Logic-based fuzzy networks: A study in system modeling with triangular norms and uninorms

Liang, Xiaofeng; Pedrycz, Witold

doi:10.1016/j.fss.2009.04.014

Cited by 39 publications

(15 citation statements)

References 47 publications

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“…Once the information granules have been formed by using the Fuzzy C-Means (FCM) clustering algorithm, the parameters of the linear functions present in the conclusion parts of the rules were estimated by running a standard Least Square Error (LSE) method. The number of rules itself is subject to optimization and here we resort ourselves to a successive enumeration by designing the fuzzy model for increasing the number of rules while monitoring the values of the corresponding performance index (11). The values of Q treated as a function of the number of rules (clusters) for all the models are shown in Fig.…”

Section: Concrete Compressive Strength Datamentioning

confidence: 99%

“…Along with the associated tangible benefits and better rapport with reality (distributed systems, various modeling perspectives), this shift brings a number of new challenges irrespectively from the development technologies one has started with. There is no surprise that in fuzzy modeling and computing with words [21] with its plethora of design techniques, see [1][2][3]6,[10][11][12]18] involving criteria of accuracy and interpretability [4,9] and invoking promising methods of global optimization [17], this concept has to translate into sound concepts, methodology, design strategies, and finally detailed algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Granular fuzzy models: a study in knowledge management in fuzzy modeling

Pedrycz

Song

2012

International Journal of Approximate Reasoning

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a b s t r a c tIn system modeling, knowledge management comes vividly into the picture when dealing with a collection of individual models. These models being considered as sources of knowledge, are engaged in some collective pursuits of a collaborative development to establish modeling outcomes of global character. The result comes in the form of a so-called granular fuzzy model, which directly reflects upon and quantifies the diversity of the available sources of knowledge (local models) involved in knowledge management. In this study, several detailed algorithmic schemes are presented along with related computational aspects associated with Granular Computing. It is also shown how the construction of information granules completed through the use of the principle of justifiable granularity becomes advantageous in the realization of granular fuzzy models and a quantification of the quality (specificity) of the results of modeling. We focus on the design of granular fuzzy models considering that the locally available models are those fuzzy rule-based. It is shown that the model quantified in terms of two conflicting criteria, that is (a) a coverage criterion expressing to which extent the resulting information granules ''cover'' include data and (b) specificity criterion articulating how detailed (specific) the obtained information granules are. The overall quality of the granular model is also assessed by determining an area under curve (AUC) where the curve is formed in the coverage-specificity coordinates. Numeric results are discussed with intent of displaying the most essential features of the proposed methodology and algorithmic developments.

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Section: Concrete Compressive Strength Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Granular fuzzy models: a study in knowledge management in fuzzy modeling

Pedrycz

Song

2012

International Journal of Approximate Reasoning

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“…If x 1 is A 1j with relevancy w 1j · · · and/or x k is A kj with relevancy w kj · · · and/or x n is A nj with relevancy w nj Then y j is v j (11) where v j for i = 1 · · · , m is a fuzzy singleton. The last layer (output layer) uses a classic neuron, denoted by W , to compute the network output.…”

Section: Unineuronmentioning

confidence: 99%

Universal approximation with uninorm-based fuzzy neural networks

Lemos

Kreinovich

Caminhas

et al. 2011

2011 Annual Meeting of the North American Fuzzy Information Processing Society

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Abstract-Fuzzy neural networks are hybrid models capable to approximate functions with high precision and to generate transparent models, enabling the extraction of valuable information from the resulting topology. In this paper we will show that the recently proposed fuzzy neural network based on weighted uninorms aggregations uniformly approximates any real functions on any compact set. We will describe the network topology and inference mechanism and show that the universal approximation property of this network is valid for a given choice of operators.

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“…Some sets were determined which, under some special conditions, are lattices with respect to T . For more details on t-norms on bounded lattices, we refer to [3,9,10,11,13,15,16,17,19].…”

Section: Introductionmentioning

confidence: 99%

“…In [7], an equivalence relation on the class of the t-norms on [0, 1] was defined. It was DOI: 10.14736/kyb-2016- [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] showed that the equivalence class of the weakest t-norm T D on [0, 1] contains a t-norm which was different from T D .…”

Section: Introductionmentioning

confidence: 99%