Partitioned Bonferroni Mean 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.

An interaction and feedback mechanism-based group decision-making for emergency medical supplies supplier selection using T-spherical fuzzy information

Selecting a supplier for emergency medical supplies during disasters can be considered a typical multiple attribute group decision-making (MAGDM) problem. MAGDM is an intriguing common problem that is rife with ambiguity and uncertainty. It becomes much more challenging when governments and medical care enterprises adjust their priorities in response to the escalating problems and the effectiveness of the actions taken in different countries. As decision-making problems become increasingly complicated nowadays, a growing number of experts are likely to use T-spherical fuzzy sets (T-SFSs) rather than exact numbers. T-SFS is a novel extension of fuzzy sets that can fully convey ambiguous and complicated information in MAGDM. The objective of this paper is to propose a MAGDM methodology based on interaction and feedback mechanism (IFM) and T-SFS theory. In it, we first introduce T-SF partitioned Bonferroni mean (T-SFPBM) and T-SF weighted partitioned Bonferroni mean (T-SFWPBM) operators to fuse the evaluation information provided by experts. Then, an IFM is designed to achieve a consensus between multiple experts. In the meantime, we also find the weights of experts by using T-SF information. Furthermore, in light of the combination of IFM and T-SFWPBM operator, an MAGDM algorithm is designed. Finally, an example of supplier selection for emergency medical supplies is provided to demonstrate the viability of the suggested approach. The influence of parameters on decision results and comparative analysis with the existing methods confirmed the reliability and accuracy of the suggested approach.

Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM

In this article, we propose the generalized version of the extended, partitioned Bonferroni mean (EPBM) operator with a systematic investigation of its behavior and properties. It can aggregate data of various dimensions in one formulation by modeling mandatory conditions along with partitioned structure interrelationships amongst the criterion set. In addition, we generate the condition for weight vectors satisfied by the weighting triangle associated with the proposed extended aggregation operator. We employed the proposed operator to aggregate a dataset following a hierarchical structure. We found that by implementing the proposed operator one can even rank the alternatives more intuitively with respect to any intermediate perspective of the hierarchical system. Finally, we present an application of the proposed extended aggregation operator in a case-based example of a child’s home environment quality evaluation with detailed analysis.

A Novel Decision-Making Method for Selecting Superintendent Based on a Q-Rung Dual Hesitant Fuzzy Power Partitioned Bonferroni Mean Operator

The Q-rung dual hesitant fuzzy (q-RDHF) set is famous for expressing information composed of asymmetry evaluations, because it allows for several possible evaluations in both the membership degree and non-membership degree. Compared with some existing extended fuzzy theories, the q-RDHF set is more superior and flexible because it can handle asymmetric assessments. In order to assemble the evaluation information expressed by q-RDHF elements, this paper aims to propose new operators to integrate q-RDHF elements. The partitioned Bonferroni mean (PBM) operator is well-known for its advantages in coping with the inhomogeneous relationship between asymmetry input arguments. In this paper, we combine the PBM operator with the power average operator, and propose a family of q-RDHF power PBM operators. Some theorems and special cases for the new proposed operators are discussed. Furthermore, we provide a general framework for dealing with multiple attribute decision-making (MADM) problems using the novel proposed method. To better show the calculation details, a numerical case study of the application of the proposed method in a superintendent selection problem is introduced. In addition, we utilize the proposed method to compare it with some existing methods in order to show its flexibility and superiority. The results show that our method is much more advantageous when considering flexible actual situations. Finally, the conclusion is given. The main contributions of this study are to propose an appropriate method to solve unbalanced and asymmetry information in a q-RDHF environment, and to apply it into a realistic superintendent selection problem.

A group decision‐making algorithm considering interaction and feedback mechanisms for dynamic supplier selection under q‐ rung orthopair fuzzy information

Supplier selection is vital for enterprises to operate stably and achieve and sustain a competitive advantage. However, from the initial establishment to the gradual development and maturity of the enterprise, the supplier selection criteria change dynamically, and decision-makers are hardly in agreement in each stage, which creates challenges for enterprises when choosing suitable suppliers. As such, this paper proposes a multicriteria group decision-making method based on an interaction and feedback mechanism (IFM) and q-rung orthopair fuzzy sets theory. We introduce an IFM to achieve consensus among different decision-makers. We then develop the q-rung orthopair fuzzy weighted partitioned Bonferroni mean (q-ROFWPBM) operator to address the aggregation problem of dynamic multicriteria. A group decision-making algorithm combining the IFM and q-ROFWPBM operator is proposed to analyze the Hongxing Erke supplier selection. The results show that the proposed method can not only account for large differences of opinion among decision-makers during group decision-making but also consider the dynamic changes of supplier selection criteria in different stages of enterprise development and help enterprises choose suppliers suitable for their own development characteristics.

