Topic
Fuzzy associative matrix
About: Fuzzy associative matrix is a research topic. Over the lifetime, 8027 publications have been published within this topic receiving 194790 citations.
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TL;DR: This paper proposes the creation of a new paradigm for fuzzy system comprehensibility analysis based on fuzzy systems' inference maps, so-called fuzzy inference-grams (fingrams), by analogy with scientograms used for visualizing the structure of science.
Abstract: Since Zadeh's proposal and Mamdani's seminal ideas, interpretability is acknowledged as one of the most appreciated and valuable characteristics of fuzzy system identification methodologies. It represents the ability of fuzzy systems to formalize the behavior of a real system in a human understandable way, by means of a set of linguistic variables and rules with a high semantic expressivity close to natural language. Interpretability analysis involves two main points of view: readability of the knowledge base description (regarding complexity of fuzzy partitions and rules) and comprehensibility of the fuzzy system (regarding implicit and explicit semantics embedded in fuzzy partitions and rules, as well as the fuzzy reasoning method). Readability has been thoroughly treated by many authors who have proposed several criteria and metrics. Unfortunately, comprehensibility has usually been neglected because it involves some cognitive aspects related to human reasoning, which are very hard to formalize and to deal with. This paper proposes the creation of a new paradigm for fuzzy system comprehensibility analysis based on fuzzy systems' inference maps, so-called fuzzy inference-grams (fingrams), by analogy with scientograms used for visualizing the structure of science. Fingrams show graphically the interaction between rules at the inference level in terms of co-fired rules, i.e., rules fired at the same time by a given input. The analysis of fingrams offers many possibilities: measuring the comprehensibility of fuzzy systems, detecting redundancies and/or inconsistencies among fuzzy rules, identifying the most significant rules, etc. Some of these capabilities are explored in this study for the case of fuzzy models and classifiers.
51 citations
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TL;DR: A new approach to fuzzy rule generation from a set of examples with fuzzy representation is proposed, which incorporates the fuzzy entropy to search for paths and generalizes the concept of crisp extension matrix.
51 citations
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TL;DR: The mxn inconsistent fuzzy linear system is studied and the fuzzy least squares solution and therefore the weak fuzzy most squares solution to the fuzzy system are expressed by using the generalized inverses of the coefficient matrix.
51 citations
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TL;DR: Compared with the fuzzy neural network (FNN) model, the Fnu-SVM method requires fewer samples and enjoys higher estimating precision.
Abstract: This paper presents a new version of fuzzy support vector machine (FSVM) developed for product design time estimation. As there exist problems of finite samples and uncertain data in the estimation, the input and output variables are described as fuzzy numbers, with the metric on fuzzy number space defined. Then, the fuzzy nu-support vector machine (Fnu-SVM) is proposed on the basis of combining the fuzzy theory with the nu-support vector machine, followed by the presentation of a time estimation method based on Fnu-SVM and its relevant parameter-choosing algorithm. The results from the applications in injection mold design and software product design confirm the feasibility and validity of the estimation method. Compared with the fuzzy neural network (FNN) model, our Fnu-SVM method requires fewer samples and enjoys higher estimating precision
51 citations
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TL;DR: A comparative analysis demonstrates that the proposed model leads to the superior performance when compared with other fuzzy models reported in the literature.
51 citations