Adaptive neuro fuzzy inference system

<h2 id="anfis-architecture">ANFIS architecture</h2>
It is possible to identify two parts in the network structure, namely premise and consequence parts. In more details, the architecture is composed by five layers.

<ol><li>The first layer takes the input values and determines the <a href="/facts/Membership_function_(mathematics)/NlIzCXrR">membership functions</a> belonging to them. It is commonly called fuzzification layer. The membership degrees of each function are computed by using the premise parameter set, namely {a,b,c}.</li>
<li>The second layer is responsible of generating the firing strengths for the rules. Due to its task, the second layer is denoted as "rule layer".</li>
<li>The role of the third layer is to normalize the computed firing strengths, by dividing each value for the total firing strength.</li>
<li>The fourth layer takes as input the normalized values and the consequence parameter set {p,q,r}.</li>
<li>The values returned by this layer are the defuzzificated ones and those values are passed to the last layer to return the final output.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a></li></ol>
<h3>Fuzzification layer</h3>
The first layer of an ANFIS network describes the difference to a vanilla neural network. Neural networks in general are operating with a <a href="/facts/Data_pre-processing/CS2W8m5B">data pre-processing</a> step, in which the <a href="/facts/Feature_(machine_learning)/nzAhYxfu">features</a> are converted into normalized values between 0 and 1. An ANFIS neural network doesn't need a <a href="/facts/Sigmoid_function/lAXu3AwW">sigmoid function</a>, but it's doing the preprocessing step by converting numeric values into fuzzy values.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a>
Here is an example: Suppose, the network gets as input the distance between two points in the 2d space. The distance is measured in pixels and it can have values from 0 up to 500 pixels. Converting the numerical values into <a href="/facts/Fuzzy_number/p76dqPeY">fuzzy numbers</a> is done with the membership function which consists of <a href="/facts/T-norm_fuzzy_logics/aWqmfG6W">semantic descriptions</a> like near, middle and far.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> Each possible linguistic value is given by an individual <a href="/facts/Artificial_neuron/TSH6nsgg">neuron</a>. The neuron “near” fires with a value from 0 until 1, if the distance is located within the category "near". While the neuron “middle” fires, if the distance in that category. The input value “distance in pixels” is split into three different neurons for near, middle and far.

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Jang, Jyh-Shing R (1991). Fuzzy Modeling Using Generalized Neural Networks and Kalman Filter Algorithm (PDF). Proceedings of the 9th National Conference on Artificial Intelligence, Anaheim, CA, USA, July 14–19. Vol. 2. pp. 762–767. <a href="http://www.aaai.org/Papers/AAAI/1991/AAAI91-119.pdf" target="_blank">http://www.aaai.org/Papers/AAAI/1991/AAAI91-119.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Jang, J.-S.R. (1993). "ANFIS: adaptive-network-based fuzzy inference system". IEEE Transactions on Systems, Man, and Cybernetics. 23 (3): 665–685. doi:10.1109/21.256541. S2CID 14345934. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Abraham, A. (2005), "Adaptation of Fuzzy Inference System Using Neural Learning", in Nedjah, Nadia; de Macedo Mourelle, Luiza (eds.), Fuzzy Systems Engineering: Theory and Practice, Studies in Fuzziness and Soft Computing, vol. 181, Germany: Springer Verlag, pp. 53–83, CiteSeerX 10.1.1.161.6135, doi:10.1007/11339366_3, ISBN 978-3-540-25322-8 <a href="978-3-540-25322-8" target="_blank">978-3-540-25322-8</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Jang, Sun, Mizutani (1997) – Neuro-Fuzzy and Soft Computing – Prentice Hall, pp 335–368, ISBN 0-13-261066-3 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Tahmasebi, P. (2012). "A hybrid neural networks-fuzzy logic-genetic algorithm for grade estimation". Computers & Geosciences. 42: 18–27. Bibcode:2012CG.....42...18T. doi:10.1016/j.cageo.2012.02.004. PMC 4268588. PMID 25540468. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4268588" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4268588</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Tahmasebi, P. (2010). "Comparison of optimized neural network with fuzzy logic for ore grade estimation". Australian Journal of Basic and Applied Sciences. 4: 764–772. <a href="https://www.researchgate.net/publication/266881168" target="_blank">https://www.researchgate.net/publication/266881168</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">Kamal, Mohasinina Binte; Mendis, Gihan J.; Wei, Jin (2018). "Intelligent Soft Computing-Based Security Control for Energy Management Architecture of Hybrid Emergency Power System for More-Electric Aircrafts [sic]". IEEE Journal of Selected Topics in Signal Processing. 12 (4): 806. Bibcode:2018ISTSP..12..806K. doi:10.1109/JSTSP.2018.2848624. S2CID 51908378. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Karaboga, Dervis; Kaya, Ebubekir (2018). "Adaptive network based fuzzy inference system (ANFIS) training approaches: a comprehensive survey". Artificial Intelligence Review. 52 (4): 2263–2293. doi:10.1007/s10462-017-9610-2. ISSN 0269-2821. S2CID 40548050. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">J.-S.R. Jang (1992). "Self-learning fuzzy controllers based on temporal backpropagation". IEEE Transactions on Neural Networks. 3 (5). Institute of Electrical and Electronics Engineers (IEEE): 714–723. doi:10.1109/72.159060. PMID 18276470. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Anish Pandey and Saroj Kumar and Krishna Kant Pandey and Dayal R. Parhi (2016). "Mobile robot navigation in unknown static environments using ANFIS controller". Perspectives in Science. 8. Elsevier BV: 421–423. Bibcode:2016PerSc...8..421P. doi:10.1016/j.pisc.2016.04.094. <a href="https://doi.org/10.1016%2Fj.pisc.2016.04.094" target="_blank">https://doi.org/10.1016%2Fj.pisc.2016.04.094</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
</ol>

Adaptive neuro fuzzy inference system open-in-new

Adaptive neuro fuzzy inference system