Zhifu Tao

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.

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.

A New Interval-valued 2-Tuple Linguistic Bonferroni Mean Operator and Its Application to Multiattribute Group Decision Making

The purpose of this paper is to introduce some new Bonferroni mean operators under interval-valued 2-tuple linguistic environment. First, a class of new operational laws of interval-valued 2-tuple linguistic are proposed. Then, we put forward some new interval-valued 2-tuple linguistic Bonferroni mean (IV2TLBM) operators. Moreover, properties and special cases of new aggregation operators are investigated. The main characteristic of the IV2TLBM is that the interrelationship among the input arguments and the closed operations are taken into account. Finally, an approach to multiple attributes group decision making is presented, and a numerical example is given to illustrate the proposed method.

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.

Ranking Interval-Valued Fuzzy Numbers with Intuitionistic Fuzzy Possibility Degree and Its Application to Fuzzy Multi-Attribute Decision Making

In this paper, we present the concept of intuitionistic fuzzy possibility degree (IFPD) for ranking interval-valued fuzzy numbers. This method overcomes the shortcomings of the previous techniques by giving the possibility degree in the form of intuitionistic fuzzy value, which contains positive degree, negative degree, and hesitant degree to compare any two intervals. The prominent characteristic of this method is that it can deal with the incomparable cases effectively, i.e., the two interval numbers have the same center or one interval number is nested in another one. As an application of the proposed method, a fuzzy multi-attribute decision-making method based on the IFPD is studied. Finally, we use a numerical example of selecting a laptop to illustrate the application of the proposed method.

A MAGDM Method Based on 2-Tuple Linguistic Heronian Mean and New Operational Laws

In this paper, we investigate the multiple attributes group decision making (MAGDM) problem with 2-tuple linguistic information. According to some closed operational laws of 2-tuple linguistic, some Algebra t-norm and s-norm based Heronian aggregation operators of 2-tuple linguistic information are put forward, the desired properties and the special cases where the parameters take different values are also discussed. Furthermore, a method of MAGDM under 2-tuple linguistic environment is proposed based on the Algebra t-norm and s-norm based 2-tuple linguistic Heronian mean operator or the Algebra t-norm and s-norm based 2-tuple linguistic weighted Heronian mean operator. Finally, a numerical example is presented to demonstrate the proposed method.

Generalized ordered weighted logarithmic harmonic averaging operators and their applications to group decision making

We present a new aggregation operator called the generalized ordered weighted logarithmic harmonic averaging (GOWLHA) operator, which is based on an optimal deviation model. We study some properties and different particular cases of the GOWLHA operator. We also generalize the GOWLHA operator. The key advantage of the GOWLHA operator is that it is an aggregation operator with theoretic basis on aggregation. Moreover, we indicate some properties of the GOWLHA operator weights and propose an orness measure of the GOWLHA operator. Furthermore, we introduce the generalized least squares method to determine the GOWLHA operator weights based on its orness measure. In the end, we develop an application of the new approach in a case of group decision making in political management.

On the properties of the generalized OWHA operators and their application to group decision making

Harmonic mean is suitable to aggregate negative indicators. In order to improve the flexibility of harmonic mean for modeling many situations, the ordered weighted harmonic averaging (OWHA) operator is extended to provide a new class of operators called the generalized OWHA (GOWHA) operators, and investigate some desirable properties of them. When different parameter of the GOWHA operator is employed, various conventional aggregation operators can be deduced, such as the ordered weighted averaging (OWA) operator and the ordered weighted geometric averaging (OWGA) operator. We further demonstrate that the OWHA operator and the GOWHA operator exhibit monotonicity with respect to the weighting vector. Furthermore, we introduce the generalized hybrid harmonic averaging (GHHA) operator, which can reflect the importance degrees of both the given arguments and the ordered position of the arguments. Finally, a new approach on the basis of the GHHA operator is presented in an example of an investment project with group decision making.