Bonferroni Mean Operator Research Articles

Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean

In this paper, we proposed a single-valued neutrosophic normalized weighted Bonferroni mean (SVNNWBM) operator on the basis of Bonferroni mean, the weighted Bonferroni mean (WBM), and the normalize...

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

In this paper, we point out that two theorems in a previous paper by Wei et al. (2013) are incorrect by some counterexamples in detail, and present the modified theorems.

Simplified neutrosophic linguistic normalized weighted Bonferroni mean operator and its application to multi-criteria decision-making problems

Simplified neutrosophic linguistic normalized weighted Bonferroni mean operator and its application to multi-criteria decision-making problems

2-tuple Linguistic Bonferroni Mean Operators and Their Application to Multiple Attribute Group Decision Making

Aims: The aim of this paper is to develop the 2-tuple linguistic Bonferroni mean and the weighted 2-tuple linguistic Bonferroni mean. Study Design: Some desirable properties and special cases of the developed operators are discussed. The geometric Bonferroni mean (GBM) is a generalization of the Bonferroni mean and geometric mean. In this paper, we also investigate the GBM under 2-tuple linguistic environments. We develop the 2-tuple linguistic geometric Bonf erroni mean and the weighted 2tuple linguistic geometric Bonferroni mean. We investiga te some fundamental properties and special cases of them. Place and Duration of Study: The Bonferroni Mean (BM) operator is a traditional mean t ype aggregation operator, which can capture the expressed interrelat ionship of the individual arguments and which is only suitable to aggregate crisp data. Methodology: This paper extends the BM operator to 2-tuple linguistic en vironments. Results: Based on these operators, we develop two approaches for m ultiple attribute group decision making with 2-tuple linguistic information. Conclusion: Two numerical examples are provided to illustrate the effec tiveness and practicality of the proposed approaches.

Some Bonferroni mean operators with 2-tuple linguistic information and their application to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making (MADM) problems with 2-tuple linguistic information. Motivated by the ideal of Bonferroni mean and geometric Bonferroni mean, we develop two aggregation techniques called the 2-tuple linguistic Bonferroni mean (2TLBM) operator and the 2-tuple linguistic geometric Bonferroni mean (2TLGBM) operator for aggregating the 2-tuple linguistic information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define the 2-tuple linguistic weighted Bonferroni mean (2TLWBM) operator and the 2-tuple linguistic weighted geometric Bonferroni mean (2TLWGBM) operator, based on which we develop two procedure for multiple attribute decision making under the 2-tuple linguistic environments. Finally, a practical example with comprehensive evaluating modeling of brand extension is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Intuitionistic linguistic weighted Bonferroni mean operator and its application to multiple attribute decision making.

The intuitionistic linguistic variables are easier to describe the fuzzy information which widely exists in the real world, and Bonferroni mean can capture the interrelationship of the individual arguments. However, the traditional Bonferroni mean can only process the crisp number. In this paper, we will extend Bonferroni mean to the intuitionistic linguistic environment and propose a multiple attribute decision making method with intuitionistic linguistic information based on the extended Bonferroni mean which can consider the interrelationship of the attributes. Firstly, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic Bonferroni mean (ILBM) operator and an intuitionistic linguistic weighted Bonferroni mean (ILWBM) operator are developed, and some desirable characteristics of them are studied. At the same time, some special cases with respect to the parameters p and q in Bonferroni are analyzed. Based on the ILWBM operator, the approach to multiple attribute decision making with intuitionistic linguistic information is proposed. Finally, an illustrative example is given to verify the developed approach and to demonstrate its effectiveness.

An Approach to Evaluating Enterprise Financial Performance Based on the Control Inheritance of Family Businesses with Intuitionistic Fuzzy Information

We investigate the multiple attribute decision making problems for evaluating the enterprise financial performance based on the control inheritance of family businesses with intuitionistic fuzzy information. We utilize the intuitionistic fuzzy Bonferroni mean (IFBM) operator to aggregate the intuitionistic fuzzy information corresponding to each alternative and get the overall value of enterprise financial performance and then rank the enterprises and select the most desirable one(s) by using the overall value of enterprise financial performance. Finally, an illustrative example for evaluating the enterprise financial performance based on the control inheritance of family businesses is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Generalized Fuzzy Bonferroni Harmonic Mean Operators and Their Applications in Group Decision Making

The Bonferroni mean (BM) operator is an important aggregation technique which reflects the correlations of aggregated arguments. Based on the BM and harmonic mean operators, H. Sun and M. Sun (2012) developed the fuzzy Bonferroni harmonic mean (FBHM) and fuzzy ordered Bonferroni harmonic mean (FOBHM) operators. In this paper, we study desirable properties of these operators and extend them, by considering the correlations of any three aggregated arguments instead of any two, to develop generalized fuzzy weighted Bonferroni harmonic mean (GFWBHM) operator and generalized fuzzy ordered weighted Bonferroni harmonic mean (GFOWBHM) operator. In particular, all these operators can be reduced to aggregate interval or real numbers. Then based on the GFWBHM and GFOWBHM operators, we present an approach to multiple attribute group decision making and illustrate it with a practical example.