Complex q-Rung Orthopair Uncertain Linguistic Partitioned Bonferroni Mean Operators with Application in Antivirus Mask Selection

In this paper, complex q-rung orthopair uncertain linguistic sets (CQROULSs) for handling multi-attribute decision making (MADM) issues are proposed so that the assessed estimation of each trait can be presented by CQROULS. Another aggregation operator, called the partitioned Bonferroni mean (PBM) operator, is then considered to manage the circumstances under fuzziness. At that point, the PBM operator is stretched out to CQROULSs in which a complex q-rung orthopair uncertain linguistic partitioned Bonferroni mean (CQROULPBM) operator is then proposed. To wipe out the negative impact of preposterous assessment estimations of characteristics on total outcomes, complex q-rung orthopair uncertain linguistic weighted partitioned Bonferroni mean (CQROULWPBM) operator is further considered. These properties, idempotency, boundedness, and commutativity of the CQROULWPBM operator are obtained. The proposed CQROULSs with the CQROULWPBM operator is novel and important for MADM issues. Finally, an MADM based on CQROULSs is constructed with a numerical case given to delineate the proposed approach and then applied for selecting an antivirus mask for the COVID-19 pandemic. The advantages and comparative analysis with graphical interpretation of the explored operators are also presented to demonstrate the effectiveness and usefulness of the proposed method.

Generalized hesitant fuzzy information fusion using extended partitioned Bonferroni mean operator with application in decision-making

The partitioned Bonferroni mean operator (PBM), which was formulated to outspread the family of the Bonferroni mean operator, has augmented the class of aggregation functions for information accumulation by modeling interrelationship among pairwise disjoint partition sets. It is constructed with the presupposition that the criteria set is subdivided into mutually disjoint partition sets, with homogeneous interconnection among input arguments of intra-partition sets. The PBM operator has accomplished a lot of desirability from the researchers due to its capability of apprehending interconnection among arguments in the information accumulation technique. The central idea of this study is to amplify the existing PBM definition systematically so that heterogeneous interconnections among the criteria of intra-partition sets can be captured. This contemplation prompted us to focus on the systematized proposition of extended partitioned Bonferroni mean (EPBM) operator based on heterogeneous connections of the information retrieved from the partition sets. In this aspect, we also propose the hesitant fuzzy extended partitioned Bonferroni mean (HFEPBM) operator, along with its weighted generalization (WHFEPBM operator), by fitting the concept of strict t-norms and t-conorms into it. To intensify the capacity for modeling real-life decision situations, the extended TOPSIS method and the proposed operator have been employed to detect the weights of decision-makers. A numerical example has been presented to demonstrate the experimental results obtained by utilizing the WHFEPBM operator. The contribution ends by providing a detailed comparative analysis of the proposed method with other existing methods by availing data through the simulation experiment.

Grey Fuzzy Multiple Attribute Group Decision-Making Methods Based on Interval Grey Triangular Fuzzy Numbers Partitioned Bonferroni Mean

Considering the characteristics such as fuzziness and greyness in real decision-making, the interval grey triangular fuzzy number is easy to express fuzzy and grey information simultaneously. And the partition Bonferroni mean (PBM) operator has the ability to calculate the interrelationship among the attributes. In this study, we combine the PBM operator into the interval grey triangular fuzzy numbers to increase the applicable scope of PBM operators. First of all, we introduced the definition, properties, expectation, and distance of the interval grey triangular fuzzy numbers, and then we proposed the interval grey triangular fuzzy numbers partitioned Bonferroni mean (IGTFPBM) and the interval grey triangular fuzzy numbers weighted partitioned Bonferroni mean (IGTFWPBM), the adjusting of parameters in the operator can bring symmetry effect to the evaluation results. After that, a novel method based on IGTFWPBM is developed for solving the grey fuzzy multiple attribute group decision-making (GFMAGDM) problems. Finally, we give an example to expound the practicability and superiority of this method.

