Peide Liu

Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which the attribute weights and the expert weights take the form of real numbers and the attribute values take the form of intuitionistic uncertain linguistic variables, new group decision making methods have been developed. First, operational laws, expected value definitions, score functions and accuracy functions of intuitionistic uncertain linguistic variables are introduced. Then, an intuitionistic uncertain linguistic weighted geometric average (IULWGA) operator and an intuitionistic uncertain linguistic ordered weighted geometric (IULOWG) operator are developed. Furthermore, some desirable properties of these operators, such as commutativity, idempotency, monotonicity and boundedness, have been studied, and an intuitionistic uncertain linguistic hybrid geometric (IULHG) operator, which generalizes both the IULWGA operator and the IULOWG operator, was developed. Based on these operators, two methods for multiple attribute group decision making problems with intuitionistic uncertain linguistic information have been proposed. Finally, an illustrative example is given to verify the developed approaches and demonstrate their practicality and effectiveness.

Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information

This paper develops a method for solving the multiple attribute decision-making problems with the single-valued neutrosophic information or interval neutrosophic information. We first propose two discrimination functions referred to as score function and accuracy function for ranking the neutrosophic numbers. An optimization model to determine the attribute weights that are partly known is established based on the maximizing deviation method. For the special situations where the information about attribute weights is completely unknown, we propose another optimization model. A practical and useful formula which can be used to determine the attribute weights is obtained by solving a proposed nonlinear optimization problem. To aggregate the neutrosophic information corresponding to each alternative, we utilize the neutrosophic weighted averaging operators which are the single-valued neutrosophic weighted averaging operator and the interval neutrosophic weighted averaging operator. Thus, we can determine the order of alternatives and choose the most desirable one(s) based on the score function and accuracy function. Finally, some illustrative examples are presented to verify the proposed approach and to present its effectiveness and practicality.

Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators

Abstract 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.

An extended TODIM method for multiple attribute group decision-making based on 2-dimension uncertain linguistic Variable

The significant characteristic of the TODIM (an acronym in Portuguese of Interactive and Multiple Attribute Decision Making) method is that it can consider the bounded rationality of the decision makers. However, in the classical TODIM method, the rating of the attributes only can be used in the form of crisp numbers. Because 2-dimension uncertain linguistic variables can easily express the fuzzy information, in this article, we extend the TODIM method to 2-dimension uncertain linguistic information. First of all, the definition, characteristics, expectation, comparative method and distance of 2-dimension uncertain linguistic information are introduced, and the steps of the classical TODIM method for Multiple attribute decision making (MADM) problems are presented. Second, on the basis of the classical TODIM method, the extended TODIM method is proposed to deal with MADM problems in which the attribute values are in the form of 2-dimension uncertain linguistic variables, and detailed decision steps are given. Its significant characteristic is that it can fully consider the bounded rationality of the decision makers, which is a real action in real decision making. Finally, a numerical example is provided to verify the developed approach and its practicality and effectiveness.

Multiattribute group decision making based on intuitionistic 2-tuple linguistic information

Abstract In this paper, we propose a new method for multiattribute group decision making (MAGDM) with the intuitionistic 2-tuple linguistic (I2L) information based on the proposed I2L generalized aggregation (I2LGA) operator. Firstly, we extend the Archimedean T-norm (TN) and T-conorm (TC) from the range [0, 1] to [0, t] (t > 0), and propose the extended TN and TC. Then, we develop general operational laws for the I2L information (I2LI) and propose the I2L generalized aggregation (I2LGA) operator for the I2LI based on extended TN and TC, and give some special cases and some of their properties with respect to some types of the extended TN and TC. Then, we propose a new MAGDM method with the I2LI based on the proposed I2LGA operator. Finally, we use an application example to verify the validity of the proposed MAGDM method and to show its advantages compared to existing MAGDM methods.

Some Improved Linguistic Intuitionistic Fuzzy Aggregation Operators and Their Applications to Multiple-Attribute Decision Making

Linguistic intuitionistic fuzzy numbers (LIFNs) is a new concept in describing the intuitionistic fuzzy information, which membership and non-membership are expressed by linguistic terms, so it can more easily express the fuzzy information, and some research results on LIFNs have been achieved. However, in the existing researches, some linguistic intuitionistic fuzzy aggregation operators are based on the traditional operational rules, and they have some drawbacks for multi-attribute decision making (MADM) in the practical application. In order to overcome these problems, in this paper, we proposed some improved operational rules based on LIFNs and verified their some properties. Then we developed some aggregation operators to fuse the decision information represented by LIFNs, including the improved linguistic intuitionistic fuzzy weighted averaging (ILIFWA) operator and the improved linguistic intuitionistic fuzzy weighted power average (ILIFWPA) operator. Further, we proved their some desirable properties. Based on the ILIFWA operator and the ILIFWPA operator, we presented some new methods to deal with the multi-attribute group decision making (MAGDM) problems under the linguistic intuitionistic fuzzy environment. Finally, we used some practical examples to illustrate the validity and feasibility of the proposed methods by comparing with other methods.

