni mean (PBM) operator and the partitioned geometric Bonferroni mean (PGBM) operator assume that all attributes are partitioned into several parts, where the members in the same part are interrelated, while the members in different parts are not interrelated. They can be used to process multiple attribute group decision making (MAGDM) problems in which attributes are partitioned into serval parts. In this paper, we extend the PBM operator and the PGBM operator based on the interaction operational laws of intuitionistic fuzzy sets (IFSs) to propose the interaction PBM (IFIPBM) operator for intuitionistic fuzzy numbers (IFNs), the weighted interaction PBM (IFWIPBM) operator for IFNs, the interaction PGBM (IFIPGBM) operator for IFNs and the weighted interaction PGBM (IFWIPGBM) operator for IFNs. We also analyze some properties and some special cases of these proposed operators (including the IFIPBM operator, the IFWIPBM operator, the IFIPGBM and the IFWIPGBM operator). Based on the proposed IFWIPBM operator and the proposed IFWIPGBM operator, a novel MAGDM method for IFNs is proposed, and some examples are used to compare the experimental results of the proposed method with the ones of the existing methods. The experimental results show that the proposed method outperforms the existing methods for MAGDM with INFs.

Interval-Valued Intuitionistic Fuzzy Power Bonferroni Aggregation Operators and Their Application to Group Decision Making

The power Bonferroni mean (PBM) operator can take the advantages of power operator and Bonferroni mean operator, which can overcome the influence of the unreasonable attribute values and can also consider the interaction between two attributes. However, it cannot be used to process the interval-valued intuitionistic fuzzy numbers (IVIFNs). It is importantly meaningful to extend the PBM operator to IVIFNs. We extend PBM operator to process IVIFNs and propose some new PBM operators for IVIFNs and apply them to solve the multi-attribute group decision-making (MAGDM) problems. Firstly, the definition, properties, score function, and operational rules of IVIFNs are introduced briefly. Then, the power Bonferroni mean (IVIFPBM) operator, the weighted PBM (IVIFWPBM) operator, the power geometric BM (IVIFPGBM) operator, and the weighted power geometric BM (IVIFWPGBM) operator for IVIFNs are proposed. Furthermore, some deserved properties of them are explored, and several special cases are analyzed. The decision-making methods are developed to deal with the MAGDM problems with the information of the IVIFNs based on the proposed operators, and by an illustrative example, the proposed methods are verified, and their advantages are explained by comparing with the other methods. The proposed methods can effectively solve the MAGDM problems with the IVIFNs, and they can consider the interaction between two attributes and overcome the influence of the unreasonable attribute values.

Pythagorean uncertain linguistic partitioned Bonferroni mean operators and their application in multi-attribute decision making

In this paper, a new extension of linguistic term sets called Pythagorean uncertain linguistic sets (PULSs) is defined, which is based on uncertain linguistic term sets and Pythagorean fuzzy sets (PFSs) originally introduced by Yager [41]. This new fuzzy linguistic set has a greater membership repr esentation space and a more powerful expression ability than the intuitionistic uncertain linguistic sets (IULSs) proposed by Liu [18]. Based on the defined operations of PULSs, the Pythagorean uncertain linguistic Bonferroni mean (PULBM) operator and its weighted form are developed to capture the interrelationship among attributes. Taking into account that the classical BM operator is based on the assumption that all attributes are interrelated, and such assumption does not always exist in most of the practical decision-making situations, we further present a Pythagorean uncertain linguistic Partitioned Bonferroni mean (PULPBM) operator and its weighted form (WPULPBM) to solve such situations where all attributes may be divided into several different categories based on specific correlation characteristics and members in the same category are interrelated while no correlation exists among different categories. Then, based on the WPULPBM operator, an approach for MADM problems with Pythagorean uncertain linguistic information is proposed. Finally, a practical example is given to illustrate the application of the proposed approach and comparison analysis is investigated with other existing methods to show the effectiveness of the proposed approach.

