Geometric Bonferroni Mean Operator Research Articles

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.

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.

Interval Neutrosophic Einstein Prioritized Normalized Weighted Geometric Bonferroni Mean Operator and its Application to Multicriteria Decision making

Interval Neutrosophic Einstein Prioritized Normalized Weighted Geometric Bonferroni Mean Operator and its Application to Multicriteria Decision making

An MCDM Method under Neutrosophic Cubic Fuzzy Sets with Geometric Bonferroni Mean Operator

An MCDM Method under Neutrosophic Cubic Fuzzy Sets with Geometric Bonferroni Mean Operator

Multiple criteria decision making based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades

In this paper, a multiple criteria decision making (MCDM) method based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades (GOMGs) is proposed. Bonferroni mean operator, geometric Bonferroni mean operator, power average operator, partitioned average operator, and Archimedean T-norm and T-conorm operations are introduced into generalised orthopair fuzzy sets to develop the Bonferroni aggregation operators. Their formal definitions are provided, and generalised and specific expressions are constructed. On the basis of the specific operators, a method for solving the MCDM problems based on GOMGs is designed. The working process, characteristics, and feasibility of the method are, respectively, demonstrated via a numerical example, a qualitative comparison at the aspect of characteristics, and a quantitative comparison using the example as benchmark. The demonstration results show that the proposed method is feasible that has desirable generality and flexibility in the aggregation of criterion values and concurrently has the capabilities to deal with the heterogeneous interrelationships of criteria, reduce the negative influence of biased criterion values, and capture the risk attitudes of decision makers.

An additive manufacturing process selection approach based on fuzzy Archimedean weighted power Bonferroni aggregation operators

Selecting an appropriate additive manufacturing (AM) process or machine to fabricate an end-use product is an important issue in design for AM. One of many types of approaches for AM process selection is based on multi-criteria decision making (MCDM). Most of the MCDM based approaches have an advantage in taking into account the relative importance of performance parameter types and a few of them also consider the interrelationships of performance parameter types. Each of these approaches can work well in its specific context. They are however not entirely satisfactory, as they do not have the capabilities to reduce the influence of the deviation of performance parameter values on the decision-making result and to capture the risk attitudes of users in their decision-making models. In this paper, an MCDM approach based on fuzzy Archimedean weighted power Bonferroni aggregation operators with such capabilities is proposed for AM process selection. A fuzzy Archimedean weighted power Bonferroni mean operator and a fuzzy Archimedean weighted power geometric Bonferroni mean operator are firstly constructed. Based on these operators, an MCDM approach for selection of AM processes are then developed. After that, four practical examples are adopted to illustrate the developed approach and a set of sensitivity analysis experiments on the basis of these examples are carried out. Finally, qualitative and quantitative comparisons between the approach and the existing MCDM based approaches are reported to demonstrate its feasibility, effectiveness, and advantages.

Research on the security of information system authentication scheme based on the fuzzy number intuitionistic fuzzy information

The aim of this paper is to investigate the fuzzy number intuitionistic fuzzy multiple attribute decision making problems based on the fuzzy number intuitionistic fuzzy sets and Geometric Bonferroni mean operator. Then, we have proposed two aggregation operators: fuzzy number intuitionistic fuzzy g eometric Bonferroni mean (FNIFGBM) operator and fuzzy number intuitionistic fuzzy weighted geometric Bonferroni mean (FNIFWGBM) operator. Then, we have utilized FNIFWGBM operator to tackle the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information. Finally, to testify the effectiveness of the proposed method, we present an example to evaluate the corporate credit risk based on supply chain finance with the fuzzy number intuitionistic fuzzy information.

Hesitant Pythagorean fuzzy interaction aggregation operators and their application in multiple attribute decision-making

The aim of this paper is to develop hesitant Pythagorean fuzzy interaction aggregation operators based on the hesitant fuzzy set, Pythagorean fuzzy set and interaction between membership and non-membership. The new operation laws can overcome shortcomings of existing operation laws of hesitant Pythagorean fuzzy values. Several new hesitant Pythagorean fuzzy interaction aggregation operators have been developed including the hesitant Pythagorean fuzzy interaction weighted averaging operator, the hesitant Pythagorean fuzzy interaction weighted geometric averaging operator and the generalized hesitant Pythagorean fuzzy interaction weighted averaging operator. Using the Bonferroni mean, some hesitant Pythagorean fuzzy interaction Bonferroni mean operators have been developed including the hesitant Pythagorean fuzzy interaction Bonferroni mean operator, the hesitant Pythagorean fuzzy interaction weighted Bonferroni mean (HPFIWBM) operator, the hesitant Pythagorean fuzzy interaction geometric Bonferroni mean operator and the hesitant Pythagorean fuzzy interaction geometric weight Bonferroni mean (HPFIGWBM) operator. Some properties have been studied. A new multiple attribute decision-making method based on the HPFIWBM operator and the HPFIGWBM operator has been presented. Numerical example is presented to illustrate the new method.