Interval-Valued Intuitionistic Fuzzy Power Bonferroni Aggregation Operators and Their Application to Group Decision Making

The power Bonferroni mean (PBM) operator can take the advantages of power operator and Bonferroni mean operator, which can overcome the influence of the unreasonable attribute values and can also consider the interaction between two attributes. However, it cannot be used to process the interval-valued intuitionistic fuzzy numbers (IVIFNs). It is importantly meaningful to extend the PBM operator to IVIFNs. We extend PBM operator to process IVIFNs and propose some new PBM operators for IVIFNs and apply them to solve the multi-attribute group decision-making (MAGDM) problems. Firstly, the definition, properties, score function, and operational rules of IVIFNs are introduced briefly. Then, the power Bonferroni mean (IVIFPBM) operator, the weighted PBM (IVIFWPBM) operator, the power geometric BM (IVIFPGBM) operator, and the weighted power geometric BM (IVIFWPGBM) operator for IVIFNs are proposed. Furthermore, some deserved properties of them are explored, and several special cases are analyzed. The decision-making methods are developed to deal with the MAGDM problems with the information of the IVIFNs based on the proposed operators, and by an illustrative example, the proposed methods are verified, and their advantages are explained by comparing with the other methods. The proposed methods can effectively solve the MAGDM problems with the IVIFNs, and they can consider the interaction between two attributes and overcome the influence of the unreasonable attribute values.

Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making

The Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters, but it only can deal with crisp values. In recent years, many extended BM operators have been proposed to deal with fuzzy information. Dombi Bonferroni mean operators are special cases of general T-conorm and T-norm, which have the advantage of good flexibility with a general parameter. In this paper, we extend the BM operator based on the Dombi operations to propose the intuitionistic fuzzy Dombi Bonferroni mean (IFDBM) operator, the intuitionistic fuzzy weighted Dombi Bonferroni mean (IFWDBM) operator, the intuitionistic fuzzy Dombi geometric Bonferroni mean (IFDGBM) operator and the intuitionistic fuzzy weighted Dombi geometric Bonferroni mean (IFWDGBM) operator for dealing with the aggregation of intuitionistic fuzzy numbers (IFNs) and propose some multi-attribute group decision-making (MAGDM) methods. Firstly, we introduce the concept, the characteristics, the score function, the accuracy function and the operational rules of IFNs. Then, we propose the IFDBM operator, the IFWDBM operator, the IFDGBM operator and the IFWDGBM operator for aggregating IFNs. Then, we propose two MAGDM methods based on the proposed IFWDBM operator and the proposed IFWDGBM operator for dealing with MAGDM problems. Finally, we use an example to illustrate the MAGDM process of the proposed MAGDM methods. The proposed intuitionistic fuzzy Dombi Bonferroni mean operators are very useful to deal with MAGDM problems.

Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making

Abstract As a combination of the hesitant fuzzy set (HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truth-hesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS. Correlation and correlation coefficient have been applied widely in many research domains and practical fields. This paper, motivated by the idea of correlation coefficients derived for HFSs, IFSs, DHFSs and SVNSs, focuses on the correlation and correlation coefficient of SVNHFSs and investigates their some basic properties in detail. By using the weighted correlation coefficient information between each alternative and the optimal alternative, a decision-making method is established to handling the single-valued neutrosophic hesitant fuzzy information. Finally, an effective example is used to demonstrate the validity and applicability of the proposed approach in decision making, and the relationship between the each existing method and the developed method is given as a comparison study.

Multiple criteria decision making method based on normal interval-valued intuitionistic fuzzy generalized aggregation operator

On the basis of the normal intuitionistic fuzzy numbers (NIFNs), we proposed the normal interval-valued intuitionistic fuzzy numbers (NIVIFNs) in which the values of the membership and nonmembership were extended to interval numbers. First, the definition, the properties, the score function and accuracy function of the NIVIFNs are briefly introduced, and the operational laws are defined. Second, some aggregation operators based on the NIVIFNs are proposed, such as normal interval-valued intuitionistic fuzzy weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy ordered weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy hybrid weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy weighted geometric averaging operator, normal interval-valued intuitionistic fuzzy ordered weighted geometric averaging operator, normal interval-valued intuitionistic fuzzy hybrid weighted geometric averaging operator, and normal interval-valued intuitionistic fuzzy generalized weighted averaging operator, normal interval-valued intuitionistic fuzzy generalized ordered weighted averaging operator, normal interval-valued intuitionistic fuzzy generalized hybrid weighted averaging operator, and some properties of these operators, such as idempotency, monotonicity, boundedness, commutativity, are studied. Further, an approach to the decision making problems with the NIVIFNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.