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Hybrid Systems: Fuzzy Neural Integration
Published in Jay Liebowitz, The Handbook of Applied Expert Systems, 2019
Consequently, those input variables that do not have a dominant effect on the output, will have membership grades equal to “one” all across their domain. This is the result of the antecedent aggregation of the fuzzy rules that is performed by t-norm operators. Since “one” is the neutral element for these operators, the ineffective input candidates with membership grades of “one” in their entire range can be canceled from the fuzzy rules. Thus, the remaining variables become selected as input variables.
Fuzzy logic systems
Published in A. W. Jayawardena, Environmental and Hydrological Systems Modelling, 2013
A T-norm represents a fuzzy intersection, whereas a T-conorm (S-norm) represents a fuzzy union. They can be used to combine criteria in multicriteria problems. g. Alpha (α)-cut is a set of elements with degree of membership ≥ α.
Basic elements and definitions
Published in András Bárdossy, Lucien Duckstein, Fuzzy Rule-Based Modeling with Applications to Geophysical, Biological and Engineering Systems, 2000
András Bárdossy, Lucien Duckstein
The intersection of fuzzy sets can be defined with a so called t-norm function. This function assigns the membership value for an element in the intersection depending on the individual membership values in the intersecting sets.
Novel Aczel–Alsina operations-based hesitant fuzzy aggregation operators and their applications in cyclone disaster assessment
Published in International Journal of General Systems, 2022
Tapan Senapati, Guiyun Chen, Radko Mesiar, Ronald R. Yager, Abhijit Saha
Some examples of t-norms are Minimum t-norm: ,Product t-norm: ,Lukasiewicz t-norm: ,Drastic t-norm: for all .
A global optimality result in probabilistic spaces using control function
Published in Optimization, 2021
P. Saha, S. Guria, Samir Kumar Bhandari, Binayak S. Choudhury
The following are three examples of t-norm: The minimum t-norm, defined by .The product t-norm, , defined by .The Lukasiewicz t-norm, , defined by .
Urban growth modelling in Qazvin, Iran: an investigation into the performance of three ANFIS methods
Published in Journal of Spatial Science, 2022
Yousef Ghobadiha, Hamid Motieyan
where x and y are ANFIS inputs, A and B are fuzzy sets, Fi is an output function, and pi, qi, and ri are consequence parameters belonging to the output function. Any T-norm (a function that can be utilised for interpretation of the intersection of fuzzy sets in fuzzy logic) that performs the AND part of fuzzy rule can be deployed in the second layer as the fuzzy implication function. Hence, this layer utilises the minimum T-norm and multiplies the membership grades coming from the first layer in order to obtain the weight of each rule. Eq.3 represents the functionality of this layer for two x and y inputs.