International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

We deal with the expressive power of if-then rules called fuzzy attribute implications (FAIs) which can be seen as formulas A ⇒ B where both A and B are conjunctions of subformulas containing propositional variables and constants for truth degrees and whose interpretation is parameterized by linguistic hedges. The formulas admit the following model-theoretical property: a system of fuzzy sets is a fuzzy closure system satisfying an additional condition of being closed under a*-shifts (so-called L*-closure system) if and only if is a system of models of a set of FAIs. In this paper, we point out the importance of constants of truth degrees in the antecedents of formulas by showing that simpler formulas are not sufficient to describe all L*-closure systems. As a practical consequence, the simpler formulas cannot be used as an alternative description of concept lattices with linguistic hedges.

An adaptive fuzzy control scheme with only one adjusted parameter is developed for a class of nonlinear time-varying delays systems. Three kinds of uncertainties: time-varying delays, control directions, and nonlinear functions are all assumed to be completely unknown, which is different from the previous work. During the controller design procedure, appropriate Lyapunov-Krasovskii functionals are used to compensate the unknown time-varying delays terms and the Nussbaum-type function is used to detect the unknown control direction. It is proved that the proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood around zero. The two main advantages of the developed scheme are that (i) by combining the appropriate Lyapunov-Krasovskii functionals with the Nussbaum-gain technique, the control scheme is proposed for a class of nonlinear time-varying delays systems with unknown control directions, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the computational burden greatly. Finally, two examples are used to show the effectiveness of the proposed approach.

The concept of moving average is studied. We analyze several extensions by using generalized aggregation operators, obtaining the generalized moving average. The main advantage is that it provides a general framework that includes a wide range of specific cases including the geometric and the quadratic moving average. This analysis is extended by using the generalized ordered weighted averaging (GOWA) and the induced GOWA (IGOWA) operator. Thus, we get the generalized ordered weighted moving average (GOWMA) and the induced GOWMA (IGOWMA) operator. Some of their main properties are studied. We further extend this approach by using distance measures suggesting the concept of distance moving average and generalized distance moving average. We also consider the case with the OWA and the IOWA operator, obtaining the generalized ordered weighted moving averaging distance (GOWMAD) and the induced GOWMAD (IGOWMAD) operator. The paper ends with an application in multi-period decision making.

Often, in situations of uncertainty in portfolio management, it is difficult to apply the numerical methods based on the linearity principle. When this happens it is possible to use nonnumeric techniques to assess the situations with a non linear attitude. One of the concepts that can be used in these situations is the concept of grouping. In the last thirty years, several studies have tried to give good solutions to the problems of homogeneous groupings. For example, we could mention the Pichat algorithm, the affinities algorithms and several studies developed by the authors of this work. In this paper, we use some topological axioms in order to develop an algorithm that is able to reduce the number of elements of the power sets of the related sets by connecting them to the sets that form the topologies. We will apply this algorithm in the grouping of titles listed in the Stock Exchange or in its dual perspective.

We develop some new cases of the induced continuous ordered weighted averaging (ICOWA) operator and study their desirable properties, which are very suitable to deal with group decision making (GDM) with interval fuzzy preference relations. First, we present the consensus indicator ICOWA (CI-ICOWA) operator which uses the consensus indicator of the interval fuzzy preference as the order inducing variable in the ICOWA operator. Then the concept of compatibility degree (CD) for two interval fuzzy preference relations is defined based on the continuous ordered weighted averaging (COWA) operator and the compatibility degree ICOWA (CD-ICOWA) operator is proposed which uses the CD as the order inducing variable in the ICOWA operator. Next, we investigate some desirable properties of the CD-ICOWA operator. Additionally, we construct an optimization model to obtain the weights of experts by minimizing the compatibility degree in the GDM. Finally, an illustrative numerical example is used to verify the developed approaches.

In this paper, we investigate the uncertain linguistic multiple attribute group decision making (MAGDM) problems in which the attributes and experts are in different priority level. Motivated by the idea of prioritized aggregation operators (R. R. Yager, Prioritized aggregation operators, Int. J. Approximate Reasoning48 (2008) 263–274.), we develop some prioritized aggregation operators for aggregating uncertain linguistic information, and then apply them to develops some models for uncertain linguistic multiple attribute group decision making (MAGDM) problems in which the attributes and experts are in different priority level. Finally, a practical example about talent introduction is given to verify the developed approach and to demonstrate its practicality and effectiveness.

A new approach to solve Fuzzy Complex System of Linear Equations (FCSLE) based on fuzzy complex centre procedure is presented here. Few theorems related to the investigation are stated and proved. Finally the presented procedure is used to analyze an example problem of linear time invariant electric circuit with complex crisp coefficient and fuzzy complex sources. The results obtained are also compared with the known solutions and are found to be in good agreement.