Generalization and extension of partitioned Bonferroni mean operator to model optional prerequisites

The partitioned Bonferroni mean (PBM) operator, which was oriented as an elementary attempt to outstretch the Bonferroni mean (BM) operator, has enlarged the class of BM-type aggregation operators for information accumulation by modeling interrelationship among pairwise disjoint partition sets with the presupposition that the criteria of intra-partition are homogeneously related to each other, while no relationship exists among criteria of inter-partition. Although PBM has encountered a lot of attraction from the researchers due to its versatility in information aggregation technique, the principal disadvantage of the existing PBM definitions evolution is that they do not provide any specification regarding the relationship among criteria of partition structure during design, development, and applications of PBM over unalike situations of information fusion. This consideration propels us to focus on the systematic investigation of different variations of PBM operators based on various mandatory requisites to be imposed on information retrieved from the partition sets. In this regard, we propose the construction of novel generalized partitioned Bonferroni mean (GPBM) operator by befitting its suitable components to provide a descriptive configuration, which is quite interpretable, understandable and thus facilitates the ability to model specific mandatory prerequisites in a single operator. To enrich the capacity for modeling real-life decision situations, the PBM operator is customized to propose optional partitioned Bonferroni mean (OPBM) operator that captures partition-wise interrelationship among attributes while taking into consideration optional conditions jumbled in each partition set. Furthermore, we demonstrate the construction methodology of generalized OPBM operator that amalgamate the concept of GPBM and OPBM operator to enhance and model-specific requirements along with optional requirements as per the desires of decision makers.

Constructing interval-valued generalized partitioned Bonferroni mean operator with several extensions for MAGDM

In group decision making, each expert’s background and the level of knowledge and ability differ, which makes the expert’s information inputs to the decision-making process heterogeneous. Such heterogeneity in the information can affect the outcome of the selection of the decision alternatives. This paper therefore attempts to partition the heterogeneous information into homogeneous groups to elicit similar (related) and dissimilar (unrelated) data using a clustering algorithm. We then develop an aggregation approach to gather the collective opinions from the homogeneous clusters to accurately model the decision problem in a group setting. The proposed aggregation approach, labeled as the generalized partitioned Bonferroni mean (GPBM), is studied to investigate the characteristics of the aggregation operator. Further, we extend the GPBM concept to an interval-valued fuzzy set context using the additive generators of the strict t-conorms and we develop two other new aggregation operators: the interval-valued GPBM (IVGPBM) and the weighted IVGPBM (WIVGPBM). We analyze the aggregation of fuzzy numbers by the IVGPBM operator using interval arithmetic involving $$\alpha$$ -cuts and the $$\alpha$$ -cut-based decomposition principle of fuzzy numbers. Two practical examples are presented to illustrate the applicability of these operators, and a comparison is conducted to highlight the effects of the confidence level and the sensitivity of the parameters chosen, analyzing the results with the parameterized strict t-conorm. Finally, we compare the experimental results of the proposed method with existing methods.

New q-Rung Orthopair Fuzzy Bonferroni Mean Dombi Operators and Their Application in Multiple Attribute Decision Making

Some q-rung orthopair fuzzy Bonferroni mean Dombi aggregation operators have been developed based on the Bonferroni mean, Dombi T-norm and T-conorm in q-rung orthopair fuzzy environment. The q-rung orthopair fuzzy Bonferroni mean Dombi averaging (q-ROFBMDA) operator and the q-rung orthopair fuzzy geometric Bonferroni mean Dombi averaging (q-ROFGBMDA) operator are first developed. Then the q-rung orthopair fuzzy weighted Bonferroni mean Dombi averaging (q-ROFWBMDA) operator and the q-rung orthopair fuzzy weighted geometric Bonferroni mean Dombi averaging (q-ROFWGBMDA) operator have been developed. Based on the partitioned operation, the q-rung orthopair fuzzy partitioned Bonferroni mean Dombi averaging (q-ROFPBMDA) operator and the q-rung orthopair fuzzy partitioned geometric Bonferroni mean Dombi averaging (q-ROFPGBMDA) operator have been presented. Some desirable properties of the new aggregation operators have been studied. A new multiple attribute decision making method based on the q-ROFWBMDA (q-ROFWGBMDA) operator is proposed. Finally, a numerical example of new campus site selection has been presented to illustrate the new method.

Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators

In this paper, we propose a new multiattribute group decision making (MAGDM) method based on the proposed weighted partitioned Maclaurin symmetric mean (IFWPMSM) operators for intuitionistic fuzzy numbers (IFNs). Firstly, motivated by the partitioned Bonferroni mean (PBM) and the Maclaurin symmetric mean (MSM), we present the partitioned MSM (PMSM) operator considering the hypothesis that all attributes can be cut into some groups, where the attributes in the same group are relevant to other multiple attributes of the same group, but the attributes in different groups are irrelevant. Then, we present its characteristics and some special cases. Then, we generalize the PMSM operator to propose the intuitionistic fuzzy PMSM (IFPMSM) operator for IFNs and its weighted form (IFWPMSM) for IFNs. Then, we present several characteristics and special examples of the presented IFPMSM operator and the proposed IFWPMSM operator. Finally, we propose a new MAGDM method based on the proposed IFWPMSM operator and make a comparison with the existing approaches to interpret the usability and the validity of the proposed method.

