Jinpei Liu

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.

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.

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.

Generalized Linguistic Ordered Weighted Hybrid Logarithm Averaging Operators and Applications to Group Decision Making

In this paper, we develop the generalized linguistic weighted logarithm averaging (GLWLA) operator and the generalized linguistic ordered weighted logarithm averaging (GLOWLA) operator in the group decision making under the linguistic surrounding. Then some properties of the families of the GLOWLA operator by different weighting vector are investigated. Furthermore, we present the generalized linguistic ordered weighted hybrid logarithm averaging (GLOWHLA) operator, which extends the GLOWLA operator. We also construct a nonlinear goal programming model to determine GLOWHLA weights from observational linguistic variable values under partial weight information. Finally, a numerical example is given to illustrate the new approach to evaluating university faculty for tenure and promotion, which indicates the feasibility and effectiveness of the new approach.

Generalized logarithmic proportional averaging operators and their applications to group decision making

In this paper, we present a new operator called the generalized ordered weighted logarithmic proportional averaging (GOWLPA) operator based on an optimal model, which is an extension of the generalized ordered weighted logarithm averaging (GOWLA) operator. The key advantage of the GOWLPA operator is not only that it is an aggregation operator with theoretic basis on aggregation, but also that the weighting vector of the GOWLPA operator depends on the input arguments. We analyze some properties and families of the GOWLPA operator and further develop generalizations of this operator including the generalized hybrid logarithmic proportional averaging (GHLPA) operator and the quasi ordered weighted logarithmic proportional averaging (QOWLPA) operator. To determine the GOWLPA operator weights, we propose the generalized logarithm chi-square method (GLCSM) which does not follow a regular distribution. Finally, we give a numerical example of an investment selection to illustrate the application of the GOWLPA operator to multiple attribute group decision making.

Penalty-based continuous aggregation operators and their application to group decision making

Penalty-based aggregation operators, which are obtained by minimizing the deviation between the input values and the aggregated value, have a direct intuitive interpretation in terms of practical problems. In order to aggregate continuous interval arguments based on penalty, we present penalty-based continuous (PC) aggregation operators, and investigate some desirable properties of them. When different forms of the associated dissimilarity function are employed, various continuous aggregation operators can be deduced, such as the C-OWA operator and the QC-OWA operator. Moreover, several extensions of the PC aggregation operators are developed for the aggregation of multiple interval arguments. Finally, we apply these aggregation operators to developing an approach to multi-attribute group decision making. A numerical example is illustrated to show the feasibility and effectiveness of the developed approach.

2-Tuple linguistic soft set and its application to group decision making

The aim of this paper is to put forward the 2-tuple linguistic soft set by combining the concepts of 2-tuple linguistic term set and soft set. The traditional set operations and corresponding properties are investigated. We develop the algebraic operations and discuss their corresponding properties based on which we introduce the applications of this theory in solving decision making problems. Four algorithms using the notion of 2-tuple linguistic soft information aggregation function are developed to handle group decision making problem. Finally, a selection problem of investment strategy is shown to illustrate the feasibility and validity of our approach.