Publications

Clustering is commonly exploited in engineering, management, and science fields with the objective of revealing structure in pattern data sets. In this article, through clustering we construct meaningful collections of information granules (clusters). Although the underlying goal is obvious, its realization is fully challenging. Given their nature, clustering is a well-known NP-complete problem. The existing algorithms commonly produce some suboptimal solutions. As a vehicle of pattern clustering, we discuss in this article how to use a DNA-based algorithm. We also discuss the details of encoding being used here with statistical methods combined with the DNA-based algorithm for pattern clustering.

Consistency and consensus study for group decision making (GDM) with fuzzy preference relations (FPRs) are necessary, which have a decisive impact on the quality of decision results. Consistency can prevent self-contradictory judgments, and consensus limits the deviation among individual judgments within the preset threshold. Because acceptably multiplicative consistency still cannot avoid self-contradictory judgments, this article considers the ordinal consistency and acceptably multiplicative consistency simultaneously. In view of these aspects, we introduce a new optimal model-based method for GDM with FPRs. As minimum total adjustment and minimum individual adjustment may be inconsistent, we introduce the Solidarity consistency and consensus adjustment mechanism to allocate the minimum total adjustment, which fully considers the cooperation and solidarity among decision makers. When the So-CCAM does not exhibit stability, we present the nucleolus CCAM, which is the best element in the core according to lexicographical order. After that, an algorithm is offered. To demonstrate the application and efficiency of the new method, an illustrative example is offered, and a comparison is carried out. It offers the first optimization models-based method for GDM with FPRs in view of ordinal consistency, acceptably multiplicative consistency, and consensus analysis. Further, it provides two rational consistency and CCAMs by cooperative game theory.

In this study, we introduce and discuss a concept of an incremental granular model. In contrast to typical rule-based systems encountered in fuzzy modeling, the underlying principle exploited here is to consider a two-phase development of fuzzy models. First, we build a standard regression model which could be treated as a preliminary construct capturing the linear part of the data and in this way forming a backbone of the entire construct. Next, all modeling discrepancies are compensated by a collection of rules that become attached to the regions of the input space where the error is localized. The incremental model is constructed by building a collection of information granules through some specialized fuzzy clustering, called context-based (conditional) fuzzy C-means that is guided by the distribution of error of the linear part of the model. The architecture of the model is discussed along with the major algorithmic phases of its development. In particular, the issue of granularity of fuzzy sets of context and induced clusters is discussed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vis-a-vis</i> the performance of the model. Numeric studies concern some low-dimensional synthetic data and several datasets coming from the machine learning repository.

Data mining and fuzzy systems share an important common feature that is information granulation. Information granules, and fuzzy sets exploited in the setting of this study, are used to reveal stable, transparent and meaningful patterns in databases. While there exists panoply of various forms of patterns, we focus on associations and rules as the two commonly encountered constructs that exist both in data mining and fuzzy systems. Associations are modeled in the language of fuzzy relations and are direction-free concepts meaning that they are not concerned as to the question "what implies what". Rules, on the other hand, are direction — based constructs with clearly delineated cause and effect (condition and conclusion). Moreover, it is shown that associations and rules are tied together: associations may entail rules but no other way around. We discuss the role of information granularity in determining consistency of the rules and analyze an impact that linguistic quantification of fuzzy sets has on the consistency of the individual rules. An idea of rule growing is also discussed.

A novel analytical approach based on interval arithmetic is proposed to investigate the effect of material thickness and properties errors on the average power pattern in the conformal load‐bearing antenna structures (CLAS) for both local and global errors conditions. The uncertainties of the thickness or properties error of CLAS composite material are modelled as interval‐valued parameters. The dominant expressions between the thickness or properties error interval and the power pattern interval are derived by interval arithmetic along with some main electromagnetic characteristics (side‐lobe level, peak power, and half‐power beamwidth) expressed as intervals can be produced through interval analysis (IA). Some numerical examples are reported to validate the proposed approach and to show its reliability and efficiency when considering different thickness and property errors. The obtained results show that the proposed IA‐based approach offers tangible advantages and effectiveness against some traditional statistical techniques (such as the Monte Carlo method).

Discusses the application of neural networks to routing in telecommunications networks under normal and abnormal conditions. Concepts related to optimal routing are discussed from the theoretical and telecommunications networks perspective to define a translation to the neural network paradigm. A sample network is then used to determine optimal neural network parameters, which are then tested to determine routing accuracy and performance under normal and abnormal routing conditions. Following the analysis of the results, conclusions and recommendations on the results are provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We introduce a logic-driven clustering in which prototypes are formed and evaluated in a sequential manner. The way of revealing a structure in data is realized by maximizing a certain performance index (objective function) that takes into consideration an overall level of matching (to be maximized) and a similarity level between the prototypes (the component to be minimized). The prototypes identified in the process come with the optimal weight vector that serves to indicate the significance of the individual features (coordinates) in the data grouping represented by the prototype. Since the topologies of these groupings are in general quite diverse the optimal weight vectors are reflecting the anisotropy of the feature space, i.e., they show some local ranking of features in the data space. Having found the prototypes we consider an inverse similarity problem and show how the relevance of the prototypes translates into their granularity.