Fuzzy modeling by hierarchically built fuzzy rule bases

AbstractAlthough Mamdani-type fuzzy rule-based systems (FRBSs) became successfully performing clearly interpretable fuzzy models, they still have some lacks related to their accuracy when solving complex problems. A variant of these kinds of systems, which allows to perform a more accurate model representation, are the so-called approximate FRBSs. This alternative representation still cannot avoid the problems concerning the fuzzy rule learning methods, which as prototype identification algorithms, try to extract those approximate rules from the object problem space. In this paper we deal with the previous problems, viewing fuzzy models as a class of local modeling approaches which attempt to solve a complex problem by decomposing it into a number of simpler subproblems with smooth transitions between them. In order to develop this class of models, we first propose a common framework to characterize available approximate fuzzy rule learning methods, and later we modify it by introducing a fuzzy rule base hierarchical learning methodology (FRB-HLM). This methodology is based on the extension of the simple building process of the fuzzy rule base of FRBSs in a hierarchical way, in order to make the system more accurate. This flexibilization will allow us to have fuzzy rules with different degrees of specificity, and thus to improve the modeling of those problem subspaces where the former models have bad performance, as a refinement. This approach allows us not to have to assume a fixed number of rules and to integrate the good local behavior of the hierarchical model with the global model, ensuring a good global performance

Systems Statistical Engineering – Hierarchical Fuzzy Constraint Propagation

Driven by a growing requirement during the 21st century for the integration of rigorous statistical analyses in engineering research, there has been a movement within the statistics and quality communities to evolve a unified statistical engineering body of knowledge (Hoerl & Snee, 2010). Systems Statistical Engineering research seeks to integrate causal Bayesian hierarchical modeling (Pearl, 2009) and cybernetic control theory within Beer\u27s Viable System Model (S Beer, 1972; Stafford Beer, 1979, 1985) and the Complex Systems Governance framework (Keating, 2014; Keating & Katina, 2015, 2016) to produce multivariate systemic models for robust dynamic systems mission performance. (Cotter & Quigley, 2018) set forth the Bayesian systemic hierarchical constraint propagation theoretical basis for modeling the amplification and attenuation effects of environmental constraints propagated into systemic variability and variety. In their theoretical development, they simplified the analysis to only deterministic constraints, which models only the effect of statistical risks of failure. Imprecision and uncertainty in the assessment of environmental constraints will induce additional variance components in systemic variability and variety. To make causal Bayesian hierarchical modeling more capable of capturing and representing the imprecise and uncertain nature of environments, we must incorporate rough or fuzzy functions and boundaries to model imprecision and grey boundaries to model uncertainty in constraint propagation at each system level to measure the overall impact on the organization variability and variety. This paper sets forth a proposed research method to incorporate rough, fuzzy, and Grey set theories into Systems Statistical Engineering causal Bayesian hierarchical constraints modeling

Using Extensible Modeling in Systems Engineering and Architectural Search

The system architecting process is the hierarchical reduction of ambiguity associated with user needs and system design. Design allocation, and subsequent integration, implicitly requires a mechanism by which levels of detail can be added and removed from a decision scenario. This paper addresses the idea of engineering model sharing through the concept of vertical and horizontal extensibility as one mechanism by which hierarchical reduction in ambiguity can be facilitated. Extensible modeling introduces a systems architecting approach to the modeling community by identifying model interfaces and carefully decomposing the model domain. While the actual system hardware is not known at the time of initial design, performance sensitivities can be explored and formally communicated back to the system architect by determining membership in a fuzzy performance metric such as an architectural safety factor. This paper uses a notional vehicle mounted wireless communication system to illustrate the importance of considering environmental coupling variables through the use of extensible modeling and illustrates how fuzzy thinking can communicate the sensitivity of a system design

The role of human factors in stereotyping behavior and perception of digital library users: A robust clustering approach

To deliver effective personalization for digital library users, it is necessary to identify which human factors are most relevant in determining the behavior and perception of these users. This paper examines three key human factors: cognitive styles, levels of expertise and gender differences, and utilizes three individual clustering techniques: k-means, hierarchical clustering and fuzzy clustering to understand user behavior and perception. Moreover, robust clustering, capable of correcting the bias of individual clustering techniques, is used to obtain a deeper understanding. The robust clustering approach produced results that highlighted the relevance of cognitive style for user behavior, i.e., cognitive style dominates and justifies each of the robust clusters created. We also found that perception was mainly determined by the level of expertise of a user. We conclude that robust clustering is an effective technique to analyze user behavior and perception

A hierarchical Mamdani-type fuzzy modelling approach with new training data selection and multi-objective optimisation mechanisms: A special application for the prediction of mechanical properties of alloy steels

In this paper, a systematic data-driven fuzzy modelling methodology is proposed, which allows to construct Mamdani fuzzy models considering both accuracy (precision) and transparency (interpretability) of fuzzy systems. The new methodology employs a fast hierarchical clustering algorithm to generate an initial fuzzy model efficiently; a training data selection mechanism is developed to identify appropriate and efficient data as learning samples; a high-performance Particle Swarm Optimisation (PSO) based multi-objective optimisation mechanism is developed to further improve the fuzzy model in terms of both the structure and the parameters; and a new tolerance analysis method is proposed to derive the confidence bands relating to the final elicited models. This proposed modelling approach is evaluated using two benchmark problems and is shown to outperform other modelling approaches. Furthermore, the proposed approach is successfully applied to complex high-dimensional modelling problems for manufacturing of alloy steels, using ‘real’ industrial data. These problems concern the prediction of the mechanical properties of alloy steels by correlating them with the heat treatment process conditions as well as the weight percentages of the chemical compositions