Feifei Jin

Multiple attribute group decision making based on interval-valued hesitant fuzzy information measures

Three axiomatic definitions of information measures are introduced.Several continuous information measure formulas for IVHFEs are constructed.The relationship among the entropy, similarity measures and cross-entropy are discussed.MAGDM method based on the proposed continuous information measures is developed.A numerical example is given to illustrate the behavior of the proposed MAGDM method. Under the interval-valued hesitant fuzzy environment, we investigate a multiple attribute group decision making (MAGDM) method on the basis of some information measures. We first introduce three axiomatic definitions of information measures under interval-valued hesitant fuzzy environment, including the entropy, similarity measures and cross-entropy. Several information measure formulas for interval-valued hesitant fuzzy elements (IVHFEs) are further constructed, which is based on the continuous ordered weighted averaging (COWA) operator. Then, the relationship among the entropy, similarity measures and cross-entropy is discussed, from which we find that three information measures can be transformed by each other based on their axiomatic definitions. The programming model is established to determine optimal weight of attribute with the principle of minimum entropy and maximum cross-entropy. Furthermore, an approach to MAGDM is developed, in which the attribute values take the form of IVHFEs. Finally, a numerical example for emergency risk management (ERM) evaluation is provided to illustrate the application of the developed approach.

Approaches to group decision making with intuitionistic fuzzy preference relations based on multiplicative consistency

The intuitionistic fuzzy preference relation (IFPR) was introduced by Xu to efficiently deal with situations in which the decision makers (DMs) exhibit the characteristics of affirmation, negation and hesitation for the preference degrees over paired comparisons of alternatives. In this paper, two new approaches to group decision making (GDM) are proposed to derive the normalized intuitionistic fuzzy priority weights from IFPRs based on the order consistency and the multiplicative consistency. First, the concepts of order consistency and weak transitivity for IFPRs are introduced, and followed by a discussion of their desirable properties. Then, in order to convert the normalized intuitionistic fuzzy priority weights into multiplicative consistent IFPR, a transformation approach is investigated. Two linear optimization models are further developed to derive the normalized intuitionistic fuzzy weight vector for both individual and group IFPRs with the principle of minimizing the deviations between any provided IFPR and the converted multiplicative consistent IFPR, and the optimal deviation values obtained from the models enable us to improve the multiplicative consistency of IFPRs. Finally, based on the order consistency and the multiplicative consistency, two new algorithms for GDM are presented. Several numerical examples are provided, and comparative analyses with existing approaches are performed to demonstrate that the proposed methods are both valid and practical to deal with group decision making problems.

Approaches to decision making with linguistic preference relations based on additive consistency

Display Omitted The new concepts of order consistency and additive consistency of LPRs are introduced.The characterization about additive consistent LPRs is discussed.Two new automatic iterative algorithms are proposed.The convergences of algorithms are shown.A numerical example is provided. The linguistic preference relation (LPR) is introduced to efficiently deal with situations in which the decision makers (DMs) provide their preference information by using linguistic labels over paired comparisons of alternatives. However, the lack of consistency in decision making with LPRs can lead to inconsistent conclusions. In this paper, two new decision making methods are developed to improve the additive consistency of LPRs until they are acceptable, and eventually obtain the reliable decision making results. First, the new concepts of order consistency and additive consistency of LPRs are introduced, and followed by a discussion of the characterization about additive consistent LPRs. Then, a consistency index is defined to measure whether an LPR is of acceptable additive consistency. For an unacceptable additive consistent LPR, two automatic iterative algorithms are further proposed to help DMs improve additive consistency level until it is acceptable. In addition, the proposed algorithms can derive the priority weight vector from LPRs and obtain the ranking of the alternatives. Finally, the proposed methods are applied to an emergency operating center (EOC) selection problem. The comparative analysis demonstrates the applicability and effectiveness of the proposed methods.

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

Motivated by the idea of prioritized aggregation (PA) operators, Wei (2012) developed two hesitant fuzzy prioritized aggregation (HFPA) operators, and discussed their desirable properties, but the definitions for the HFPA operators and their properties still need to be improved. In this short note, a numerical example is given to show that the idempotency of the HFPA operators suffers from certain shortcomings. Then, based on some adjusted operations on the hesitant fuzzy elements (HFEs), two improved aggregation operators are investigated to aggregate the collective of attribute values. We further prove that the improved operators have the properties of idempotency and boundedness. Finally, the comparison with the method proposed by Wei (2012) is performed to demonstrate that the proposed information aggregation method is both valid and practical to deal with decision making problems.

Goal programming approach to derive intuitionistic multiplicative weights based on intuitionistic multiplicative preference relations

The intuitionistic multiplicative preference relation (IMPR) was introduced by Xia et al. [25] to deal with situations in which the decision makers (DMs) exhibit the characteristics of affirmation, negation and hesitation for the preference degrees over paired comparisons of alternatives. The IMPR can reflect the preference information of the DMs over alternatives more comprehensively than the multiplicative preference relation (MPR). In this paper, a new method for decision making is proposed to derive normalized intuitionistic multiplicative weights on the basis of the order consistent IMPR and the consistent IMPR. We first define the concepts of order consistent IMPR, consistent IMPR and normalized intuitionistic multiplicative weights, and then discuss some properties of the consistent IMPR. After that, we investigate a transformation formula to convert the normalized intuitionistic multiplicative priority weights into a consistent IMPR. An optimization model is constructed to generate the normalized intuitionistic multiplicative weights of IMPR, and the optimal deviation values obtained from the model enable us to improve the consistency of the given IMPR, such that the repaired IMPR is consistent. In the end, a numerical example is provided, and comparative analysis with Xu’s approach [26] is performed to demonstrate the validity and applicability of the proposed method.

