On weighted unbalanced linguistic aggregation operators in group decision making

A Novel Algorithm for Group Decision Making Based on Continuous Optimal Aggregation Operator and Shapley Value

Interval linguistic preference relation is an effective tool for expressing experts’ preference in group decision making under uncertain linguistic environment. A new aggregation operator called continuous chi-square deviation based 2-tuple linguistic ordered weighted quasi-averaging (C-CDLOWQ) operator is proposed to transform the interval linguistic preference relations into precise linguistic preference relations. Some desirable properties and special cases of the C-CDLOWQ operator are analyzed in detail. To take the interactive phenomenon among experts into account, the Shapley weighting vector is presented to integrate the expected linguistic preference relations. The λ-fuzzy measure is employed to simplify the fuzzy measure on expert set. A CS-GDM algorithm is developed to group decision making with interval linguistic preference relations. The application in commercial investment problem is provided to illustrate the effectiveness of CS-GDM algorithm.

An Approach to Linguistic Multiple Attribute Decision-Making Based on Unbalanced Linguistic Generalized Heronian Mean Aggregation Operator

This paper proposes an approach to linguistic multiple attribute decision-making problems with interactive unbalanced linguistic assessment information by unbalanced linguistic generalized Heronian mean aggregation operators. First, some generalized Heronian mean aggregation operators with unbalanced linguistic information are proposed, involving the unbalanced linguistic generalized arithmetic Heronian mean operator and the unbalanced linguistic generalized geometric Heronian mean operator. For the situation that the input arguments have different degrees of importance, the unbalanced linguistic generalized weighted arithmetic Heronian mean operator and the unbalanced linguistic generalized weighted geometric Heronian mean operator are developed. Then we investigate their properties and some particular cases. Finally, the effectiveness and universality of the developed approach are illustrated by a low-carbon tourist instance and comparison analysis. A sensitivity analysis is performed as well to test the robustness of proposed methods.

The Novel Computational Model of Unbalanced Linguistic Variables Based on Archimedean Copula

We develop a novel computation model of unbalanced linguistic variables on the basis of Archimedean copulas and corresponding co-copulas, which provides a new tool to aggregate unbalanced linguistic information. The properties of the proposed computational model are also studied. We present the concepts of weighted unbalanced Archimedean copula arithmetic aggregation operators and weighted unbalanced Archimedean copula geometric aggregation operators. The properties of these aggregation operators are further investigated. Finally, a group decision making of sensory evaluation is introduced to illustrate the feasibility and validity of our proposed computational model.

Similarity-Based Approach for Group Decision Making with Multi-Granularity Linguistic Information

The aim of this article is to investigate the approach for multi-attribute group decision-making, in which the attribute values take the form of multi-granularity multiplicative linguistic information. Firstly, to process multiple sources of decision information assessed in different multiplicative linguistic label sets, a method for transforming multi-granularity multiplicative linguistic information into multiplicative trapezoidal fuzzy numbers is proposed. Then, a formula for ranking multiplicative trapezoidal fuzzy numbers is given based on geometric mean. Furthermore, the concept of similarity degree between two multiplicative trapezoidal fuzzy numbers is defined. The attribute weights are obtained by solving some optimization models. An effective approach for group decision making with multi-granularity multiplicative linguistic information is developed based on the ordered weighted geometric mean operator and proposed formulae. Finally, a practical example is provided to illustrate the practicality and validity of the proposed method.

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 LINGUISTIC AGGREGATION OPERATOR INCLUDING WEIGHTS FOR LINGUISTIC VALUES AND EXPERTS IN GROUP DECISION MAKING

Different linguistic aggregation methods have been proposed and applied in the linguistic decision making problems. Generally, weights for experts or criteria are considered in linguistic aggregation processes. In this paper, we provide a method to discovery new forms to compute weights and new interpretations in the linguistic ordered weighted averaging operator. In linguistic decision analysis, it can be noticed that some of initial linguistic values used by experts have priority over others linguistic values in evaluation processes. We formalize the priority over initial linguistic values as weights for linguistic values, by considering weights for linguistic values as well as weights for experts, we provide an alternative method to discovery weights information of the linguistic ordered weighted averaging operator, its properties show that such linguistic aggregation operator is extensions of the 2-tuple arithmetic mean, the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator. By an illustrative example, we compare the linguistic aggregation operator with the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator in a decision making problem. From the practical point of view, we provide an optimization model to obtain such weights information in linguistic aggregation processes, examples show the linguistic aggregation operator as an alternative linguistic ordered weighted averaging operator in practice.