Pythagorean fuzzy Bonferroni means based on T‐norm and its dual T‐conorm

For multiple-attribute decision making problems in Pythagorean fuzzy environment, few existing aggregation operators consider interrelationships among the attributes. To deal with this issue, this article extends the Bonferroni means to Pythagorean fuzzy sets (PFSs) to provide Pythagorean Fuzzy Bonferroni means. We first extend t-norm and its dual t-conorm to propose the generalized operational laws for PFSs, which can be considered as the extensions of the known ones. Based on these new laws, Pythagorean fuzzy weighted Bonferroni mean operator and Pythagorean fuzzy weighted geometric Bonferroni mean operator are developed, both of them can capture the correlations among Pythagorean fuzzy input arguments and their desired properties and special cases are also investigated in detail. At last, a novel approach is proposed based on the developed operators with its effectiveness being proved by an investment selection problem.

Dual Generalized Nonnegative Normal Neutrosophic Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

For multiple attribute decision making, ranking and information aggregation problems are increasingly receiving attention. In a normal neutrosophic number, the ranking method does not satisfy the ranking principle. Moreover, the proposed operators do not take into account the correlation between any aggregation arguments. In order to overcome the deficiencies of the existing ranking method, based on the nonnegative normal neutrosophic number, this paper redefines the score function, the accuracy function, and partial operational laws. Considering the correlation between any aggregation arguments, the dual generalized nonnegative normal neutrosophic weighted Bonferroni mean operator and dual generalized nonnegative normal neutrosophic weighted geometric Bonferroni mean operator were investigated, and their properties are presented. Here, these two operators are applied to deal with a multiple attribute decision making problem. Example results show that the proposed method is effective and superior.

Autocratic decision making using group recommendations based on hesitant fuzzy sets for green hotels selection and bidders selection

In this paper, we propose a new method for autocratic decision making using group recommendations (ADMUGRs) based on hesitant fuzzy sets (HFSs), where hesitant fuzzy decision matrices (HFDMs) provided by decision makers (DMs) are represented by hesitant fuzzy elements (HFEs). The proposed method is simpler than He et al.’s method (2015) due to the fact that He et al.’s method uses the complicated hesitant fuzzy power Bonferroni mean operator and the complicated hesitant fuzzy power geometric Bonferroni mean operator for hesitant fuzzy multiple attribute group decision making. We also use the proposed method for dealing with the “green hotels selection problem” and the “bidders selection problem”. The proposed method for ADMUGRs based on HFSs provides us with a very useful way for autocratic decision making using group recommendations in hesitant fuzzy environments.

NORMALIZED WEIGHTED GEOMETRIC BONFERRONI MEAN OPERATOR OF INTERVAL ROUGH NUMBERS – APPLICATION IN INTERVAL ROUGH DEMATEL-COPRAS

This paper presents a new approach to the treatment of uncertainty and imprecision in multi-criteria decision-making based on interval rough numbers (IRN). The IRN-based approach provides decision-making using only internal knowledge for the data and operational information of a decision-maker. A new normalized weighted geometric Bonferroni mean operator is developed on the basis of the IRN for the aggregation of the IRN (IRNWGBM). Testing of the IRNWGBM operator is performed through the application in a hybrid IR-DEMATEL-COPRAS multi-criteria model which is tested on real case of selection of optimal direction for the creation of a temporary military route. The first part of hybrid model is the IRN DEMATEL model, which provides objective expert evaluation of criteria under the conditions of uncertainty and imprecision. In the second part of the model, the evaluation is carried out using the new interval rough COPRAS technique.

Application of Dual Hesitant Fuzzy Geometric Bonferroni Mean Operators in Deciding an Energy Policy for the Society

Dual hesitant fuzzy geometric Bonferroni mean is defined for dual hesitant fuzzy sets. Different properties of dual hesitant fuzzy geometric Bonferroni mean are discussed. Some special cases are studied in detail for dual hesitant fuzzy geometric Bonferroni mean. In addition, dual hesitant fuzzy weighted geometric Bonferroni mean and dual hesitant fuzzy Choquet geometric Bonferroni mean are proposed. A multicriteria decision-making method is discussed to find the best alternative among different alternatives by using proposed aggregated operators and an illustrated example is also given to understand our proposal.

Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence

Failure mode and effects analysis is an effective and powerful risk evaluation technique in the field of risk management, and it has been extensively used in various industries for identifying and decreasing known and potential failure modes in systems, processes, products, and services. Traditionally, a risk priority number is applied to capture the ranking order of failure modes in failure mode and effects analysis. However, this method has several drawbacks and deficiencies, which need to be improved for enhancing its application capability. For instance, this method ignores the consensus-reaching process and the correlations among the experts’ preferences. Therefore, the aim of this study was to present a new risk priority method to determine the risk priority of failure modes under an interval-valued Pythagorean fuzzy environment, which combines the extended Geometric Bonferroni mean operator, a consensus-reaching process, and an improved Multi-Attributive Border Approximation area Comparison approach. Finally, a case study concerning product development is described to demonstrate the feasibility and effectiveness of the proposed method. The results show that the risk priority of failure modes obtained by the proposed method is more reasonable in practical application compared with other failure mode and effects analysis methods.