A Multiple Attribute Group Decision-making Method Based on the Partitioned Bonferroni Mean of Linguistic Intuitionistic Fuzzy Numbers

As a more effective linguistic information representation model, the linguistic intuitionistic fuzzy number (LIFN), made up of the linguistic membership degree (LMD) and the linguistic non-membership degree (LNMD), plays an important role in describing uncertain-decision information in cognitive activity. The partitioned Bonferroni mean (PBM) operator is constructed based on real conditions, considering that some factors considered by decision-makers are interrelated and some are independent. The PBM operator can aggregate evaluation information under various attributes, which are divided into several independent groups; the factors interact with each other within the same group, but the factors are independent of each other when located in different groups. The classical PBM operators and their extensions can handle many decision-making problems but are unable to handle decision-making problems under a linguistic intuitionistic environment. To take full advantage of the PBM operator and LIFNs, this paper combines the PBM operator with LIFNs to propose several PBM operators for aggregating LIFNs. First, the relative theories about LIFNs are reviewed in brief. Then, linguistic intuitionistic fuzzy partitioned BM aggregation operators and partitioned geometric BM aggregation operators are discussed, including the linguistic intuitionistic fuzzy partitioned Bonferroni mean (LIFPBM) operator, the linguistic intuitionistic fuzzy weighted partitioned Bonferroni mean (LIFWPBM) operator, the linguistic intuitionistic fuzzy partitioned geometric Bonferroni mean (LIFPGBM) operator, and the linguistic intuitionistic fuzzy weighted partitioned geometric Bonferroni mean (LIFWPGBM) operator. Moreover, a novel method constructed on the developed operators is presented to address multiple attribute group decision-making (MAGDM) problems with the LIFNs. The feasibility of the proposed method is given by a numeric example, and the comparative analysis of our proposed method and other methods shows some advantages of these new methods. The developed method is constructed based on LIFNs and the PBM operator, and it is more practical and general than other existing methods and easily describes qualitative information that stems from a decision maker’s cognition. In addition, it can more effectively handle the complex relationship among multiple attributes in MAGDM problems.

Q‐Rung orthopair uncertain linguistic partitioned Bonferroni mean operators and its application to multiple attribute decision‐making method

q‐Rung orthopair uncertain linguistic partitioned Bonferroni mean operators and its application to multiple attribute decision‐making method

Novel green supplier selection method by combining quality function deployment with partitioned Bonferroni mean operator in interval type-2 fuzzy environment

Green supplier selection (GSS) plays a significant role in promoting enterprise development. Quality function deployment (QFD) ensures that green supplier assessment criteria are in accordance with the characteristics that purchased products ought to possess. The partitioned Bonferroni mean (PBM) operator assumes that all criteria are partitioned into several clusters, where criteria in the same clusters are interrelated, while criteria in different clusters are irrelevant, and it can be used to deal with GSS problems in which all criteria are partitioned into several clusters. Furthermore, interval type-2 fuzzy sets (IT2FSs) can efficiently express vagueness and imprecision, and possess powerful processing abilities. In this paper, we propose a novel GSS method by combining QFD with the PBM operator in the context of IT2FSs. Firstly, we present the interval type-2 fuzzy PBM (IT2FPBM) operator and interval type-2 fuzzy weighted PBM (IT2FWPBM) operator, and discuss several of their properties. Thereafter, we transform the preference values of the importance degrees of customer needs (CNs) into those of technical criteria (TC) through the relationships between CNs and TC, based on QFD. Moreover, the criteria are partitioned on the basis of the literature review on GSS criteria. Finally, a bike-share case is used to illustrate the applicability of the presented method, and various comparisons are used to display the superiority of the presented method.

