Skip to main content

Design and Validation of an Explainable Fuzzy Beer Style Classifier

  • Chapter
  • First Online:
Explainable Fuzzy Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 970))

Abstract

We describe step by step how to design, implement and validate an interpretable fuzzy rule-based beer style classifier endowed with explanation capability. First, we revise some preliminary work regarding both interpretable fuzzy modeling methodologies and related software. Second, we introduce the use case on beer style classification. Third, we build and validate a fuzzy rule-based classifier with a good interpretability-accuracy trade-off for this use case. Fourth, we endow this classifier with explanation capability through a general linguistic interface that is tuned ad-hoc for the use case under consideration. Fifth, we show how the designed explainable classifier can be refined and exploited with several interoperable software tools. Finally, we compare two kinds of multi-modal (i.e., textual and graphical) explanations: (1) explanations which are inherently natural and fully-meaningful to users, because they are supported by an interpretable fuzzy rule-based classifier which is carefully designed (i.e., it is grounded in common-sense expert knowledge and global semantics); and (2) explanations which are supported by the linguistic approximation of a fuzzy rule-based classifier extracted from data with the focus only on accuracy (thus lacking of linguistic interpretability). The use case is implemented with open source software and all related datasets, tools and scripts are available online for the sake of reproducibility.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    European Commission, Artificial Intelligence for Europe, Brussels, Belgium, “Communication from the Commission to the European Parliament, the European Council, the Council, the European Economic and Social Committee and the Committee of the Regions”, Tech. Rep., 2018, (SWD(2018) 137 final) https://ec.europa.eu/digital-single-market/en/news/communication-artificial-intelligence-europe.

  2. 2.

    https://www.unglobalpulse.org/.

  3. 3.

    ACM US Public Policy Council: Statement on Algorithmic Transparency and Accountability, 2017, https://www.acm.org/binaries/content/assets/public-policy/2017_usacm_statement_algorithms.pdf.

  4. 4.

    https://gitlab.citius.usc.es/jose.alonso/guaje/.

  5. 5.

    GUAJE makes suggestions but the user always makes the final decision. Anyway, unsolved consistency issues can be automatically fixed during the “KB improvement” stage, if the user selects this option.

  6. 6.

    There is some overlapping between the two stages named as “Linguistic rule integration” and “KB improvement”. They may run independently, but if they ran in sequence then tasks (RS.1), (RS.2), (PS.1) and (PS.2) in the “KB improvement” stage would make no sense because the KB should be free of redundant and/or unused elements after fixing consistency issues previously identified during the “Linguistic rule integration” stage.

  7. 7.

    As far as we know, this kind of explanations are only available in GUAJE and ExpliClas (Alonso and Bugarín 2019). The latter is a web service for automatic generation of multi-modal explanations associated to Weka classifiers (Witten et al. 2016).

  8. 8.

    https://scikit-learn.org.

  9. 9.

    An illustrative example is provided in the next section (see Fig. 6.14).

  10. 10.

    We adopt the notation given in Alonso et al. (2019), even if this notation is slightly different from the rest of the book. Namely, \(U\) is an input vector while it refers to the universe of discourse in the rest of the book. In addition, \(T\) is a text generation algorithm while the same symbol refers to the set of linguistic terms in the rest of the book.

  11. 11.

    https://cran.r-project.org/web/packages/rLDCP/index.html.

  12. 12.

    SimpleNLG in Spanish: https://github.com/citiususc/SimpleNLG-ES.

  13. 13.

    SimpleNLG in English: https://github.com/simplenlg/.

  14. 14.

    We recommend to install and run GUAJE (Alonso 2020) in order to appreciate all details. GUAJE lets you zoom in and zoom out of the figures provided as screenshots in the rest of this chapter. Thus, you are not to miss any detail when analyzing the given pictures even if they were printed into black and white.

  15. 15.

    The Beer dataset in arff format is available online at https://gitlab.citius.usc.es/jose.alonso/xai/-/blob/master/BEER3.txt.aux.arff.

  16. 16.

    It is worth noting that GUAJE can run batch scripts from command line with the aim of building models for all the folds at once.

  17. 17.

    The interested reader is kindly invited to revisit Sect. 6.3 and the references there in for further details about how an IFS/GLMP is defined. IFS stands for Interpretable Fuzzy System and GLMP is the acronym of Granular Linguistic Model of a Phenomenon.

  18. 18.

    This Python script is available online along with the rest of files needed to reproduce the use cases illustrated in this chapter (Alonso et al. 2020).

  19. 19.

    The ExpliClas web service:https://demos.citius.usc.es/ExpliClas/.

  20. 20.

    The Waikato Environment for Knowledge Analysis (WEKA): https://www.cs.waikato.ac.nz/ml/weka/.

