Partitioned 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.

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.

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.

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.

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.

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.

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).

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). First of all, inspired by the merits of the generalized partitioned Bonferroni mean (GPBM) operator and LNNs, we combine the GPBM operator and LNNs to propose the linguistic neutrosophic GPBM (LNGPBM) operator, which supposes that the relationships are heterogeneous among the attributes in MAGDM. Then, we discuss its desirable properties and some special cases. In addition, aimed at the different importance of each attribute, the weighted form of the LNGPBM operator is investigated, which we call the LNGWPBM operator. Then, we discuss some of its desirable properties and special examples accordingly. In the end, we propose a novel MAGDM method on the basis of the introduced LNGWPBM operator, and illustrate its validity and merit by comparing it with the existing methods.

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.

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.