Yejun Xu

Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment

The aim of this paper is to develop some new linguistic aggregation operators, such as 2-tuple linguistic power average (2TLPA) operator, 2-tuple linguistic weighted PA operator, 2TLPOWA operator which are based on PA operator. We have studied some desired properties of the developed operators, such as idempotency, boundary, etc. Moreover, we have developed two approaches to deal with group decision making problems under linguistic environment. If the weighting vector of the decision makers is known, we develop an approach which is based on the 2-tuple linguistic weighted PA operator. On the other hand, if the weighting vector of the decision makers is unknown, we develop another approach which is based on the 2TLPOWA operator. Finally, a practical example is given to illustrate the multiple attribute group decision making process, a comparative study to fuzzy additive weighted averaging (FAWA) operator method is also demonstrated.

The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making

In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (I-GIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for intuitionistic fuzzy information, including all the particular cases of the I-IFOWA operator, GIFOWA operator and the induced intuitionistic fuzzy ordered geometric (I-IFOWG) operator. We also present the induced generalized interval-valued intuitionistic fuzzy ordered weighted averaging (I-GIIFOWA) operator to accommodate the environment in which the given arguments are interval-valued intuitionistic fuzzy sets. Further, we develop procedures to apply them to solve group multiple attribute decision making problems with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. Finally, we present their application to show the effectiveness of the developed methods.

A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress

This position paper studies the necessity of hesitant fuzzy sets.A discussion about current proposals are introduced.Some challenges of hesitant fuzzy sets are proposed. The necessity of dealing with uncertainty in real world problems has been a long-term research challenge which has originated different methodologies and theories. Recently, the concept of Hesitant Fuzzy Sets (HFSs) has been introduced to model the uncertainty that often appears when it is necessary to establish the membership degree of an element and there are some possible values that make to hesitate about which one would be the right one. Many researchers have paid attention on this concept who have proposed diverse extensions, relationships with other types of fuzzy sets, different types of operators to compute with this type of information, applications on information fusion and decision-making, etc.Nevertheless, some of these proposals are questionable, because they are straightforward extensions of previous works or they do not use the concept of HFSs in a suitable way. Therefore, this position paper studies the necessity of HFSs and provides a discussion about current proposals including a guideline that the proposals should follow and some challenges of HFSs.

Group decision making under hesitant fuzzy environment with application to personnel evaluation

In many personnel evaluation scenarios, decision makers are asked to provide their preferences anonymously to both ensure privacy and avoid psychic contagion. The use of hesitant fuzzy sets is a powerful technique for representing this type of information and has been well studied. This paper explores aggregation methods for prioritized hesitant fuzzy elements and their application on personnel evaluation. First, the generalized hesitant fuzzy prioritized weighted average (GHFPWA) and generalized hesitant fuzzy prioritized weighted geometric (GHFPWG) operators are presented. Some desirable properties of the methods are discussed and special cases are investigated in detail. Previous research has indicated that many existing hesitant fuzzy aggregation operators are special cases of the proposed operators. Then, a procedure and algorithm for group decision making is provided using these proposed generalized hesitant fuzzy aggregation operators. Finally, the group decision making method is applied to a representative personnel evaluation problem that involves a prioritization relationship over the evaluation index.

Least square completion and inconsistency repair methods for additively consistent fuzzy preference relations

In this paper, we explore the group decision making (GDM) problems with incomplete additively consistent fuzzy preference relations. Some properties of additively consistent fuzzy preference relations are also discussed. A sufficient and necessary condition is proposed to keep the additive consistency of fuzzy preference relations. Methods for determining the priority weights of fuzzy preference relations are provided. Least square completion and inconsistency repair methods are developed to deal with incomplete and inconsistent fuzzy preference relations. Some numerical examples are also given to illustrate the proposed approaches.

Standard and mean deviation methods for linguistic group decision making and their applications

This paper proposes two methods for multi-attribute decision making problems with linguistic information, in which the preference values take the form of linguistic variables. Based on the ideal that the attribute with a larger deviation value among alternatives should be assigned a large weight, two methods named standard deviation method and mean deviation method are proposed to determine the optimal weighting vector objectively under the assumption that attribute weights are completely unknown. Two numerical examples are examined using the proposed methods to show the advantages from the other methods. It is shown that the proposed methods are straightforward and no loss of information.

Distance-based consensus models for fuzzy and multiplicative preference relations

This paper proposes a distance-based consensus model for fuzzy preference relations where the weights of fuzzy preference relations are automatically determined. Two indices, an individual to group consensus index (ICI) and a group consensus index (GCI), are introduced. An iterative consensus reaching algorithm is presented and the process terminates until both the ICI and GCI are controlled within predefined thresholds. The model and algorithm are then extended to handle multiplicative preference relations. Finally, two examples are illustrated and comparative analyses demonstrate the effectiveness of the proposed methods.

Normalizing rank aggregation method for priority of a fuzzy preference relation and its effectiveness

The aim of this paper is to show that the normalizing rank aggregation method can not only be used to derive the priority vector for a multiplicative preference relation, but also for the additive transitive fuzzy preference relation. To do so, a simple functional equation between fuzzy preferences element and priority weight is derived firstly, then, based on the equation, three methods are proposed to prove that the normalizing rank aggregation method is simple and effective for deriving the priority vector. Finally, a numerical example is used to illustrate the proposed methods.

A method for multiple attribute decision making with incomplete weight information under uncertain linguistic environment

The multi-attribute decision making problems are studied, in which the information about the attribute values take the form of uncertain linguistic variables. The concept of deviation degree between uncertain linguistic variables is defined, and ideal point of uncertain linguistic decision making matrix is also defined. A formula of possibility degree for the comparison between uncertain linguistic variables is proposed. Based on the deviation degree and ideal point of uncertain linguistic variables, an optimization model is established, by solving the model, a simple and exact formula is derived to determine the attribute weights where the information about the attribute weights is completely unknown. For the information about the attribute weights is partly known, another optimization model is established to determine the weights, and then to aggregate the given uncertain linguistic decision information, respectively. A method based on possibility degree is given to rank the alternatives. Finally, an illustrative example is also given.

The ordinal consistency of a fuzzy preference relation

In this paper, we first analyze the rationality of weak transitivity of a fuzzy preference relation defined by Tanino [Fuzzy preference orderings in group decision making, Fuzzy Sets and Systems 12 (1984) 117-131]. We then propose a revised definition of weak transitivity (we call it ordinal consistency). We propose the ordinal consistency index (OCI) to measure the degree of ordinal consistency of a fuzzy preference relation, which is to count the unreasonable 3-cycles in a directed graph that represents the fuzzy preference relation. Afterwards, a procedure to compute the order consistency index and to locate each cycle, as well as to find the inconsistent judgments in the fuzzy preference relation is proposed. In order to repair the inconsistency of a fuzzy preference relation, an algorithm is developed to find and remove 3-cycles in the graph. The algorithm eliminates 3-cycles in a graph more effectively and the proposed method for improving consistency method aims to preserve the initial preference information of the decision maker. Furthermore, the method can be used not only for a strict fuzzy preference relation, but also for non-strict fuzzy preference relation. Finally, we provide some examples to show the effectiveness and validity of the proposed method.