Ligang Zhou

An approach to group decision making with interval fuzzy preference relations based on induced generalized continuous ordered weighted averaging operator

The aim of this paper is to develop a new class of operator called the induced generalized continuous ordered weighted averaging (IGCOWA) operator, which extends the GOWA operator, the IGOWA operator and the ICOWG operator. We study the desirable properties of the IGCOWA operator and describe families of IGCOWA operator according to the special weighting vector and generalized mean parameter. Particularly, we present the consistency induced generalized continuous ordered weighted averaging (C-IGCOWA) operator, in which the consistency indicator is the induced ordering variable to reflect the importance of interval fuzzy preference relation. Finally, the C-IGCOWA operator is applied to group decision making with interval fuzzy preference relations in a numerical example.

Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making

This paper proposes some new geometric operations on intuitionistic fuzzy sets (IFSs) based on probability non-membership (PN) function operator, probability membership (PM) function operator and probability hetergeneous (PH) operator, which are constructed from the probability point of view. The geometric interpretations of these operations are given. Moreover, we develop some intuitionistic fuzzy geometric interaction averaging (IFGIA) operators. The properties of these aggregation operators are investigated. The key advantage of the IFGIA operators is that the interactions between non-membership function and membership function of different IFSs are considered. Finally, an approach to multiple attributes decision making is given based on the proposed aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of the proposed approach.

Uncertain generalized aggregation operators

The aim of this paper is to extend the generalized ordered weighted averaging operator and provide a new class of operators called the uncertain generalized ordered weighted averaging (UGOWA) operator. It provides a very general formulation that includes as special cases a wide range of aggregation operators and aggregates the input arguments taking the form of intervals rather than exact numbers. We further generalize the UGOWA operator to obtain the uncertain generalized hybrid averaging operator, the quasi uncertain ordered weighted averaging operator and the uncertain generalized Choquet integral aggregation operator. In the meanwhile, a new approach to determining the UGOWA weights is proposed based on the relative deviation measure. Finally, a numerical example is presented to illustrate the proposed approach to group decision making with UGOWA operator.

Generalized intuitionistic fuzzy geometric interaction operators and their application to decision making

Considering that there may exist some interactions between membership function and non-membership function of different intuitionistic fuzzy sets, we present some new operational laws from the probability point of view and give a geometric interpretation of the new operations. Based on which, a new class of generalized intuitionistic fuzzy aggregation operators are developed, including the generalized intuitionistic fuzzy weighted geometric interaction averaging (GIFWGIA) operator, the generalized intuitionistic fuzzy ordered weighted geometric interaction averaging (GIFOWGIA) operator and the generalized intuitionistic fuzzy hybrid geometric interaction averaging (GIFHGIA) operator. The properties of these new generalized aggregation operators are investigated. Moreover, approaches to multiple attributes decision making are given based on the generalized aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of new approach. Finally, we give a systematic comparison between the work of this paper and that of other papers.

Multi-attribute decision making based on neutral averaging operators for intuitionistic fuzzy information

The neutral operation and scalar neutral operation are proposed.The geometric meaning of the PS function is interpreted.The proportional distribution rules of membership function and non-membership function of IFSs are explained.We develop the IFWNA operator and the IFOWNA operator and investigate the properties.The new operators are applied to decision making and given the comparisons. In this paper, we construct the probability sum (PS) function and the proportional distribution rules of membership function and non-membership function of intuitionistic fuzzy sets (IFSs), and give their corresponding geometric interpretations. Based on which, we present the neutrality operation and the scalar neutrality operation on intuitionistic fuzzy numbers (IFNs). We propose the intuitionistic fuzzy weighted neutral averaging (IFWNA) operator and the intuitionistic fuzzy ordered weighted neutral averaging (IFOWNA) operator. The properties of the IFWNA operator and the IFOWNA operator are investigated. The principal advantages of the proposed operators are that both the attitude of the decision makers and the interactions between different intuitionistic fuzzy numbers (IFNs) are considered. Furthermore, approaches to multi-criteria decision making based on the proposed IFWNA and IFOWNA operator are given. Finally, an example is illustrated to show the feasibility and validity of the new approaches to the application of decision making.

The optimal group continuous logarithm compatibility measure for interval multiplicative preference relations based on the COWGA operator

The calculation of compatibility measures is an important technique employed in group decision-making with interval multiplicative preference relations. In this paper, a new compatibility measure called the continuous logarithm compatibility, which considers risk attitudes in decision-making based on the continuous ordered weighted geometric averaging (COWGA) operator, is introduced. We also develop a group continuous compatibility model (GCC Model) by minimizing the group continuous logarithm compatibility measure between the synthetic interval multiplicative preference relation and the continuous characteristic preference relation. Furthermore, theoretical foundations are established for the proposed model, such as the sufficient and necessary conditions for the existence of an optimal solution, the conditions for the existence of a superior optimal solution and the conditions for the existence of redundant preference relations. In addition, we investigate certain conditions for which the optimal objective function of the GCC Model guarantees its efficiency as the number of decision-makers increases. Finally, practical illustrative examples are examined to demonstrate the model and compare it with previous methods.

Continuous intuitionistic fuzzy ordered weighted distance measure and its application to group decision making

AbstractThe aim of this paper is to develop the continuous intuitionistic fuzzy ordered weighted distance (C-IFOWD) measure by using the continuous intuitionistic fuzzy ordered weighted averaging (C-IFOWA) operator in the interval distance. We investigate some desirable properties and different families of the C-IFOWD measure. We also generalize the C-IFOWD measure. The prominent characteristics of the C-IFOWD measure are that it is not only a generalization of some widely used distance measure, but also it can deal with interval deviations in aggregation on interval-valued intuitionistic fuzzy values (IVIFVs) by using a controlled parameter, which can decrease the uncertainty of argument and improve the accuracy of decision. The desirable characteristics make the C-IFOWD measure suitable to wide range situations, such as decision making, engineering and investment, etc. In the end, we introduce a new approach to group decision making with IVIFVs in human resource management.

On new operational laws of 2-tuple linguistic information using Archimedean t-norm and s-norm

The aim of this paper is to develop some novel operational laws of linguistic 2-tuples based on the Archimedean t-norm and s-norm. The most advantage of such operational laws is that the operations are closed. The properties of such operational laws are studied, such as the commutative, associative, and distribution law of scalar-multiplication. We propose the successive weighted arithmetic and geometric operations of 2-tuple linguistic terms based on these new operational laws, which is also appropriate for cases of uncertain linguistic variables. Finally, a ranking problem of white wines is developed to illustrate the application of the proposed method.

Generalized ordered modular averaging operator and its application to group decision making

In this paper, we propose a new class of operators called the ordered quasi-modular averaging (OQMA) operators based on the ordered modular averaging (OMA) operators. It is shown that the OQMA operators are monotonic, bounded, idempotent, commutative and quasi-comonotone modular. Moreover, we introduce the generalized ordered modular averaging (GOMA) operator, which is a special case of the OQMA operator. Some special cases of the GOMA operator are discussed. An orness measure to reflect the or-like degree of the GOMA operator is proposed. We further extend the GOMA operator to the generalized ordered hybrid modular (GOHM) operator, which focuses not only on the degree of importance with respect to input arguments but also their serial positions. Finally, a new method based on the GOHM operator for multi-attribute group decision making is presented and a numerical example shows that the developed approach is feasible.

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.