Performance evaluation on the water endurance of chemical adhesive steel bar in concrete with triangular fuzzy information

Adhesively bonded bars are a new technique of bars anchorage. It has been widely used in rehabilitation, renovation and repairs of concrete structures, as it is easy to anchor steel to concrete. But the bond behavior of adhesively bonded bar is greatly different from that of ordinary bars in concre te. No analysis methods for adhesively bonded bars are presented in concrete structure code. Although there are plenty of experiment and study about this field, but they are mainly about static study. There is few experiments and study about anti-seismic, so we know little about the seismic behavior of chemically planted-bar. In this paper, we investigate the multiple attribute decision making problems for performance evaluation on the water endurance of chemical adhesive steel bar in concrete with triangular fuzzy information. Motivated by the ideal of Bonferroni mean and dependent aggregating operators, we develop the dependent triangular fuzzy Bonferroni mean (DTFBM) operator for aggregating the triangular fuzzy information. Finally, a practical example for performance evaluation on the water endurance of chemical adhesive steel bar in concrete is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Multiattribute Group Decision Making Methods Based on Linguistic Intuitionistic Fuzzy Power Bonferroni Mean Operators

This paper focuses on the multiattribute group decision making problems with linguistic intuitionistic fuzzy information. Firstly the concept of linguistic intuitionistic fuzzy numbers (LIFNs) is introduced, and then based on the LIFNs, some new aggregation operators based on Bonferroni mean and power operator are proposed, such as linguistic intuitionistic fuzzy power Bonferroni mean (LIFPBM) operator, linguistic intuitionistic fuzzy weighted power Bonferroni mean (LIFWPBM) operator, linguistic intuitionistic fuzzy geometric power Bonferroni mean (LIFGPBM) operator, and linguistic intuitionistic fuzzy weighted geometric power Bonferroni mean (LIFWGPBM) operator. Then, some properties are proved such as idempotency, permutation, and boundedness. Besides, some special situations of the operators are explored. After that, an approach based of the LIFWGPBM and LIFWGPBM operators is proposed. Finally an example is used to illustrate the validity of the developed method.

Frank prioritized Bonferroni mean operator with single-valued neutrosophic sets and its application in selecting third-party logistics providers

The selection of third-party logistics (TPL) providers can greatly influence the development of a company, and it has therefore become a hot topic for research. The process of selecting TPL providers is complicated because it includes fuzzy information that can be depicted by single-valued neutrosophic numbers (SVNNs). This paper establishes a new method for selecting TPL providers under single-valued neutrosophic environments. This method simultaneously takes into account the interrelationships among criteria and the different priority levels of criteria. To construct the method, we first introduce Frank operations of SVNNs, considering that extant operations for SVNNs lack flexibility and robustness. Then, we develop the single-valued neutrosophic Frank normalized prioritized Bonferroni mean (SVNFNPBM) operator utilizing the proposed Frank operations. The SVNFNPBM operator considers the interrelationships among criteria and their distinct priority levels by combining the Bonferroni mean and the prioritized average operators. Subsequently, we construct a method for selecting TPL providers based on the proposed operator. Finally, we describe a numerical example of selecting a TPL provider and conduct a comparative analysis to verify the applicability and feasibility of the proposed method.

Simplified Neutrosophic Linguistic NormalizedWeighted Bonferroni Mean Operator and Its Application to Multi-Criteria Decision-Making Problems

Simplified Neutrosophic Linguistic NormalizedWeighted Bonferroni Mean Operator and Its Application to Multi-Criteria Decision-Making Problems

Multi-criteria group decision-making method based on interdependent inputs of single-valued trapezoidal neutrosophic information

Single-valued trapezoidal neutrosophic numbers (SVTNNs) are very useful tools for describing complex information, because they are able to maintain the completeness of the information and describe it accurately and comprehensively. This paper develops a method based on the single-valued trapezoidal neutrosophic normalized weighted Bonferroni mean (SVTNNWBM) operator to address multi-criteria group decision-making (MCGDM) problems. First, the limitations of existing operations for SVTNNs are discussed, after which improved operations are defined. Second, a new comparison method based on score function is proposed. Then, the entropy-weighted method is established in order to obtain objective expert weights, and the SVTNNWBM operator is proposed based on the new operations of SVTNNs. Furthermore, a single-valued trapezoidal neutrosophic MCGDM method is developed. Finally, a numerical example and comparison analysis are conducted to verify the practicality and effectiveness of the proposed approach.