New q-rung orthopair fuzzy partitioned Bonferroni mean operators and their application in multiple attribute decision making

The q-rung orthopair fuzzy sets are superior to intuitionistic fuzzy sets or Pythagorean fuzzy sets in expressing fuzzy and uncertain information. In this paper, some partitioned Bonferroni means (BMs) for q-rung orthopair fuzzy values have been developed. First, the q-rung orthopair fuzzy partitioned BM (q-ROFPBM) operator and the q-rung orthopair fuzzy partitioned geometric BM (q-ROFPGBM) operator are developed. Some desirable properties and some special cases of the new aggregation operators have been studied. The q-rung orthopair fuzzy weighted partitioned BM (q-ROFWPBM) operator and the q-rung orthopair fuzzy partitioned geometric weighted BM (q-ROFPGWBM) operator are also developed. Then, a new multiple-attribute decision-making method based on the q-ROFWPBM (q-ROFPGWBM) operator is proposed. Finally, a numerical example of investment company selection problem is given to illustrate feasibility and practical advantages of the new method.

Partitioned Bonferroni mean based on two‐dimensional uncertain linguistic variables for multiattribute group decision making

The two-dimensional uncertain linguistic variables (2DULVs) add a self-evaluation on the reliability of the assessment results given by decision makers (DMs), so they can better describe some uncertain information, and the partition Bonferroni mean (PBM) operator has the advantages, which assumes that all aggregated arguments are partitioned into several subparts, and members in the same subpart are interrelated and members in different subparts are no interrelationships. However, the traditional PBM can only deal with the crisp numbers and cannot aggregate the 2DULVs. In this paper, we extend the PBM operator to deal with the 2DULVs and propose some PBM operators for 2DULVs. First, we introduce the concepts, properties, operational laws, and comparison methods of 2DULVs, and then we propose the PBM operator for 2DULVs (2DULPBM), the weighted PBM operator for 2DULVs (2DULWPBM), the partitioned geometric Boferroni mean (PGBM) operator for 2DULVs (2DULPGBM), and weighted PGBM operator for 2DULVs (2DULWPGBM). Further, we develop a method to solve multiattribute group decision-making (MAGDM) problems with the 2DULVs. Finally, we give an example to verify that the method based on the proposed operators is effective and influential.

Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators

The partitioned Bonferroni mean (PBM) operator can efficiently aggregate inputs, which are divided into parts based on their interrelationships. To date, it has not been used to aggregate linguistic Pythagorean fuzzy numbers (LPFNs). In this paper, we extend the PBM operator and partitioned geometric Bonferroni mean (PGBM) operator to the linguistic Pythagorean fuzzy sets (LPFSs) and use them to develop a novel multiattribute group decision-making model under the linguistic Pythagorean fuzzy environment. We first define some novel operational laws for LPFNs, which take into consideration the interactions between the membership degree (MD) and nonmembership degree (NMD) from two different LPFNs. Based on these novel operational laws, we put forward the interaction PBM (LPFIPBM) operator, the weighted interaction PBM (LPFWIPBM) operator, the interaction PGBM (LPFIPGBM) operator, and the weighted interaction PGBM (LPFWIPGBM) operator. Then, we study some properties of these proposed operators and discuss their special cases. Based on the proposed LPFWIPBM and LPFWIPGBM operators, a novel multiattribute group decision-making model is developed to process the linguistic Pythagorean fuzzy information. Finally, some illustrative examples are introduced to compare our proposed methods with the existing ones.

Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Operators and Their Application in Multiple-Attribute Decision-Making

The aim of this paper is to develop partitioned Pythagorean fuzzy interaction Bonferroni mean operators based on the Pythagorean fuzzy set, Bonferroni mean, and interaction between membership and nonmembership. Several new aggregation operators are developed including the Pythagorean fuzzy interaction partitioned Bonferroni mean (PFIPBM) operator, the Pythagorean fuzzy weighted interaction partitioned Bonferroni mean (PFWIPBM) operator, the Pythagorean fuzzy interaction partitioned geometric Bonferroni mean (PFIPGBM) operator, and the Pythagorean fuzzy weighted interaction partitioned geometric Bonferroni mean (PFWIPGBM) operator. Some main properties and some special particular cases of the new operators are studied. Many existing operators are the special cases of new aggregation operators. Moreover, a multiple-attribute decision-making method based on the proposed operator has been developed and the investment company selection problem is presented to illustrate feasibility and practical advantages of the new method.

Linguistic Neutrosophic Generalized Partitioned Bonferroni Mean Operators and Their Application to Multi-Attribute Group Decision Making

To solve the problems related to inhomogeneous connections among the attributes, we introduce a novel multiple attribute group decision-making (MAGDM) method based on the introduced linguistic neutrosophic generalized weighted partitioned Bonferroni mean operator (LNGWPBM) for linguistic neutrosophic numbers (LNNs).