Informatica

Intuitionistic uncertain linguistic variables (IULVs) are useful to express the qualitative and quantitative recognitions of decision makers. However, after reviewing the previous operational laws on IULVs, we find there are some limitations. To address these issues, we define several new operations on IULVs and give a new ranking method. To improve the utilization of IULVs, this paper defines two Choquet operators: the intuitionistic uncertain linguistic symmetrical Choquet averaging (IULSCA) operator and the intuitionistic uncertain linguistic symmetrical Choquet geometric mean (IULSCGM) operator, which can address the internal correlations among elements. To globally reflect the interactive characteristics of the importance of elements, two generalized Shapley intuitionistic uncertain linguistic symmetrical Choquet operators are presented. Subsequently, a new distance measure is defined, which is then used to build models to ascertain fuzzy measures on decision maker and criteria sets to address the case where the weighting information is partly known. After that, a new procedure to intuitionistic uncertain linguistic group decision making is developed. Finally, a specific example is offered to illustrate the practicality of the new procedure, and the comparison analysis is also made.

The 2-tuple linguistic computational model is an important tool to deal with linguistic information. To extend the application of hesitant fuzzy linguistic term sets and avoid information loss, this paper introduces hesitant fuzzy 2-tuple linguistic term sets that are expressed by using several symbolic numbers in $[0\mathrm{,}1]$. Considering the order relationship between hesitant fuzzy 2-tuple linguistic term sets, measures of expected value and variance are defined. Meanwhile, several induced generalized hesitant fuzzy 2-tuple linguistic aggregation operators are defined, by which the comprehensive attribute values of alternatives can be obtained. Then, models for the optimal weight vector on a decision maker set, on an attribute set and on their ordered sets are constructed, respectively. Furthermore, an approach to multi-granularity group decision making with hesitant fuzzy linguistic information is developed. Finally, an example is selected to illustrate the feasibility and practicality of the proposed procedure.

This paper investigates group decision making problems in which the criterion values take the form of interval-valued intuitionistic uncertain linguistic numbers (IIULNs). First, some additive operational laws of IIULNs are defined. Subsequently, some new arithmetic aggregation operators, such as the interval-valued intuitionistic uncertain linguistic weighted averaging (IIULWA) operator, interval-valued intuitionistic uncertain linguistic ordered weighted averaging (IIULOWA) operator and interval-valued intuitionistic uncertain linguistic hybrid aggregation (IIULHA) operator, are proposed which are based on the operational laws. Furthermore, an approach to group decision making with interval-valued intuitionistic uncertain linguistic information is developed, which is based on the IIULWA and IIULHA operators. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed method.

In this paper, we propose a new aggregation operator under uncertain pure linguistic environment called the induced uncertain pure linguistic hybrid averaging aggregation (IUPLHAA) operator. Some of the main advantages and properties of the new operator are studied. Moreover, in the situations where the given arguments about all the attribute weights, the attribute values and the expert weights are expressed in the form of linguistic labels variables, we develop an approach based on the IUPLHAA operator for multiple attribute group decision making with uncertain pure linguistic environment. Finally, an illustrative example is given to verify the developed approach and to demonstrate its feasibility and practicality.

We present a new aggregation operator called the generalized ordered weighted proportional averaging (GOWPA) operator based on an optimal model with penalty function, which extends the ordered weighted geometric averaging (OWGA) operator. We investigate some properties and different families of the GOWPA operator. We also generalize the GOWPA operator. The key advantage of the GOWPA operator is that it is an aggregation operator with theoretic basis on aggregation, which focuses on its structure and importance of arguments. Moreover, we propose an orness measure of the GOWPA operator and indicate some properties of this orness measure. Furthermore, we introduce the generalized least squares method (GLSM) to determine the GOWPA operator weights based on its orness measure. Finally, we present a numerical example to illustrate the new approach in an investment selection decision making problem.