International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In the past decades, the theory of possibility has been developed as a theory of uncertainty that is compatible with the theory of probability. Whereas probability theory tries to quantify uncertainty that is caused by variability (or equivalently randomness), possibility theory tries to quantify uncertainty that is caused by incomplete information. A specific case of incomplete information is that of ill-known sets, which is of particular interest in the study of temporal databases. However, the construction of possibility distributions in the case of ill-known sets is known to be overly complex. This paper contributes to the study of ill-known sets by investigating the inference of uncertainty when constraints are specified over ill-known values. More specific, in this paper it is investigated how the knowledge about constraint satisfaction can be inferred if the constraints themselves are defined by means of ill-known values. It is shown how such reasoning can contribute to the study of (fuzzy) temporal databases.

In classical measure theory, the Radon-Nikodym theorem states in a concise condition, namely domination, how a measure can be factorized by another (bounded) measure through a density function. Several approaches have been undertaken to see under which conditions an exact factorization can be obtained with set functions that are not σ-additive (for instance finitely additive set functions or submeasures). We provide a Radon-Nikodym type theorem with respect to a measure for almost subadditive set functions with bounded disjoint variation. The necessary and sufficient condition to guarantee a superior Radon-Nikodym derivative remains the standard domination condition for measures. We show how these set functions admit an equivalent factorization under the standard domination condition for set functions.

In this paper, we aim to study intuitionistic fuzzy ordered information systems. Firstly, the concept of intuitionistic fuzzy ordered information systems is proposed by introducing an intuitionistic fuzzy relation to ordered information systems. Meanwhile, two approximation operators are defined and a rough set approach is established in intuitionistic fuzzy ordered information systems. Secondly, a ranking approach for all objects is constructed in this system. Thirdly, approximation reduction is addressed in intuitionistic fuzzy ordered decision information system. These results will be helpful for decision-making analysis in intuitionistic fuzzy ordered information systems.

Rough set theory, initiated by Pawlak, is a mathematical tool in dealing with inexact and incomplete information. Numerical characterizations of rough sets such as accuracy measure, roughness measure, etc, which aim to quantify the imprecision of a rough set caused by its boundary region, have been extensively studied in the existing literatures. However, very few of them are explored from the viewpoint of rough logic, which, however, helps to establish a kind of approximate reasoning mechanism. For this purpose, we introduce a kind of numerical approach to the study of rough logic in this paper. More precisely, we propose the notions of accuracy degree and roughness degree for each formula in rough logic with the intension of measuring the extent to which any formula is accurate and rough, respectively. Then, to measure the degree to which any two formulae are roughly included in each other and roughly similar, respectively, the concepts of rough inclusion degree and rough similarity degree are also proposed and their properties are investigated in detail. Lastly, by employing the proposed notions, we develop two types of approximate reasoning patterns in the framework of rough logic.

This paper deals with the passivity analysis problem for Takagu-Sugeno (T-S) fuzzy neural networks with mixed interval time-varying delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Delay-dependent sufficient conditions for the passivity problem are obtained by using Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique. The important feature of the results lies in that it does not make use of upper bounds to introduce some degree of conservativeness. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design procedures.

This paper is concerned with the problem of observer-based fuzzy control design for discrete-time T-S fuzzy bilinear systems. Based on the piecewise quadratic Lyapunov function (PQLF), the piecewise fuzzy observer-based controllers are designed for T-S fuzzy bilinear systems. It is shown that the stability for discrete T-S fuzzy bilinear system can be established if there exists a PQLF can be constructed and the fuzzy observer-based controller can be obtained by solving a set of nonlinear minimization problem involving linear matrix inequalities(LMIs) constraints. An iterative algorithm making use of sequential linear programming matrix method (SLPMM) to derive a single-step LMI condition for fuzzy observer-based control design. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.

Based on the current developments of fuzzy weighted average and generalized fuzzy weighted average, especially Karnik-Mendel (KM) algorithms and the works of Wang and Luo (Generalised fuzzy weighted mean and its applications, International Journal of General Systems, 2009, 38, 533–546), the paper analyses some properties of the generalized fuzzy weighted mean (GFWM) and proposes analytical solution method for the GFWM problem. The solution processes and the final solution forms are more simple and accurate than the current GFWM solution, which use samples of the alpha-cuts and get the final solutions approximately. Numerical examples illustrate the analytical solution computing processes for fuzzy weighted average (FWA), fuzzy weighted harmonic mean (FWHM), fuzzy weighted geometric mean (FWGM) and GFWM with exponential and power functions, respectively.