International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper, we concentrate on a class of linear multi-objective decision making models with level-2 TFNwTFC coefficients. Firstly, we define a level-2 triangular fuzzy number with a triangular fuzzy centre(TFNwTFC) based on level-2 fuzzy set theory, and propose a theorem on how to transform it into an (α, β)-level trapezoidal fuzzy number(TrFN). Secondly, in order to deal with the linear multi-objective decision making model with TrFN coefficients, we present an expected multi-objective model with chance constraints, and discuss its equivalent model. Then the ε-constraint method is employed to determine a solution to the crisp equivalent model. Finally, a supplier selection problem is used to illustrate the proposed models and approaches.

Information aggregation has been investigated and applied to many fields. This paper focuses on geometric aggregation operators under dual hesitant fuzzy environment. We develop some new geometric aggregation operators, such as the generalized dual hesitant fuzzy weighted geometric (GDHFWG) operator, the generalized dual hesitant fuzzy ordered weighted geometric (GDHFOWG) operator and the generalized dual hesitant fuzzy hybrid geometric (GDHFHG) operator. Some numerical examples are given to illustrate the developed operators. Finally, we give an application of our proposed operators to multi-criteria decision making with dual hesitant fuzzy information, a real decision making problem about human resource generalist selection is forwarded to show the effectiveness of our proposed method.

A generalization of the notion of intuitionistic multiplicative set (IMS) is given in this paper, which is called interval-valued intuitionistic multiplicative set (IVIMS). The IVIMS uses an unsymmetrical scale (Saaty's 1-9 scale) instead of the ordinary symmetrical scale in an intuitionistic fuzzy set or an interval-valued intuitionistic fuzzy set. IVIMSs can reflect our intuition more objectively in some special situations. The basic component of an IVIMS is interval-valued intuitionistic multiplicative number (IVIMN). To rank IVIMNs, the comparison laws are developed. Based on the pseudo-multiplication, we explore some interval-valued intuitionistic multiplicative operations and obtain several specific results when some specific forms are assigned. In addition, some distance measures and weighted distance measures between IVIMSs are developed to describe the difference of any two IVIMSs. By analyzing the range of the uncertain degree, a generalized interval-valued intuitionistic multiplicative set is presented, which is a generalization of the notions of IMS and IVIMS. Finally, a numerical example is given to illustrate our results.

The aim of this paper is to develop a new compatibility, which is very suitable to deal with group decision making (GDM) problems involving interval multiplicative preference relations, based on the continuous ordered weighted geometric averaging (COWGA) operator. First, we define some concepts of the compatibility degree and the compatibility index for the two interval multiplicative preference relations based on the COWGA operator. Then, we study some desirable properties of the compatibility index and investigate the relationship between each expert's interval multiplicative preference relation and the synthetic interval multiplicative preference relation. The prominent characteristic of the compatibility index based on the COWGA operator is that it can deal with the compatibility of all the arguments in two interval arguments considering the risk attitude of decision maker rather than the compatibility of the two simple points in intervals. Second, in order to determine the experts' weights in the GDM with the interval multiplicative preference relations, we propose an optimal model based on the criterion of minimizing the compatibility index. Finally, we give a numerical example to develop the new approach to GDM with interval multiplicative preference relations.

In this paper we present a novel associative classification algorithm for visual concept detection using interest points (color descriptors). Our algorithm relies on fuzzy (soft) partitions to generate a per-descriptor record model which is used for training associative classifiers. In this paper, we use the first 10000 images of the MIR Flickr dataset (with 38 visual concepts — 14 regular annotation topics and 24 pre-annotations) for evaluating our algorithm. Because of its fuzzy nature, our approach also handles polysemy and synonymy (common problems in most crisp (non-fuzzy) image classifiers) very well. As associative classification leverages frequent patterns mined from a given dataset, its performance as adjudged from average area under curve (AUC) values over three-fold cross validation is very good, especially for regular annotation topics and for “scenic” concepts. Our approach has the added advantage that the rules used for classification have clear semantics, and can be comprehended easily, unlike other classifiers, such as SVM, which act as black-boxes. From an empirical perspective (on the MIR Flickr dataset), the performance of our algorithm is much better, than that of either bag-of-words (Linear SVM and SVM RBF Kernel) or Linear SVM based on fuzzy (soft) partitions—both benchmark approaches are based on interest points (color descriptors).

This paper presents the stability analysis of discrete-time fuzzy-model-based adaptive control systems with time-delay, parameter uncertainties and external disturbance. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discretetime nonlinear system. A fuzzy observer is used to estimate the state of the fuzzy system, by using the estimations of states and nonlinear functions, and sufficient conditions for designing observer-based fuzzy controllers are proposed. The control and observer matrices involved can be determined by solving a set of linear matrix inequality (LMI). Finally, the numerical example carried out also demonstrate the feasibility of the design method.

Fuzziness is inherent in decision data and decision making process. In this paper, interval-valued intuitionistic fuzzy set is used to capture fuzziness in multi-criteria decision making problems. The purpose of this paper is to develop a new method for solving multi-criteria decision making problem in interval-valued intuitionistic fuzzy environments. First, we introduce and discuss the concept of interval-valued intuitionistic fuzzy point operators. Using the interval-valued intuitionistic fuzzy point operators, we can reduce the degree of uncertainty of the elements in a universe corresponding to an interval-valued intuitionistic fuzzy set. Then, we define an evaluation function for the decision-making problem to measure the degrees to which alternatives satisfy and do not satisfy the decision-maker's requirement. Furthermore, a series of new score functions are defined for multi-criteria decision making problem based on the interval-valued intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.