References

  • Acampora G, Di Stefano B, Vitiello A (2016) IEEE 1855: The first IEEE standard sponsored by IEEE computational intelligence society. IEEE Comput Intell Mag 11(4):4–7

    Google Scholar 

  • Alcala-Fdez J, Alonso JM (2016) A survey of fuzzy systems software: taxonomy, current research trends, and prospects. IEEE Transa Fuzzy Syst 24(1):40–56. https://doi.org/10.1109/TFUZZ.2015.2426212

    Article  Google Scholar 

  • Alcala-Fdez J, Alonso JM, Castiello C, Mencar C, Soto-Hidalgo JM (2019) Py4JFML: a Python wrapper for using the IEEE Std 1855-2016 through JFML. In: IEEE conference on fuzzy systems (FUZZ-IEEE). https://doi.org/10.1109/FUZZ-IEEE.2019.8858811

  • Alonso JM (2019) From Zadeh’s computing with words towards explainable Artificial Intelligence. In: Fuller R, Giove S, Masulli F (eds) Fuzzy logic and applications. WILF2018. Lecture notes in computer science. Springer Nature Switzerland AG, pp 244–248 (2019). https://doi.org/10.1007/978-3-030-12544-8_21

  • Alonso JM (2020) Java environment for generating accurate and understandable fuzzy classifiers. https://gitlab.citius.usc.es/jose.alonso/guaje/

  • Alonso JM, Bugarín A (2019) ExpliClas: automatic generation of explanations in natural language for Weka classifiers. In: IEEE international conference on fuzzy systems (FUZZ-IEEE), pp 1–6 (2019). https://doi.org/10.1109/FUZZ-IEEE.2019.8859018

  • Alonso JM, Casalino G (2019) Explainable artificial intelligence for human-centric data analysis in virtual learning environments. In: Burgos D, Cimitile M, Ducange P, Pecori R, Picerno P, Raviolo P, Stracke CM (eds) Higher education learning methodologies and technologies online, vol 1091. Springer, pp 125–138 (2019). https://doi.org/10.1007/978-3-030-31284-8_10

  • Alonso JM, Castiello C, Magdalena L, Mencar C (2020) Supplementary material for the Book entitled “Explainable Fuzzy Systems: Paving the Way from Interpretable Fuzzy Systems to Explainable AI Systems”. https://gitlab.citius.usc.es/jose.alonso/bookexfs/

  • Alonso JM, Castiello C, Mencar C (2018) A bibliometric analysis of the explainable artificial intelligence research field. In: International conference on information processing and management of uncertainty in knowledge-based systems (IPMU), pp 3–15 (2018). https://doi.org/10.1007/978-3-319-91473-2_1

  • Alonso JM, Castiello C, Mencar C (2019) The role of interpretable fuzzy systems in designing cognitive cities. In: Designing cognitive cities: linking citizens to computational intelligence to make efficient, sustainable and resilient cities a reality. Springer, pp 131–152 (2019). https://doi.org/10.1007/978-3-030-00317-3_6

  • Alonso JM, Cordon O, Guillaume S, Magdalena L (2007) Highly interpretable linguistic knowledge bases optimization: genetic tuning versus solis-wetts. Looking for a good interpretability-accuracy trade-off. In: IEEE international conference on fuzzy systems (FUZZ-IEEE), pp 901–906 (2007). https://doi.org/10.1109/FUZZY.2007.4295485

  • Alonso JM, Ducange P, Pecori R, Vilas R (2020) Building explanations for fuzzy decision trees with the expliclas software. In: IEEE international conference on fuzzy systems (FUZZ-IEEE). https://doi.org/10.1109/FUZZ48607.2020.9177725

  • Alonso JM, Magdalena L (2011a) Generating understandable and accurate fuzzy rule-based systems in a Java environment. In: Fanelli A, Pedrycz W, Petrosino A (eds) Lecture notes in artificial intelligence. Springer, Berlin, Heidelberg, pp 212–219 (ISSN: 0302-9743), Trani, Bari, Italy. https://doi.org/10.1007/978-3-642-23713-3_27

  • Alonso JM, Magdalena L (2011b) HILK++: an interpretability-guided fuzzy modeling methodology for learning readable and comprehensible fuzzy rule-based classifiers. Soft Computing 15(10):1959–1980. https://doi.org/10.1007/s00500-010-0628-5

    Article  Google Scholar 

  • Alonso JM, Magdalena L, Guillaume S (2006) Linguistic knowledge base simplification regarding accuracy and interpretability. Mathware Soft Comput 13(3):203–216

    MATH  Google Scholar 

  • Alonso JM, Magdalena L, Guillaume S (2008) HILK: A new methodology for designing highly interpretable linguistic knowledge bases using the fuzzy logic formalism. Int J Intell Syst 23(7):761–794. https://doi.org/10.1002/int.20288

  • Alonso JM, Magdalena L, Cordón O (2010) Embedding HILK in a three-objective evolutionary algorithm with the aim of modeling highly interpretable fuzzy rule-based classifiers. In: International workshop on genetic and evolutionary fuzzy systems (GEFS). IEEE, pp 15–20 (2010). https://doi.org/10.1109/GEFS.2010.5454165

