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Fuzzy models are regarded as numeric constructs and as such are optimized and evaluated at the numeric level. In this study, we depart from this commonly accepted position and propose a granular evaluation of fuzzy models and present an augmentation of fuzzy models by forming information granules around numeric values of the parameters and constructions of the models. The concepts and algorithms of granular fuzzy models are discussed in the setting of Takagi–Sugeno rule-based architectures. We show how different protocols of forming and allocating information granules lead to the improvement of the granular performance of the models. Different from the standard numeric performance measure of fuzzy models coming in the form of the root mean squared error index, two performance measures are introduced that are pertinent to granular constructs, namely coverage and specificity. Furthermore, we propose a global indicator implied by these two measures, called an area under the curve, being computed for the characteristics of the granular model expressed in the coverage-specificity coordinates. A series of experimental studies is reported, which offers a comprehensive overview of the introduced performance measure criteria as well as the underlying realization of the granular fuzzy models. [ABSTRACT FROM PUBLISHER]

Information granules form an abstract and efficient characterization of large volumes of numeric data. Fuzzy clustering is a commonly encountered information granulation approach. A reconstruction (degranulation) is about decoding information granules into numeric data. In this study, to enhance quality of reconstruction, we augment the generic data reconstruction approach by introducing a transformation mapping of the originally produced partition matrix and setting up an adjustment mechanism modifying a localization of the prototypes. We engage several population-based search algorithms to optimize interaction matrices and prototypes. A series of experimental results dealing with both synthetic and publicly available data sets are reported to show the enhancement of the data reconstruction performance provided by the proposed method. [ABSTRACT FROM AUTHOR]

In recent years, granular fuzzy models have become an intensively studied category of fuzzy models. Granular fuzzy models help elevate the existing models to the higher level of abstraction subsequently making the resulting constructs in a better rapport with real-world systems. In contrast to numeric models, granular models produce results in the form of information granules (such as intervals, fuzzy sets, rough sets and alike). A number of studies have been focused on efficient designing granular fuzzy models where the information granularity has been formalized in the form of intervals. In this study, we propose a novel conceptual and algorithmic approach by elevating existing fuzzy models to granular fuzzy models in the form of fuzzy sets. Concentrating on Takagi-Sugeno fuzzy rule-based models (being commonly used in the literature), we establish a way of an optimal allocation of information granularity across the parameters of the original model and making them fuzzy sets (fuzzy numbers). As a result, the outputs of the granular fuzzy model become fuzzy sets. In the process of allocation of information granularity, we resort ourselves to some population-based meta-heuristic optimization techniques such as particle swarm optimization and differential evolution. To evaluate the performance of granular fuzzy models, we engage the principle of justifiable information granularity leading to the assessment and optimization of the coverage and specificity of the resulting fuzzy set. Besides, we involve the defuzzification (decoding) process to evaluate the impact of granular parameters on the quality of the numeric manifestation of the model. Comprehensive experimental studies involving synthetic and publicly available data sets are reported to demonstrate the performance of the granular fuzzy models. [ABSTRACT FROM AUTHOR]

Fuzzy rule-based models have been widely used due to their interpretability and effectiveness. However, they still encounter challenges when dealing with multivariable and large-scale data. In this study, we first propose a novel approach to establish a selective sampling and mapping data reduction method. The method focuses on reducing data variables while decreasing the number of samples, and an appropriate scaling size can be chosen for different situations. Then, a multivariable data-driven fuzzy rule-based model is developed based on the processed data. Moreover, the data projection approach using the distance metric helps to preserve the structural characteristics of the original data. The results are visually presented to facilitate an interpretable description of the subsequent rule-based modeling. Furthermore, due to the inevitable inaccuracy in the projection process of numeric modeling, we introduce the allocation of information granularity to extend the model to a granular form at a more abstract level. Experimental studies on both synthetic and publicly available datasets demonstrate that the proposed method has superior effectiveness and efficiency compared to the existing state-of-the-art regression algorithms. • We propose a novel selective sampling and mapping data reduction (SSMDR) method to exploit the data structure relationship. • We exploit the advantages of the SSMDR method to handle multivariable data-driven fuzzy modeling problems. • We extend the numerical fuzzy rule-based model to a higher-level granular model that can handle potential information loss. • We develop a comprehensive visual interpretable framework to achieve interpretable analysis in terms of three aspects: visualization structure, interpretable reasoning process, and granular structure. [ABSTRACT FROM AUTHOR]

Granular Computing (GrC) is a human-centric way to discover the fundamental structure of data sets. The resulting information granules can be efficiently exploited to organize knowledge and reveal data descriptions, which can play a pivotal role in the classification problems. Furthermore, information granules are abstract collections of data entities and exhibit flexibility and tolerance when it comes to the representation of incomplete data. However, most of the existing methods focused on the data imputation and classification separately. They also require better interpretability. The crux of this study is to develop a novel information granule-based classification method for incomplete data and a way of representing missing entities and regarding them as information granules in a unified framework. The first aspect focuses on revealing the structural backbone of multiple labeled subspaces of data by fuzzy clustering of missing values. It emerges a classifier with interpretable "IF-THEN" rules by the refinement of fuzzy prototypes in a supervised mode to capture the critical relationship of the multi-class incomplete data. The second aspect concerns the construction of some information granules to impute and represent missing values according to the refined prototypes and classification findings. The experimental studies involved synthetic and publicly available datasets in quantifying the advantages of the classification and representation abilities of the proposed methods on incomplete data. • We proposed a novel information granule-based classifier to reveal the structural of the subspaces of data, which is easier to be interpreted. • We considered incomplete data among classification modeling, so that this classifier can deal with the incomplete data straightforwardly. • We present a refinement mechanism for the information granule-based classifier to optimize the prototypes of the classification rules. • As a byproduct of the classification, the imputed information granules are distinguished from present data and have more tolerance to the imputation error. [ABSTRACT FROM AUTHOR]

The notions of multi-granulation and multi-scale are two important issues for the granular computing, both of which can describe the granular structure in certain ways. In this paper, we investigate the belief structure and the plausibility structure by defining belief and plausibility functions from the multi-granulation viewpoint, and discuss how to construct multi-granulation rough set (MGRS) models in multi-scale information systems (MSISs). Based on the MGRS in MSISs, the optimal scale selection methods with various requirements are studied in two aspects of optimistic and pessimistic multi-granulation for a multi-scale decision information system (MSDIS). To interpret and understand the proposed theories, some important properties of optimistic and pessimistic multi-granulation optimal scale selection are analyzed for the MSDIS, which could indicate the inner relationships among the different selection methods of the optimal scales. Furthermore, an example is provided to illustrate and verify these investigated properties. • Multigranulation-based belief and plausibility functions and structures are proposed. • Multigranulation rough sets in multi-scale information systems are presented. • Multigranulation-based optimal scale selection for multi-scale information systems are discussed. • Important properties of multigranulation-based optimal scale selection are analyzed. [ABSTRACT FROM AUTHOR]