Bonferroni Mean Aggregation Operators Research Articles

Navigating ambiguity: A novel neutrosophic cubic shapley normalized weighted Bonferroni Mean aggregation operator with application in the investment environment

The Neutrosophic Cubic Shapley Normalized Bonferroni (NC-SNWBM) method represents a cutting-edge approach to decision making theory, combining three distinct mathematical frameworks the neutrosophic cubic sets (NCS), Shapley values, and the Bonferroni aggregation operator. This innovative method addresses the challenges posed by uncertainty, vagueness, and imprecision in decision-making (DM) processes, offering a comprehensive and versatile tool for handling complex and dynamic scenarios. Neutrosophic cubic sets offers a strong platform to handle ambiguous and vague data due to three components Membership Grade (MG), Non-Membership Grade (NMG) and Indeterminancy Grade (IG) in data. By adding Shapley Fuzzy Measures (SFM), which come from cooperative game theory, distribute values among cooperative agents equally and to account for each agent's contributions to all potential coalitions. The Bonferroni aggregation operator—a statistical aggregative tool that regulates the likelihood of many types in error in statistical tests and the interdependence of the input arguments by allowing different values to parameters involved. These values are further improved by normalization in the framework of the NC-SNWBM approach in order to consider the various degrees of impact that agents exert in various circumstances. This operator is smoothly combined with normalized Shapley values and neutrosophic cubic sets in the NC-SNWBM approach to enable the aggregation of data with different levels of imprecision and uncertainty from various sources using NCS. The MG, NMG and IG connected to NCS are important elements of the NC-SNWBM approach. To evaluate each element's contribution to the overall value distribution SFM are used, and the Bonferroni aggregation operator maintains a careful balance between conservatism and significance. Together, these components provide a thorough framework that successfully tackles the problems caused by ambiguity, imprecision, and uncertainty in scenarios involving decision-making. The NC-SNWBM operator is applied to a numerical problem as an application in investment environment and sensitive and comparative analysis are conducted. The recommendation based on sensitive and comparative analysis proposed.

Bonferroni mean aggregation operators under q-rung linear diophantine fuzzy hypersoft set environment and its application in multi-attribute decision making

Bonferroni mean aggregation operators under q-rung linear diophantine fuzzy hypersoft set environment and its application in multi-attribute decision making

Interval-valued q-rung orthopair fuzzy Aczel–Alsina operations-based Bonferroni mean aggregation operators and their applications

Interval-valued q-rung orthopair fuzzy Aczel–Alsina operations-based Bonferroni mean aggregation operators and their applications

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.

Interaction Power Bonferroni Mean Aggregation Operators Based on T-Spherical Fuzzy Information and Their Application in Multi-attribute Decision Making

Interaction Power Bonferroni Mean Aggregation Operators Based on T-Spherical Fuzzy Information and Their Application in Multi-attribute Decision Making

Picture fuzzy soft Bonferroni mean aggregation operators and their applications

Due to more advanced features of the picture fuzzy soft set and valuable characteristics of aggregation operators, in this article, we present the notion of picture fuzzy soft Bonferroni mean aggregation operators and weighted picture fuzzy soft Bonferroni mean aggregation operators. Moreover, some basic properties of these introduced aggregation operators have been given. As cancer is one of the most rapidly increasing diseases globally. But due to different kinds of cancer diseases, it is very difficult to say which type of cancer disease is increasing rapidly. So to reduce this difficulty in the medical field, we have applied our work to medical diagnosis problems to ensure that fuzzy ideas can also help in the medical field. Also, an algorithm along with a descriptive example is established that conforms to the authenticity of initiated work. Furthermore, a comparative analysis of the introduced work has been given to show how this work is more efficient and dominant than other existing theories.

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.

Group decision-making based on the aggregation of Z-numbers with Archimedean t-norms and t-conorms

Aiming at the information description and aggregation of group decision-making (GDM), this study develops an innovative GDM method based on Z-numbers and their aggregation techniques. The Z-number is a powerful tool for describing real-life information and reflecting information reliability. However, Z-numbers have a complicated three-dimensional structure, and many existing studies did not manage Z-numbers appropriately. Besides, no study has investigated Z-number aggregation considering Z-numbers’ potential probability distributions. To remove the above defects, many valid techniques are introduced. An optimisation model is constructed to determine the potential probability distributions involved in Z-numbers. Then, a mean function for comparing Z-numbers is presented, and a series of Z-number operations are defined based on Archimedean t-norms and t-conorms. Moreover, a Z-number Bonferroni mean aggregation operator for integrating Z-number information is proposed. To test the applicability and validity of the developed Z-number GDM method, a new energy investment selection problem is addressed, and the sensitivity analysis and comparison discussion are conducted. The sensitivity results show that the developed method possesses favourable stability and effectiveness. In addition, the comparison results demonstrate that it outperforms other existing methods, and it can handle existing defects effectively.

Multi-criteria decision making method based on Bonferroni mean aggregation operators of complex intuitionistic fuzzy numbers

Complex intuitionistic fuzzy sets (CIFSs), characterized by complex-valued grades of membership and non-membership, are a generalization of standard intuitionistic fuzzy (IF) sets that better speak to time-periodic issues and handle two-dimensional data in a solitary set. Under this environment, in this article, various mean-type operators, namely complex IF Bonferroni means (CIFBM) and complex IF weighted Bonferroni mean (CIFWBM) are presented along with their properties and numerous particular cases of CIFBM are discussed. Further, using the presented operators a decision-making approach is developed and is illustrated with the help of a practical example. Also, the reliability of the developed methodology is investigated with the aid of validity test criteria and the example results are compared with prevailing methods based on operators.

A Normalized Weighted Bonferroni Mean Aggregation Operator Considering Shapley Fuzzy Measure Under Interval-valued Neutrosophic Environment for Decision-Making

Previous theories have suggested that Bonferroni mean (BM) and its extensions can fulfil the desired properties to become a good aggregation operator in managing interrelationship between arguments under fuzzy decision-making environment. However, along with this growth, there are concerns regarding the limitation of the BM and its extensions where interrelationship between arguments is limited to a pair of input arguments. In contrast to previous works, a novel normalized weighted Bonferroni mean aggregation operator considering Shapley fuzzy measure has been introduced, where the overall interactions of input arguments are combined. Unlike other extensions of BM that are mostly considered under fuzzy environment, this aggregation operation introduces the Shapley fuzzy measure to deal with interactions of all arguments under the interval-valued neutrosophic environment. Specifically, the interval-valued neutrosophic Shapley normalized weighted Bonferroni mean (INSNWBM) is proposed in this paper. The properties of INSNWBM such as reducibility, idempotency, monotonicity, commutativity, and boundedness are also presented as to reflect the interrelationship among multiple input arguments. In addition, we have also proposed successive steps of a decision-making procedure in which the proposed INSNWBM is included. Together included is a numerical example as to illustrate the applicability of the INSNWBM in decision-making. The consistency of the ranking results is confirmed by variations of parameters of INSNWBM. It is shown that the ranking results are almost consistent despite the different usages of parameter values. Results obtained appear to support the idea that the proposed aggregation operator is able to address the interrelationship between arguments in decision-making.

Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making

The power Bonferroni mean (PBM) operator can relieve the influence of unreasonable aggregation values and also capture the interrelationship among the input arguments, which is an important generalization of power average operator and Bonferroni mean operator, and Pythagorean fuzzy set is an effective mathematical method to handle imprecise and uncertain information. In this paper, we extend PBM operator to integrate Pythagorean fuzzy numbers (PFNs) based on the interaction operational laws of PFNs, and propose Pythagorean fuzzy interaction PBM operator and weighted Pythagorean fuzzy interaction PBM operator. These new Pythagorean fuzzy interaction PBM operators can capture the interactions between the membership and nonmembership function of PFNs and retain the main merits of the PBM operator. Then, we analyze some desirable properties and particular cases of the presented operators. Further, a new multiple attribute decision making method based on the proposed method has been presented. Finally, a numerical example concerning the evaluation of online payment service providers is provided to illustrate the validity and merits of the new method by comparing it with the existing methods.

