Prototype-based methods are commonly used in cluster analysis and the results may be highly dependent on the prototype used. In this paper, we propose a two-level fuzzy clustering method that involves adaptively expanding and merging convex polytopes, where the convex polytopes are considered as a “flexible” prototype. Therefore, the dependency on the use of a specified prototype can be elimina...

We introduce the notion of strongly t-convex set-valued maps and present some properties of it. In particular, a Bernstein–Doetsch and Sierpiński-type theorems for strongly midconvex set-valued maps, as well as a Kuhn-type result are obtained. A representation of strongly t-convex set-valued maps in inner product spaces and a characterization of inner product spaces involving this representatio...

In this exposition the robust counterpart approach by Ben-Tal, El Ghaoui and Nemirovski is investigated with respect to its costs and benefits, with the focus on the costs of robustification. Although robust optimization has gained more and more interest among both academics and practitioners and although this certainly represents a well-established theory, it is to some extent unclear, if and ...

let $c_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{d}$. each function $f in c_{0}(alpha)$ maps the unit disk $mathbb{d}$ onto the complement of an unbounded convex set. in this paper, we study the mapping properties of this class under integral operators.

A successful controller design paradigm must take into account both model uncertainty and design specifications. Model uncertainty can he addressed using the ‘ H, or I 1 robust control theory. However, these frameworks cannot accommodate the realistic case where the design specifications include both time and frequency domain constraints. In this paper we propose an approach that takes explicit...

Article history: Received 17 April 2015 Received in revised form 18 June 2015 Accepted 6 July 2015 Available online 22 July 2015

In this paper, the guaranteed cost filtering design method for linear time delay systems with convex bounded uncertainties in discrete-time case is presented. The uncertain parameters are assumed to be unknown but belonging to known convex compact set of polytotype less conservative than norm bounded parameter uncertainty. The main purpose is to design a stable filter which minimizes the guaran...

A new method for robust fixed-order H∞ controller design by convex optimization for multivariable systems is investigated. Linear Time-Invariant Multi-Input Multi-Output (LTI-MIMO) systems represented by a set of complex values in the frequency domain are considered. It is shown that the Generalized Nyquist Stability criterion can be approximated by a set of convex constraints with respect to t...