Picture uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making

PurposeThe purpose of this paper is to develop some picture uncertain linguistic aggregation operators based on Bonferroni mean operators, which is combined with multiple attribute decision-making (MADM) and has applied the proposed MADM model for selecting the service outsourcing provider of communications industry under picture uncertain linguistic environment.Design/methodology/approachThe service outsourcing provider selection problem of communications industry can be regarded as a typical MADM problem, in which the decision information should be aggregated. In this paper, the authors investigate the MADM problems with picture uncertain linguistic information based on traditional Bonferroni mean operator.FindingsThe results show that the proposed model can solve the MADM problems within the context of picture uncertain linguistic information, in which the attributes are existing interaction phenomenon. Some picture uncertain aggregation operators based on Bonferroni mean have been developed. A case study of service outsourcing provider selection problem of communications industry is provided to illustrate the effectiveness and feasibility of the proposed methods. The results show that the proposed methods are useful to aggregate the picture uncertain linguistic decision information in which the attributes are not independent so as to select the most suitable supplier.Research limitations/implicationsThe proposed methods can solve the picture uncertain linguistic MADM problem, in which the interactions exist among the attributes. Therefore, it can be used to solve service outsourcing provider selection problems and other similar management decision problems.Practical implicationsThis paper develops some picture uncertain aggregation operators based on Bonferroni mean and further presents two methods based on the proposed operators for solving MADM problems. It is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications.Social implicationsIt is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications.Originality/valueThe paper investigates the MADM problems with picture uncertain linguistic information based on traditional Bonferroni mean operator and develops the picture uncertain linguistic Bonferroni mean operator and picture uncertain linguistic geometric Bonferroni mean operator, picture uncertain linguistic weighted Bonferroni mean operator and picture uncertain linguistic weighted geometric Bonferroni mean operator for aggregating the picture uncertain linguistic information, respectively. Finally, a numerical example concerning the service outsourcing provider selection problem of communications industry is provided to illustrate the effectiveness and feasibility of the proposed methods.

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.

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.

Multiple attribute decision-making method based on some normal neutrosophic Bonferroni mean operators

Normal neutrosophic numbers (NNNs) are a significant tool of describing the incompleteness, indeterminacy, and inconsistency of the decision-making information. In this paper, we firstly propose the definition and the properties of the NNNs, and the accuracy function, the score function, and the operational laws of the NNNs are developed. Then, some operators are presented, including the normal neutrosophic Bonferroni mean operator, the normal neutrosophic weighted Bonferroni mean (NNWBM) operator, the normal neutrosophic geometric Bonferroni mean operator, and the normal neutrosophic weighted geometric Bonferroni mean (NNWGBM) operator. We also study their properties and special cases. Further, we put forward a multiple attribute decision-making method which is based on the NNWBM and NNWGBM operators. Finally, an illustrative example is given to verify the practicality and validity of the proposed method.

Risk assessment method for mass unexpected incident in city with hesitant fuzzy linguistic information

The aim of this paper is to investigate the hesitant fuzzy linguistic multiple attribute decision making problems based on the hesitant fuzzy linguistic sets and Geometric Bonferroni mean operator. Then, we have proposed two aggregation operators: hesitant fuzzy linguistic geometric Bonferroni mean (HFLGBM) operator and hesitant fuzzy linguistic weighted geometric Bonferroni mean (HFLWGBM) operator. Then, we have utilized HFLWGBM operator to tackle the multiple attribute decision makingproblemsusinghesitantfuzzylinguisticinformation.Intheend,apracticalexampleforriskassessmentofmassunexpected incident in city is proposed to testify the method in this paper.

Multi-attribute group decision making method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers

In this paper, we investigate the fuzzy multi-attribute group decision making (FMAGDM) problems in which all the information provided by the decision makers (DMs) is expressed as the trapezoidal interval type-2 fuzzy sets (IT2 FS). We introduce the concepts of interval possibility mean value and present a new method for calculating the possibility degree of two trapezoidal IT2 FS. Then, we develop two aggregation techniques called the trapezoidal interval type-2 fuzzy geometric Bonferroni mean (TIT2FGBM) operator and the trapezoidal interval type-2 fuzzy weighted geometric Bonferroni mean (TIT2FWGBM) operator. We study its properties and discuss its special cases. Based on the TIT2FWGBM operator and the possibility degree, the method of FMAGDM with trapezoidal interval type-2 fuzzy information is proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.