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

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

Intuitionistic Fuzzy Geometric Bonferroni Means and Their Application in Multicriteria Decision Making

As a useful aggregation technique, the Bonferroni mean (BM) can capture the interrelationship between input arguments and has been a hot research topic recently. Based on the classic BM, many BM operators have been proposed and developed, such as the weighted BM, the generalized BM, the intuitionistic fuzzy BM, and so on. However, these BM operators are all based on the averaging mean, which is one of the basic aggregation approaches and focuses on the group opinion and another basic one is the geometric mean, which gives more importance to the individual opinions. To combine with the geometric mean and the BM, in this paper, we propose the geometric BM, the weighted geometric BM, and the generalized weighted geometric BM. These new geometric BMs can reflect the geometric interrelationship between the individual criterion and other criteria and keep the main advantage of BM. Furthermore, we investigate the geometric BMs under the intuitionistic fuzzy environment, which is more common phenomenon in modern life and develop three intuitionistic fuzzy geometric Bonferroni mean operators, i.e., the intuitionistic fuzzy geometric Bonferroni mean (IFGBM), the intuitionistic fuzzy weighted geometric Bonferroni mean (IFWGBM), and the intuitionistic fuzzy generalized weighted geometric Bonferroni mean (IFGWGBM) and study their desirable properties, such as idempotency, commutativity, monotonicity, and boundedness. Finally, on the basis of the IFWGBM and IFGWGBM operators, we propose an approach to multicriteria decision making under the intuitionistic fuzzy environment, and a practical example is provided to illustrate our results.

The trapezoid fuzzy linguistic Bonferroni mean operators and their application to multiple attribute decision making

The Bonferroni Mean (BM) operator is a traditional mean type aggregation operator which can capture the expressed interrelationship of the individual arguments, and is only suitable to aggregate crisp data. In this paper, we develop some Bonferroni mean operators based on trapezoid fuzzy linguistic variables, such as a Trapezoid Fuzzy Linguistic Bonferroni Mean (TFLBM) operator, a Trapezoid Fuzzy Linguistic Weighted Bonferroni Mean (TFLWBM) operator, a Trapezoid Fuzzy Linguistic Bonferroni OWA (TFLBOWA) operator and a Trapezoid Fuzzy Linguistic Weighted Bonferroni OWA (TFLWBOWA) operator. Furthermore, some desirable properties of these operators are studied. At the same time, some special cases in these operators are analyzed. Based on these operators, methods of multiple attribute decision making with trapezoid fuzzy linguistic information are proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.

Generalized Bonferroni mean operators in multi-criteria aggregation

In this paper we provide a systematic investigation of a family of composed aggregation functions which generalize the Bonferroni mean. Such extensions of the Bonferroni mean are capable of modeling the concepts of hard and soft partial conjunction and disjunction as well as that of k-tolerance and k-intolerance. There are several interesting special cases with quite an intuitive interpretation for application.

Uncertain Bonferroni Mean Operators

The Bonferroni mean is a traditional mean type aggregation operator bounded by the max and min operators, which is suitable to aggregate the crisp data. In this paper, we consider situations where the input data are interval numbers. We develop some uncertain Bonferroni mean operators, and then combine them with the well-known ordered weighted averaging operator and Choquet integral respectively for aggregating uncertain information. We also give their applications to multi-criteria decision making under uncertainty, and finally, some possible extensions for further research are discussed.

On generalized Bonferroni mean operators for multi-criteria aggregation

We introduce the idea of multi-criteria aggregation functions and describe a number of properties desired in such functions. We emphasize the importance of having an aggregation function capture the expressed interrelationship between the criteria. A number of standard aggregation functions are introduced. We next introduce the Bonferroni mean operator. We provide an interpretation of this operator as involving a product of each argument with the average of the other arguments, a combined averaging and “anding” operator. This allows us to suggest generalizations of this operator by replacing the simple averaging by other mean type operators as well as associating differing importances with the arguments.