Guiwu Wei

Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers, some new group decision making analysis methods are developed. Firstly, some operational laws, score function and accuracy function of intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers are introduced. Then two new aggregation operators: induced intuitionistic fuzzy ordered weighted geometric (I-IFOWG) operator and induced interval-valued intuitionistic fuzzy ordered weighted geometric (I-IIFOWG) operator are proposed, and some desirable properties of the I-IFOWG and I-IIFOWG operators are studied, such as commutativity, idempotency and monotonicity. An I-IFOWG and IFWG (intuitionistic fuzzy weighted geometric) operators-based approach is developed to solve the MAGDM problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic fuzzy numbers. Further, we extend the developed models and procedures based on I-IIFOWG and IIFWG (interval-valued intuitionistic fuzzy weighted geometric) operators to solve the MAGDM problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of interval-valued intuitionistic fuzzy numbers. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.

Hesitant fuzzy prioritized operators and their application to multiple attribute decision making

In this paper, we investigate the hesitant fuzzy multiple attribute decision making (MADM) problems in which the attributes are in different priority level. Motivated by the ideal of prioritized aggregation operators [R.R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning 48 (2008) 263-274], we develop some prioritized aggregation operators for aggregating hesitant fuzzy information, and then apply them to develop some models for hesitant fuzzy multiple attribute decision making (MADM) problems in which the attributes are in different priority level. Finally, a practical example about talent introduction is given to verify the developed approaches and to demonstrate its practicality and effectiveness.

GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting

The aim of this paper is to investigate the multiple attribute decision-making problems with intuitionistic fuzzy information, in which the information about attribute weights is incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method, by which the attribute weights can be determined. Then, based on the traditional GRA method, calculation steps for solving intuitionistic fuzzy multiple attribute decision-making problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution are calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of grey relation to both the positive-ideal solution (PIS) and negative-ideal solution (NIS) simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

A method for multiple attribute group decision making based on the ET-WG and ET-OWG operators with 2-tuple linguistic information

With respect to multiple attribute group decision-making problems with linguistic information of attribute values and weight values, a group decision analysis is proposed. Some new aggregation operators are proposed: the extended 2-tuple weighted geometric (ET-WG) and the extended 2-tuple ordered weighted geometric (ET-OWG) operator and properties of the operators are analyzed. Then, A method based on the ET-WG and ET-OWG operators for multiple attribute group decision-making is presented. In the approach, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.

Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making

The aim of this paper is to investigate the multiple attribute decision making problems with intuitionistic fuzzy information, in which the information about attribute weights is incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional gray relational analysis (GRA) method, by which the attribute weights can be determined. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. Then, based on the traditional GRA method, calculation steps for solving intuitionistic fuzzy multiple attribute decision-making problems with incompletely known weight information are given. Furthermore, we have extended the above results to an interval-valued intuitionistic fuzzy environment and developed modified GRA method for interval-valued intuitionistic fuzzy multiple attribute decision-making with incompletely known attribute weight information. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting

With respect to multiple attribute decision making problems with intuitionistic fuzzy information, some operational laws of intuitionistic fuzzy numbers, score function and accuracy function of intuitionistic fuzzy numbers are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the intuitionistic fuzzy weighted averaging (IFWA) operator to aggregate the intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the score function and accuracy function. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making (MADM) problems in which attribute values take the form of hesitant interval-valued fuzzy information. Firstly, definition and some operational laws of hesitant interval-valued fuzzy elements and score function of hesitant interval-valued fuzzy elements are introduced. Then, we have developed some hesitant interval-valued fuzzy aggregation operators: hesitant interval-valued fuzzy weighted averaging (HIVFWA) operator, hesitant interval-valued fuzzy ordered weighted averaging (HIVFOWA) operator, the hesitant interval-valued fuzzy weighted geometric (HIVFWG) operator, hesitant interval-valued fuzzy ordered weighted geometric (HIVFOWG) operator, hesitant interval-valued fuzzy choquet ordered averaging (HIVFCOA) operator, hesitant interval-valued fuzzy choquet ordered geometric (HIVFCOG) operator, hesitant interval-valued fuzzy prioritized aggregation operators and hesitant interval-valued fuzzy power aggregation operators. We have applied the HIVFCOA and HIVFCOG operators to multiple attribute decision making with hesitant interval-valued fuzzy information. Finally an illustrative example has been given to show the developed method.

Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making

In this paper, some multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights are usually correlative, attribute values take the form of intuitionistic fuzzy values or interval-valued intuitionistic fuzzy values, are investigated. Firstly, some operational law, score function and accuracy function of intuitionistic fuzzy values or interval-valued intuitionistic fuzzy values are introduced. Then two new aggregation operators: induced intuitionistic fuzzy correlated averaging (I-IFCA) operator and induced intuitionistic fuzzy correlated geometric (I-IFCG) operator are developed and some desirable properties of the I-IFCA and I-IFCG operators are studied, such as commutativity, idempotency and monotonicity. An I-IFCA and IFCA (intuitionistic fuzzy correlated averaging) operators-based approach is developed to solve the MAGDM problems in which both the attribute weights and the expert weights usually correlative, attribute values take the form of intuitionistic fuzzy values. Then, we extend the developed models and procedures to the interval-valued intuitionistic fuzzy environment. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.

Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information

With respect to multiple attribute decision-making problems with interval-valued intuitionistic fuzzy information, some operational laws of interval-valued intuitionistic fuzzy numbers, correlation and correlation coefficient of interval-valued intuitionistic fuzzy sets are introduced. An optimization model based on the negative ideal solution and max-min operator, by which the attribute weights can be determined, is established. We utilize the interval-valued intuitionistic fuzzy weighted averaging operator proposed by Xu (Control Decis 22(2):215–219, 2007) to aggregate the interval-valued intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the correlation coefficient. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Grey relational analysis method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information

Research highlights? The 2-tuple linguistic multiple attribute group decision making problems with incomplete weight information are investigated. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. According to the traditional ideas of grey relational analysis (GRA), the optimal alternative(s) is determined by calculating the linguistic degree of grey relation of every alternative and 2-tuple linguistic positive ideal solution and 2-tuple linguistic negative ideal solution. AbstractWith respect to 2-tuple linguistic multiple attribute group decision making problems with incomplete weight information, some basic concepts and operational laws of 2-tuple linguistic variables are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. According to the traditional ideas of grey relational analysis (GRA), the optimal alternative(s) is determined by calculating the linguistic degree of grey relation of every alternative and 2-tuple linguistic positive ideal solution and 2-tuple linguistic negative ideal solution. It is based on the concept that the optimal alternative should have the largest degree of grey relation from positive ideal solution and the smallest degree of grey relation from the negative ideal solution. The method has exact characteristic in linguistic information processing. It avoided information distortion and losing which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective and easy to calculate.