A rough set approach for the discovery of classification rules in interval-valued information systems

A novel rough set approach is proposed in this paper to discover classification rules through a process of knowledge induction which selects optimal decision rules with a minimal set of features necessary and sufficient for classification of real-valued data. A rough set knowledge discovery framework is formulated for the analysis of interval-valued information systems converted from real-valued raw decision tables. The optimal feature selection method for information systems with interval-valued features obtains all classification rules hidden in a system through a knowledge induction process. Numerical examples are employed to substantiate the conceptual arguments

Long-term learning for type-2 neural-fuzzy systems

The development of a new long-term learning framework for interval-valued neural-fuzzy systems is presented for the first time in this article. The need for such a framework is twofold: to address continuous batch learning of data sets, and to take advantage the extra degree of freedom that type-2 Fuzzy Logic systems offer for better model predictive ability. The presented long-term learning framework uses principles of granular computing (GrC) to capture information/knowledge from raw data in the form of interval-valued sets in order to build a computational mechanism that has the ability to adapt to new information in an additive and long-term learning fashion. The latter, is to accommodate new input–output mappings and new classes of data without significantly disturbing existing input–output mappings, therefore maintaining existing performance while creating and integrating new knowledge (rules). This is achieved via an iterative algorithmic process, which involves a two-step operation: iterative rule-base growth (capturing new knowledge) and iterative rule-base pruning (removing redundant knowledge) for type-2 rules. The two-step operation helps create a growing, but sustainable model structure. The performance of the proposed system is demonstrated using a number of well-known non-linear benchmark functions as well as a highly nonlinear multivariate real industrial case study. Simulation results show that the performance of the original model structure is maintained and it is comparable to the updated model's performance following the incremental learning routine. The study is concluded by evaluating the performance of the proposed framework in frequent and consecutive model updates where the balance between model accuracy and complexity is further assessed

On the incorporation of interval-valued fuzzy sets into the Bousi-Prolog system: declarative semantics, implementation and applications

In this paper we analyse the benefits of incorporating interval-valued fuzzy sets into the Bousi-Prolog system. A syntax, declarative semantics and im- plementation for this extension is presented and formalised. We show, by using potential applications, that fuzzy logic programming frameworks enhanced with them can correctly work together with lexical resources and ontologies in order to improve their capabilities for knowledge representation and reasoning

Non-constructive interval simulation of dynamic systems

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Data granulation by the principles of uncertainty

Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference