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Fuzzy rule-based models (FRBMs) are sound constructs to describe complex systems. However, in reality, we may encounter situations, where the user or owner of a system only owns either the input or output data of that system (the other part could be owned by another user); and due to the consideration of data privacy, he/she could not obtain all the needed data to build the FRBMs. Since this type of situation has not been fully realized (noticed) and studied before, our objective is to come up with some strategy to address this challenge to meet the specific privacy consideration during the modeling process. In this study, the concept and algorithm of the collaborative fuzzy clustering (CFC) are applied to the identification of FRBMs, describing either multiple-input-single-output (MISO) or multiple-input-multiple-output (MIMO) systems. The collaboration between input and output spaces based on their structural information (conveyed in terms of the corresponding partition matrices) makes it possible to build FRBMs when input and output data could not be collected and used in unison. Surprisingly, on top of this primary pursuit, with the collaboration mechanism the input and output spaces of a system are endowed with an innovative way to comprehensively share, exchange, and utilize the structural information between each other, which results in their more relevant structures that guarantee better model performance compared with performance produced by some state-of-the-art modeling strategies. The effectiveness of the proposed approach is demonstrated by experiments on a series of synthetic and publicly available datasets.

Incomplete data are frequently encountered and bring difficulties when it comes to further processing. The concepts of granular computing (GrC) help deliver a higher level of abstraction to address this problem. Most of the existing data imputation and related modeling methods are of numeric nature and require prior numeric models to be provided. The underlying objective of this study is to introduce a novel and straightforward approach that uses information granules as a vehicle to effectively represent missing data and build granular fuzzy models directly from resulting hybrid granular and numeric data. The evaluation and optimization of this method are guided by the principle of justifiable granularity engaging the coverage and specificity criteria and carried out with the help of particle swarm optimization. We provide a collection of experimental studies using a synthetic dataset and several publicly available real-world datasets to demonstrate the feasibility and analyze the main features of this method.

It becomes apparent that there are no ideal numeric models. Bringing a concept of information granularity to the original numeric model makes it well aligned with the experimental data and helps deliver a better insight into the credibility of the results provided by the model. Information granularity is regarded as a crucial design asset being optimally allocated across the numeric parameters of the originally constructed model. The underlying objective of this study is to propose a concept of a granular output space and develop an optimization process of allocation of information granularity across this space. The optimization is carried out by optimizing output information granules produced by the granular model by considering a product of the essential criteria describing information granules, namely specificity and coverage. The detailed optimization procedure involving Particle Swarm Optimization (PSO) is presented. We stress a generality of the approach that cuts across a variety of classes of models. A collection of experimental studies involving interval information granules is reported demonstrating the main features of the proposed approach. [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]