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The paper deals with a model of decision‐making given in a form of a fuzzy relational equation with relationships between imprecisely defined goals and constraints modelled by means of a fuzzy relation. The usefulness of the model and its novelty is clearly pointed out. Some basic problems concerned, e.g. with a construction of the relation of the model and ordering of goals and constraints with respect to their importance (viz. their influence on a fuzzy decision), are also discussed in a detailed manner.

In this paper we deal with fuzzy numbers that modelize uncertain quantities present in many fields of applications, such as man‐machine systems. Main attention is paid to inverse operations for fuzzy numbers which allow one to solve equations or systems of equations with fuzzy numbers. The relevance of the method proposed for the determination of parameters of fuzzy models is also stressed.

A problem of handling fuzzy quantities in a process of knowledge acquisition and deriving an inference mechanism by means of fuzzy relation equations is studied in extensive way. It is clearly pointed out that both of them are closely related and correspond to various types of fuzzy relation equations that are considered. Their relevance to the form of knowledge collected is also indicated. A problem of dimension reduction of a knowledge base is considered as well. Two modes of the use of the knowledge base (goal‐, and data‐driven) are also studied.

The paper deals with some problems of decision‐making by the use of fuzzy set theory. The application of different operators from a wide class of intersection connectives makes it possible to modelize the process of decision‐making in a very flexible manner. The method of calculation of final non‐fuzzy decision from fuzzy set of decision D is discussed in detail and the problem of the choice of a threshold level presented as appropriate to the intersection operator applied before. The notion of sensitivity of any of intersection operators discussed is introduced and considered in detail.

Develops a general framework for processes of matching fuzzy quantities. Indicates how different hierarchy levels of matching indices are constructed from a relational way of description of the matching process. Making use of max‐min and min‐max fuzzy relation equations, respectively, clarifies how the entire matching proceeds. Moreover formulates an inverse problem. The method provided here enables us to distinguish regions of the universe of discourse in which the quantities are specified, which are considered as fully supporting the given concept (completely matching observed); completely excluded with respect to this concept; and being of a borderline character. As a consequence the results of matching can have a thorough interpretation.

The purpose of this paper is to show that exploiting fundamental ideas of granular computing can lead to further conceptual developments of granular metastructures, which are inherently associated with computing involving a large number of individual datasets; and to show that such processing leads to the representatives of information granules and granular models in the form of metastructures and metamodels.

The formulation of the concept of granular metastructures is provided and presented along with some essential algorithmic developments and associated optimization strategies. The overall methodological framework is the one of granular computing, especially fuzzy sets and fuzzy sets of higher type. Given the structural facet of optimization, the paper stresses the relevance of the use of evolutionary optimization.

This paper focused on the underlying concepts and while it elaborated on some development aspects and optimization tools, it should be stressed that further refinement and a thorough exploitation of optimization techniques in application to the inherently combinatorial facet of the problem are to be pursued in detail.

The introduced approach and algorithms could be of interest when solving problems of granular metastructures, in particular those encountered in knowledge‐based systems.

The main aspects of originality concern a formulation of the concept of granular metastructures and their design, based on granular evidence (experimental data) of lower type. A constructive way of forming type‐2 fuzzy sets via the principle of justifiable granularity exhibits a significant level of originality and offers a general way of designing information granules.

Shows that signal quantization can be conveniently captured and quantified in the language of information granules. Optimal codebooks exploited in any signal quantization (discretization) lend themselves to the underlying fundamental issues of information granulation. The paper elaborates on and contrasts between various forms of information granulation such as set theory, shadowed sets, and fuzzy sets. It is revealed that a set‐based codebook can be easily enhanced by the use of the shadowed sets. This also raises awareness about the performance of the quantization process and helps increase its quality by defining additional elements of the codebook and specifying their range of applicability. We show how different information granules contribute to the performance of signal quantification. The role of clustering techniques giving rise to information granules is also analyzed. Some pertinent theoretical results are derived. It is shown that fuzzy sets defined in terms of piecewise linear membership functions with ¹/₂ overlap between any two adjacent terms of the codebook give rise to the effect of lossless quantization. The study addresses both scalar and multivariable quantization. Numerical studies are included to help illustrate the quantization mechanisms carried out in the setting of granular computing.

In this study, we introduce and discuss a concept of fuzzy plug‐ins and investigate their role in system modeling. Fuzzy plug‐ins are rule‐based constructs augmenting a given global model (arising in the form of some regression relationship, neural network, etc.) in the sense that they compensate for the mapping errors produced by the global model. The proposed design method develops around information granules of error defined in the output space and the induced fuzzy relations expressed in the space of input variables. The construction of the linguistic granules is carried out with the aid of context‐based fuzzy clustering – a generalized version of the well‐known FCM algorithm that is well‐suited to the design of fuzzy sets and relations being used as a blueprint of the plug‐ins. An overall modeling architecture combining the global model with its plug‐ins is discussed in detail and a complete design procedure is provided. Finally, some illustrative numerical examples are shown as well.

This paper sets out to design hyperbox classifiers of high interpretation capabilities. They are based on a collection of hyperboxes – generic and highly interpretable geometric descriptors of data belonging to a certain class. Such hyperboxes directly translate into conditional statements (rules) taking on the well‐known format “if feature₁ assumes values in [a,b] and feature₂ assumes values in [d,f] and … and feature_n assumes values in [w,z] then class ω” where the intervals ([a,b],…[w,z]) are the respective edges (features) of the corresponding hyperbox.

The proposed design process of hyperboxes consists of two main phases. In the first phase, a collection of “seeds” of the hyperboxes is constructed through data clustering being realized by means of the fuzzy C‐means algorithm. During the second phase, the hyperboxes are “grown” (expanded) by applying mechanisms of genetic optimization (and genetic algorithm, in particular).

It is demonstrated how the underlying geometry of the hyperboxes supports an immediate interpretation of arrhythmia data by linking the ranges of the features (parameters of the ECG signal) forming the edges of the hyperboxes with the two classes of the signals (normal – abnormal). A collection of comprehensive experiments offers an interesting insight into the geometry of the individual categories of the ECG signals and discusses how the resulting hyperbox classifiers link their geometric properties with the obtained classification rates.

The structure of the classifier is essential to enhance interpretation capabilities of the architecture and generate a collection of “if‐then” classification rules.

The study addresses an issue of design of highly interpretable, granular classifiers with the use of the technology of computational intelligence and evolutionary optimization, in particular.

A comprehensive design methodology of hybrid fuzzy controllers (HFC) is proposed. The HFC comes in a form of a convex combination of a standard PID controller and a fuzzy controller. The design procedure dwells on the use of evolutionary computing (genetic algorithm) and an auto‐tuning algorithm. The tuning of the scaling factors of the HFC is an essential component of the entire optimization process. A numerical study is presented and a detailed comparative analysis is also included.