New generalised Bonferroni mean aggregation operators of complex intuitionistic fuzzy information based on Archimedean t-norm and t-conorm

ABSTRACTThis manuscript presents aggregation operators which encapsulate the interaction among the criteria and preferences under complex intuitionistic fuzzy (CIF) conditions. The current extensions of fuzzy set theory handle the uncertain data by representing the satisfaction and dissatisfaction degrees as real values and can trade with only one-dimensional problems due to which some important knowledge may be lost in some situations. A modification to these, CIF sets are portrayed by complex-valued degrees of satisfaction and dissatisfaction and handle two-dimensional data concurrently in one set using additional terms, called phase terms, which usually give knowledge related with periodicity. Motivated by the features of the CIF model, we present some aggregation operators, namely, generalised CIF Bonferroni mean and generalised CIF weighted Bonferroni mean. Some features related to proposed operators are addressed. In light of the developed operators, a decision-making method is put forward and is drawn with the aid of an example. The reliability of the presented decision-making method is examined with the help of a validity test and by comparing the results of the example with several predominating studies.

Multi-attribute group decision making method based on some trapezoid intuitionistic fuzzy linguistic Bonferroni mean aggregation operators

Multi-attribute group decision making method based on some trapezoid intuitionistic fuzzy linguistic Bonferroni mean aggregation operators

Group Decision-Making Approach Based on Generalized Grey Linguistic 2-Tuple Aggregation Operators

To address complexity information fusion problems involving fuzzy and grey uncertainty information, we develop prioritized averaging aggregation operator and Bonferroni mean aggregation operator with grey linguistic 2-tuple variables and apply them to design a new decision-making scheme. First, the grey linguistic 2-tuple prioritized averaging (GLTPA) operator is developed to characterize the prioritization relationship among experts and employed to fuse experts’ information into an overall opinion. Second, we establish dual generalized grey linguistic 2-tuple weighted Bonferroni mean (DGGLTWBM) operator to capture the interrelationship among any attribute subsets, which can be reduced to some conventional operators by adjusting parameter vector. On that basis, a flexible group decision-making approach with fuzzy and grey information is designed and applied to an evaluation problem, in which grey relationship analysis (GRA) method and a linear programming model are combined to extract attribute weights from partially known attribute information. Furthermore, an illustrative example is employed to illustrate the practicality and flexibility of the designed method by conducting the related comparative studies.

Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their applications to decision-making

Intuitionistic fuzzy soft set (IFSS) theory is one of the successful extensions of soft set theory for handling the uncertainty in the data by introducing the parametrisation factor during the decision-making process as compared to the existing theories. Under this IFSS environment, the present paper developed some new Bonferroni mean(BM) and weighted BM averaging operator for aggregating the different preferences of the decision-maker. Some of its desirable properties have also been discussed in details. Further, a decision-making method based on proposed operators has been presented and then illustrated with a numerical example. A comparison analysis between the proposed and the existing measures under IFSS environment has been performed in terms of counter-intuitive cases for showing the validity of it.

Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading

Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading

Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

The Pythagorean fuzzy set as an extension of the intuitionistic fuzzy set characterized by membership and nonmembership degrees has been introduced recently. Accordingly, the square sum of the membership and nonmembership degrees is a maximum of one. The Pythagorean fuzzy set has been previously applied to multiattribute group decision-making. This study develops a few aggregation operators for fusing the Pythagorean fuzzy information, and a novel approach to decision-making is introduced based on the proposed operators. First, we extend the generalized Bonferroni mean to the Pythagorean fuzzy environment and introduce the generalized Pythagorean fuzzy Bonferroni mean and the generalized Pythagorean fuzzy Bonferroni geometric mean. Second, a new generalization of the Bonferroni mean, namely, the dual generalized Bonferroni mean, is proposed by considering the shortcomings of the generalized Bonferroni mean. Furthermore, we investigate the dual generalized Bonferroni mean in the Pythagorean fuzzy sets and introduce the dual generalized Pythagorean fuzzy Bonferroni mean and dual generalized Pythagorean fuzzy Bonferroni geometric mean. Third, a novel approach to multiattribute group decision-making based on proposed operators is proposed. Lastly, a numerical instance is provided to illustrate the validity of the new approach.