Approaches to group decision making with linguistic preference relations based on multiplicative consistency

Order consistency and multiplicative consistency for LPRs are introduced.A consistency index is defined.Two linear optimization models are established to generate the weight vector.Two GDM methods are investigated, and they are proved to be convergent.Several examples are provided to illustrate the behavior of the proposed methods. A key step in group decision making (GDM) with linguistic preference relations (LPRs) is to derive the priority weight vector of the alternatives. However, the lack of consistency in GDM can lead to inconsistent conclusions. In this paper, two new GDM methods are developed to improve the multiplicative consistency of LPRs until they are acceptable, and the priority weight vector of the alternatives is derived from adjusted LPRs. First, the new concepts of order consistency and multiplicative consistency for LPRs are introduced. Then, a consistency index is defined to measure whether a LPR is of acceptable multiplicative consistency. Two linear optimization models are established to generate the normalized crisp weight vector for both individual and group LPRs with the principle of minimizing the deviation values. In addition, two GDM methods are investigated to improve LPRs with unacceptable multiplicative consistency until the adjusted LPRs are acceptable multiplicative consistent, and they can help the decision makers (DMs) to obtain the reasonable and reliable decision making results. Finally, several numerical examples are provided, and comparative analyses with existing approaches are performed to demonstrate that the proposed methods are both valid and practical to deal with GDM problems.

Selective ensemble based on extreme learning machine and improved discrete artificial fish swarm algorithm for haze forecast

Urban haze pollution is becoming increasingly serious, which is considered very harmful for humans by World Health Organization (WHO). Haze forecasts can be used to protect human health. In this paper, a Selective ENsemble based on an Extreme Learning Machine (ELM) and Improved Discrete Artificial Fish swarm algorithm (IDAFSEN) is proposed, which overcomes the drawback that a single ELM is unstable in terms of its classification. First, the initial pool of base ELMs is generated by using bootstrap sampling, which is then pre-pruned by calculating the pair-wise diversity measure of each base ELM. Second, partial-based ELMs among the initial pool after pre-pruning with higher precision and with greater diversity are selected by using an Improved Discrete Artificial Fish Swarm Algorithm (IDAFSA). Finally, the selected base ELMs are integrated through majority voting. The Experimental results on 16 datasets from the UCI Machine Learning Repository demonstrate that IDAFSEN can achieve better classification accuracy than other previously reported methods. After a performance evaluation of the proposed approach, this paper looks at how this can be used in haze forecasting in China to protect human health.

A decision support model for group decision making with intuitionistic fuzzy linguistic preferences relations

As a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was introduced to efficiently cope with situations in which the membership degree and non-membership degree are represented as linguistic terms. For group decision making (GDM) problems with IFLPRs, two significant and challenging issues are individual consistency and group consensus before deriving the reliable priority weights of alternatives. In this paper, a novel decision support model is investigated to simultaneously deal with the individual consistency and group consensus for GDM with IFLPRs. First, the concepts of multiplicative consistency and weak transitivity for IFLPRs are introduced and followed by a discussion of their desirable properties. Then, a transformation approach is developed to convert the normalized intuitionistic fuzzy priority weights into multiplicative consistent IFLPR. Based on the distance of IFLPRs, the consistency index, individual consensus degree and group consensus degree for IFLPRs are further defined. In addition, two convergent automatic iterative algorithms are proposed in the investigated decision support model. The first algorithm is utilized to convert an unacceptable multiplicative consistent IFLPR to an acceptable one. The second algorithm can assist the group decision makers to achieve a predefined consensus level. The main characteristic of the investigated decision support model is that it guarantees each IFLPR is still acceptable multiplicative consistent when the predefined consensus level is achieved. Finally, several numerical examples are provided, and comparative analyses with existing approaches are performed to demonstrate the effectiveness and practicality of the investigated model.

Research on Clustering Method of Improved Glowworm Algorithm Based on Good-Point Set

As an important data analysis method in data mining, clustering analysis has been researched extensively and in depth. Aiming at the limitation of -means clustering algorithm that it is sensitive to the distribution of initial clustering center, Glowworm Swarm Optimization (GSO) Algorithm is introduced to solve clustering problems. Firstly, this paper introduces the basic ideas of GSO algorithm, -means algorithm, and good-point set and analyzes the feasibility of combining them for clustering optimization. Next, it designs a clustering method of improved GSO algorithm based on good-point set which combines GSO algorithm and classical -means algorithm together, searches data object space, and provides initial clustering centers for -means algorithm by means of improved GSO algorithm and thus obtains better clustering results. Major improvement of GSO algorithm is to optimize the initial distribution of glowworm swarm by introducing the theory and method of good-point set. Finally, the new clustering algorithm is applied to UCI data sets of different categories and numbers for clustering test. The advantages of the improved clustering algorithm in terms of sum of squared errors (SSE), clustering accuracy, and robustness are explained through comparison and analysis.