Picture 2-Tuple Linguistic Bonferroni Mean Operators and Their Application to Multiple Attribute Decision Making

In this paper, we investigate the multiple attribute decision-making problems with picture 2-tuple linguistic information. Then, we utilize Bonferroni mean and geometric Bonferroni mean operations to develop some picture 2-tuple linguistic aggregation operators: picture 2-tuple linguistic Bonferroni mean operator and picture 2-tuple linguistic geometric Bonferroni mean operator. Some desired properties and special cases of the developed operators are discussed in detail. Furthermore, considering the importance of the input arguments, we propose the picture 2-tuple linguistic weighted Bonferroni mean operator and picture 2-tuple linguistic weighted geometric Bonferroni mean operator. Finally, a practical example for selecting the service outsourcing provider of communications industry is given to verify the developed approach and to demonstrate its practicality and effectiveness.

MULTI-ATTRIBUTE DECISION MAKING METHOD BASED ON BONFERRONI MEAN OPERATOR AND POSSIBILITY DEGREE OF INTERVAL TYPE-2 TRAPEZOIDAL FUZZY SETS

This paper proposes a new approach based on Bonferroni mean operator and possibility degree to solve fuzzy multi-attribute decision making (FMADM) problems in which the attribute value takes the form of interval type-2 fuzzy numbers. We introduce the concepts of interval possibility mean value and present a new method for calculating the possibility degree of two interval trapezoidal type-2 fuzzy sets (IT2 TrFSs). Then, we develop two aggregation techniques, which are called the interval type-2 trapezoidal fuzzy Bonferroni mean (IT2TFBM) operator and the interval type-2 trapezoidal fuzzy weighted Bonferroni mean (IT2TFWBM) operator. We study their properties and discuss their special cases. Based on the IT2TFWBM operator and the possibility degree, a new method of multi-attribute decision making with interval type-2 trapezoidal fuzzy information is proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.

An Approach to Multiple Attribute Decision Making with Triangular Linguistic Information

In this paper, we investigate the multiple attribute decision making problems with triangular linguistic information. Motivated by the ideal of Bonferroni mean, we develop the aggregation techniques called the triangular linguistic Bonferroni mean (TLBM) operator for aggregating the triangular linguistic information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define the triangular linguistic weighted Bonferroni mean (TLWBM) operator, based on which we develop the procedure for multiple attribute decision making under the triangular linguistic environments. Finally, a practical example for evaluating the engineer project risk is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Multi-Valued Neutrosophic Number Bonferroni Mean Operators with their Applications in Multiple Attribute Group Decision Making

Bonferroni mean (BM) is a very useful aggregation operator, which can consider the correlations between the aggregated arguments and the multi-valued neutrosophic set can be much more convenient to denote the incomplete, indeterminate and inconsistent information, in this paper, we applied the Bonferroni mean to the multi-valued neutrosophic set, and proposed some Bonferroni mean operators of multi-valued neutrosophic numbers (MVNNs). First, we gave some operational laws and a comparison method of MVNNs, then we presented the weighted Bonferroni mean (WBM) operator and weighted geometric Bonferroni mean (WGBM) operator. Further, we proposed the multi-valued neutrosophic weighted Bonferroni mean (MVNWBM) operator and the multi-valued neutrosophic weighted geometric Bonferroni mean (MVNWGBM) operator and some properties of them are also investigated. Finally, the decision making methods are developed based on MVNWGBM operator and MVNWBM operator, and an example about investment selection is given to illustrate the applications of the developed methods and the influence of different parameter values on the decision-making results.

Research on supplier performance evaluation system based on data mining with triangular fuzzy information

From the beginning of 21th, enterprise’s competition predominance depends on capability of green supply chain. Suppliers are fountains of green supply chain, and the performance will directly influence the whole supply chain performance. The green supplier performance management is a key and diffic ult question in green supply chain manage system, which contains two cores, supplier performance evaluation and performance improvement. With the practice of two items, enterprise can control supplier performance continuously, and take improve actions in time, make the supplier performance to achieve requested level. Finally, enterprise can optimize the competition capability. In this paper, we investigate the multiple attribute decision making (MADM) problems for supplier performance evaluation with triangular fuzzy information. Motivated by the idea of Bonferroni mean and Einstein operations, we develop the aggregation techniques called the triangular fuzzy Einstein Bonferroni mean (TFEBM) operator for aggregating the triangular fuzzy information. For the situations where the input arguments have different importance, we then define the triangular fuzzy weighted Einstein Bonferroni mean (TFWEBM) operator, based on which we develop the procedure for multiple attribute decision making under the triangular fuzzy environments. Finally, a practical example for supplier performance evaluation is given to verify the developed approach.