Huchang Liao

Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making

The hesitant fuzzy linguistic term sets (HFLTSs), which can be used to represent an expert’s hesitant preferences when assessing a linguistic variable, increase the flexibility of eliciting and representing linguistic information. The HFLTSs have attracted a lot of attention recently due to their distinguished power and efficiency in representing uncertainty and vagueness within the process of decision making. To enhance and extend the applicability of HFLTSs, this paper investigates and develops different types of distance and similarity measures for HFLTSs. The paper first proposes a family of distance and similarity measures between two HFLTSs. Then a variety of weighted or ordered weighted distance and similarity measures between two collections of HFLTSs are proposed and analyzed for discrete and continuous cases respectively. After that, the application of these measures to multi-criteria decision making problems is given. Based on the proposed distance and similarity measures, the satisfaction degrees for different alternatives are established and are then used to rank alternatives in multi-criteria decision making. Finally a practical example concerning the evaluation of the quality of movies is given to illustrate the applicability and advantage of the proposed approach and the differences between the proposed distance and similarity measures.

Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets

The hesitant fuzzy linguistic term set (HFLTS) is a new and flexible tool in representing hesitant qualitative information in decision making. Correlation measures and correlation coefficients have been applied widely in many research domains and practical fields. This paper focuses on the correlation measures and correlation coefficients of HFLTSs. To start the investigation, the definition of HFLTS is improved and the concept of hesitant fuzzy linguistic element (HFLE) is introduced. Motivated by the idea of traditional correlation coefficients of fuzzy sets, intuitionistic fuzzy sets and hesitant fuzzy sets, several different types of correlation coefficients for HFLTSs are proposed. The prominent properties of these correlation coefficients are then investigated. In addition, considering that different HFLEs may have different weights, the weighted correlation coefficients and ordered weighted correlation coefficients are further investigated. Finally, an application example concerning the traditional Chinese medical diagnosis is given to illustrate the applicability and validation of the proposed correlation coefficients of HFLTSs in the process of qualitative decision making.

Intuitionistic Fuzzy Analytic Hierarchy Process

The intuitionistic fuzzy set has shown definite advantages in handling vagueness and uncertainty over a fuzzy set. Taking the powerfulness of the analytic hierarchy process (AHP) and the fuzzy AHP (FAHP) into account when tackling comprehensive multi-criteria decision-making problems, in this paper, we extend the classic AHP and the FAHP into the intuitionistic fuzzy AHP (IFAHP) in which the preferences are represented by intuitionistic fuzzy values. The IFAHP can be used to handle more complex problems, where the decision maker has some uncertainty in assigning preference values to the objects considered. The paper proposes a new way to check the consistency of an intuitionistic preference relation and then introduces an automatic procedure to repair the inconsistent one. It is worth pointing out that our proposed method can improve the inconsistent intuitionistic preference relation without the participation of the decision maker, and thus, it can save much time and show some advantages over the AHP and the FAHP. This paper also develops a novel normalizing rank summation method to derive the priority vector of an intuitionistic preference relation, on which the priorities of the hierarchy in the IFAHP are derived. The procedure of the IFAHP is given in detail, and an example concerning global supplier development is used to demonstrate our results.

MULTIPLICATIVE CONSISTENCY OF HESITANT FUZZY PREFERENCE RELATION AND ITS APPLICATION IN GROUP DECISION MAKING

As we may have a set of possible values when comparing alternatives (or criteria), the hesitant fuzzy preference relation becomes a suitable and powerful technique to deal with this case. This paper mainly focuses on the multiplicative consistency of the hesitant fuzzy preference relation. First of all, we explore some properties of the hesitant fuzzy preference relation and develop some new aggregation operators. Then we introduce the concepts of multiplicative consistency, perfect multiplicative consistency and acceptable multiplicative consistency for a hesitant fuzzy preference relation, based on which, two algorithms are given to improve the inconsistency level of a hesitant fuzzy preference relation. Furthermore, the consensus of group decision making is studied based on the hesitant fuzzy preference relations. Finally, several illustrative examples are given to demonstrate the practicality of our algorithms.

Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making

We introduce a family of novel distance and similarity measures for HFLTSs.We develop a cosine-distance-based HFL-TOPSIS method.We develop a cosine-distance-based HFL-VIKOR method.We use a numerical example to illustrate the proposed methods. Qualitative and hesitant information is common in practical decision making process. In such complicated decision making problem, it is flexible for experts to use comparative linguistic expressions to express their opinions since the linguistic expressions are much closer than single or simple linguistic term to human way of thinking and cognition. The hesitant fuzzy linguistic term set (HFLTS) turns out to be a powerful tool in representing and eliciting the comparative linguistic expressions. In order to develop some approaches to decision making with hesitant fuzzy linguistic information, in this paper, we firstly introduce a family of novel distance and similarity measures for HFLTSs, such as the cosine distance and similarity measures, the weighted cosine distance and similarity measures, the order weighted cosine distance and similarity measures, and the continuous cosine distance and similarity measures. All these distance and similarity measures are proposed from the geometric point of view while the existing distance and similarity measures over HFLTSs are based on the different forms of algebra distance measures. Afterwards, based on the hesitant fuzzy linguistic cosine distance measures between hesitant fuzzy linguistic elements, the cosine-distance-based HFL-TOPSIS method and the cosine-distance-based HFL-VIKOR method are developed to dealing with hesitant fuzzy linguistic multiple criteria decision making problems. The step by step algorithms of these two methods are given for the convenience of applications. Finally, a numerical example concerning the selection of ERP systems is given to illustrate the validation and efficiency of the proposed methods.

