Publications

The paper is focused on man-machine communication, which is perceived in terms of data exchange. Understanding of data being exchanged is the fundamental property of intelligent communication. The main objective of this paper is to introduce the paradigm of intelligent data understanding. The paradigm stems from syntactic and semantic characterization of data and is soundly based on the paradigm of granular structuring of data and computation. The paper does not introduce a formal theory of intelligent data understanding. Instead this paradigm as well as notions of granularity, semantics and syntax are cast on the domain of music information. The domain immersion is forced by heavy dependence of details of the paradigm of automatic data understanding on application in a given domain.

In decision analysis, uncertainty is usually described in the framework of probability. However, a large number of experimental and theoretical studies showed that a single nature of probability does not accurately capture human preferences. To avoid this drawback, they use imprecise probabilities. But, as decision maker is usually uncertain about first-order imprecise probabilities, imprecise hierarchical probability models are used. For most of such models, the second levels are precise. There also exist studies on two-level imprecise hierarchical models, which use imprecise probabilities or possibilities at the second level. Most of these works are based on lower prevision theory leading to a large number of optimization problems. In the present paper, we propose an imprecise hierarchical decision-making model where the first and the second level are described by interval probabilities. The method associates with the construction of a nonadditive measure as a lower prevision and uses this capacity in Choquet integral for constructing a utility function.

The use of fuzzy logic to control purposes is closely related to implementation of a main scheme of reasoning with fuzzy premises such as generalized modus ponens.lts realization by the use of fuzzy relation equations is put into exhaustive discussion.

In contrast to numeric models, granular models produce results coming in a form of some information granules. Owing to the granularity of information these constructs dwell upon, such models become highly transparent and interpretable as well as operationally effective. Given also the fact that information granules come with a clearly defined semantics, granular models are often referred to as linguistic models. The crux of the design of the linguistic models studied in this paper exhibits two important features. First, the model is constructed on a basis of information granules which are assembled in the form of a web of associations between the granules formed in the output and input spaces. Given the semantics of information granules, we envision that a blueprint of the granular model can be formed effortlessly and with a very limited computing overhead. Second, the interpretability of the model is retained as the entire construct dwells on the conceptual entities of a well-defined semantics. The granulation of available data is accomplished by a carefully designed mechanism of fuzzy clustering which takes into consideration specific problem-driven requirements expressed by the designer at the time of the conceptualization of the model. We elaborate on a so-called context – based (conditional) Fuzzy C-Means (cond-FCM, for brief) to demonstrate how the fuzzy clustering is engaged in the design process. The clusters formed in the input space become induced (implied) by the context fuzzy sets predefined in the output space. The context fuzzy sets are defined in advance by the designer of the model so this design facet provides an active way of forming the model and in this manner becomes instrumental in the determination of a perspective at which a certain phenomenon is to be captured and modeled. This stands in a sharp contrast with most modeling approaches where the development is somewhat passive by being predominantly based on the existing data. The linkages between the fuzzy clusters induced by the given context fuzzy set in the output space are combined by forming a blueprint of the overall granular model. The membership functions of the context fuzzy sets are used as granular weights (connections) of the output processing unit (linear neuron) which subsequently lead to the granular output of the model thus identifying a feasible region of possible output values for the given input. While the above design is quite generic addressing a way in which information granules are assembled in the form of the model, we discuss further refinements which include (a) optimization of the context fuzzy sets, (b) inclusion of bias in the linear neuron at the output layer.

The papers in this special section focus on fuzzy rough sets for Big Data. Recent advances in computing technology imply collecting vast amount of data coming from various sources, such as the Internet, senor monitoring systems, social networks, mobile communication systems, transportation systems, and so on. We continue to encounter an explosive growth in big data coming with highly visible aspects of volume, variety, velocity, veracity, and value.

This paper presents a quantitative decision making methodology for evaluating best alternative using benefits, opportunities, costs, and risks (BOCR) models together with the interval computation. The quantification using BOCR-interval arithmetic modeling is performed in association with two types of models: analytic network process (ANP) and analytic hierarchy process (AHP) via consensus of multiple experts. The former is illustrated as BOCR-ANP in the form of a control network, whereas the latter BOCR-AHP as a strategic hierarchy network. We apply interval arithmetic operations — addition, subtraction, multiplication and division on the results obtained from BOCR-ANP/AHP models evaluated by different experts. This has been illustrated with an example of constructing a quantitative model for preserving the high quality of eggs and increasing the farm management effectiveness in the context of Salmonella Enteritidis (SE) outbreak.