Informatica

To solve the problem of choosing the appropriate cloud computing vendors in small and medium-sized enterprises (SMEs), this paper boils it down to a group decision making (GDM) problem. To facilitate the judgment, this paper uses preference relation as the decision making technology. Considering the situation where uncertain positive and negative judgments exist simultaneously, interval-valued intuitionistic fuzzy preference relations (IVIFPRs) are employed to express the decision makers’ judgments. In view of the multiplicative consistency and consensus analysis, a new GDM algorithm with IVIFPRs is offered. To accomplish this goal, a new multiplicative consistency is first defined, which can avoid the limitations of the previous ones. Then, a programming model is built to check the consistency of IVIFPRs. To deal with incomplete IVIFPRs, two programming models are constructed to determine the missing values with the goal of maximizing the level of multiplicative consistency and minimizing the total uncertainty. To achieve the minimum adjustment of original preference information, a programming model is established to repair inconsistent IVIFPRs. In addition, programming models for getting the decision makers (DMs)’ weights and improving the consensus degree are offered. Finally, a practical decision making example is given to illustrate the effectiveness of the proposed method and to compare it with previous methods.

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.

In this paper, at first, we develop some new geometric distance measures for interval-valued intuitionistic fuzzy information, including the interval-valued intuitionistic fuzzy weighted geometric distance (IVIFWGD) measure, the interval-valued intuitionistic fuzzy ordered weighted geometric distance (IVIFOWGD) measure and the interval-valued intuitionistic fuzzy hybrid weighted geometric distance (IVIFHWGD) measure. Also, several desirable properties of these new distance measures are studied and a numerical example is given to show application of the distance measure to pattern recognition problems. And then, based on the developed distance measures a consensus reaching process with interval-valued intuitionistic fuzzy preference information for group decision making is proposed. Finally, an illustrative example with interval-valued intuitionistic fuzzy information is given.

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.

In this paper, we focus on group decision making problems with uncertain preference ordinals, in which the weight information of decision makers is completely unknown or partly unknown. First of all, the consistency and deviation measures between two uncertain preference ordinals are defined. Based on the two measures, a multi-objective optimization model which aims to maximize the deviation of each decision maker’s judgements and the consistency among different decision makers’ judgements is established to obtain the weights of decision makers. The compromise solution method, i.e. the VIKOR method is then extended to derive the compromise solution of alternatives for group decision making problems with uncertain preference ordinals. Finally, three examples are utilized to illustrate the feasibility and effectiveness of the proposed approach.

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.