Priorities of Intuitionistic Fuzzy Preference Relation Based on Multiplicative Consistency

The intuitionistic fuzzy preference relation (IFPR), whose elements are intuitionistic fuzzy values (IFVs), is more powerful than the traditional multiplicative preference relation and the fuzzy preference relation in expressing comprehensive preference information of a decision maker. The aim of this paper is to investigate a new approach to derive the priority weights from an IFPR. To do so, we give a new definition of multiplicative consistent IFPR, which is based on the membership and nonmembership degrees of the intuitionistic fuzzy judgments. After that, a formula, which involves the underlying intuitionistic fuzzy weights of the IFPR, is proposed to construct such a multiplicative consistent IFPR. Based on the formula, some fractional programming models are built to generate the intuitionistic fuzzy priority weighting vector of the IFPR. Several numerical examples are given to illustrate the validity and applicability of the proposed method.

Subtraction and division operations over hesitant fuzzy sets

Hesitant fuzzy set (HFS), which permits the membership having a set of possible values, has turned out to be a powerful structure in expressing uncertainty and vagueness. In this paper, we propose two new basic operations over HFSs, which are the subtraction operation and the division operation. Several operational laws of these two operations over HFSs are given. The relationship between intuitionistic fuzzy set (IFS) and HFS is further verified in terms of these two operations. In addition, the relationships between these two operations are also established in this paper. The operations can be immediately extended into interval-valued hesitant fuzzy sets and dual hesitant fuzzy sets. The subtraction and division operations are significantly important in forming the integral theoretical framework of HFS and may have many practical applications in decision making.

Multi-criteria decision making with intuitionistic fuzzy PROMETHEE

This paper investigates one of the outranking based methods, PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation), for multi-criteria decision making, and extends it into intuitionistic fuzzy circumstance. Our enhancement of the PROMETHEE with intuitionistic fuzzy set, named IF-PROMETHEE, takes not only intuitionistic fuzzy preferences, but also intuitionistic fuzzy weights into account. Two practical examples are carried out to illustrate the applicability and efficiency of our proposed method in solving multi-criteria decision making problems. The first example concerning the evaluation of alternative energy exploitation projects shows that IF-PROMETHEE can depict more comprehensive preference information than PROMETHEE and F-PROMETHEE. The second example further illustrates the application of IF-PROMETHEE.

An enhanced consensus reaching process in group decision making with intuitionistic fuzzy preference relations

Group decision making (GDM) with intuitionistic fuzzy preference relations (IFPRs) has been an important and active research topic recently, in which one of the most challenging issues is how to reach the group consensus so as to get the best decision. As the uniform consensus is often unachievable in practice, in order to achieve the consensus, the existing method needs to remove the experts with the most different opinions from the decision group. It has two drawbacks: the first is the loss of the valuable judgments and opinions of the removed experts. This is especially harmful in practice where most experts or decision makers often have the biased knowledge in the sense of in-depth expertise in some aspects and naive views in other aspects. The second is demotivating the experts in GDM. To overcome these weaknesses in the existing method, this paper presents an enhanced consensus reaching process for GDM with IFPRs, which only removes some opinions of an expert for alternative(s) instead of removing the expert from the decision group. A numerical example concerning the selection of outstanding PhD students for China Scholarship Council is given to show the feasibility and effectiveness of the enhanced consensus reaching process.

Satisfaction Degree Based Interactive Decision Making under Hesitant Fuzzy Environment with Incomplete Weights

Multi-criteria decision making with hesitant fuzzy information is a new research topic since the hesitant fuzzy set was firstly proposed. This paper investigates a multi-criteria decision making problem where the weight information is partially known. We firstly propose the hesitant fuzzy positive ideal solution and the hesitant fuzzy negative ideal solution. Motivated by the TOPSIS (Technique for Order Preference by Similarity to an ideal Solution) method, we definite the satisfaction degree of an alternative, based on which several optimization models are derived to determinate the weights. Subsequently, in order to make a more reasonable decision, we introduce an interactive method based on some optimization models for multi-criteria decision making problems with hesitant fuzzy information. Finally, a practical example on evaluating the service quality of airlines is provided to illustrate our models and method.