  • Alonso JM, Magdalena L, Guillaume S, Sotelo M, Bergasa L, Ocaña M, Flores R (2007) Knowledge-based intelligent diagnosis of ground robot collision with non detectable obstacles. J Intell Robot Syst 48(4):539–566. https://doi.org/10.1007/s10846-006-9125-6

    Article  Google Scholar 

  • Alonso JM, Castiello C, Lucarelli M, Mencar C (2012) Modelling interpretable fuzzy rule-based classifiers for medical decision support. In: Magdalena R, Soria E, Guerrero J, Gomez-Sanchis J, Serrano A (eds) Medical applications of intelligent data analysis: research advancements. IGI Global, pp 254–271. https://doi.org/10.4018/978-1-4666-1803-9.ch017

  • Alonso JM, Castiello C, Magdalena L, Mencar C (2021a) An overview of fuzzy systems. In: Explainable fuzzy systems: paving the way from interpretable fuzzy systems to explainable AI systems. Studies in computational intelligence, Chap. 2. Springer, pp 25–48. https://doi.org/10.1007/978-3-030-71098-9_2

  • Alonso JM, Castiello C, Magdalena L, Mencar C (2021b) Designing interpretable fuzzy systems. In: Explainable fuzzy systems: paving the way from interpretable fuzzy systems to explainable AI systems. Studies in computational intelligence, Chap. 5. Springer, pp 119–168. https://doi.org/10.1007/978-3-030-71098-9_5

  • Alonso JM, Castiello C, Magdalena L, Mencar C (2021c) Interpretability constraints and criteria for fuzzy systems. In: Explainable fuzzy systems: paving the way from interpretable fuzzy systems to explainable AI systems. Studies in computational intelligence, Chap. 3. Springer, pp 49–89. https://doi.org/10.1007/978-3-030-71098-9_3

  • Alonso JM, Castiello C, Magdalena L, Mencar C (2021d) Revisiting indexes for assessing interpretability of fuzzy systems. In: Explainable fuzzy systems: paving the way from interpretable fuzzy systems to explainable AI systems. Studies in computational intelligence, Chap. 4. Springer, pp 91–118. https://doi.org/10.1007/978-3-030-71098-9_4

  • Alonso JM, Ocaña M, Hernandez N, Herranz F, Llamazares A, Sotelo M, Bergasa L, Magdalena L (2011) Enhanced WiFi localization system based on soft Computing techniques to deal with small-scale variations in wireless sensors. Appl Soft Comput 11(8):4677–4691. https://doi.org/10.1016/j.asoc.2011.07.015

    Article  Google Scholar 

  • Alonso JM, Pancho DP, Cordón O, Quirin A, Magdalena L (2013) Social network analysis of co-fired fuzzy rules. In: Yager RR, Abbasov AM, Reformat MZ, Shahbazova SN (eds) Soft computing: state of the art theory and novel applications, Studies in fuzziness and soft computing, Chap. 9. Springer, pp 113–128 (2013). https://doi.org/10.1007/978-3-642-34922-5_9

  • Alonso JM, Ramos-Soto A, Reiter E, Van Deemter K (2017) An exploratory study on the benefits of using natural language for explaining fuzzy rule-based systems. In: IEEE international conference on fuzzy systems (FUZZ-IEEE). https://doi.org/10.1109/FUZZ-IEEE.2017.8015489

  • Altug S, Chow MY, Trussell H (1999) Heuristic constraints enforcement for training of and rule extraction from a fuzzy/neural architecture. II. Implementation and application. IEEE Trans Fuzzy Syst 7(2):151–159. https://doi.org/10.1109/91.755397

  • Barrientos F, Sainz G (2011) Interpretable knowledge extraction from emergency call data based on fuzzy unsupervised decision tree. Knowl-Based Syst 25(1):77–87. https://doi.org/10.1016/j.knosys.2011.01.014

    Article  Google Scholar 

  • Bezdek J (1981) Pattern recognition with fuzzy objective function algorithms. Plenum, New York

    Book  Google Scholar 

  • Breiman L (2001) Random forest. Mach Learn 45(1):5–32

    Article  Google Scholar 

  • Carmona C, Gonzalez P, del Jesus M, Navio-Acosta M, Jimenez-Trevino L (2011) Evolutionary fuzzy rule extraction for subgroup discovery in a psychiatric emergency department. Soft computing-a fusion of foundations, methodologies and applications 15(12):2435–2448. https://doi.org/10.1007/s00500-010-0670-3

    Article  Google Scholar 

  • Castellano G, Castiello C, Fanelli A (2017a) The FISDeT software: application to beer style classification. In: IEEE international conference on fuzzy systems (FUZZ-IEEE), pp 1–6 (2017). https://doi.org/10.1109/FUZZ-IEEE.2017.8015503

  • Castellano G, Castiello C, Pasquadibisceglie V, Zaza G (2017b) FISDeT: fuzzy inference system development tool. Int J Comput Intell Syst 10:13–22. https://doi.org/10.2991/ijcis.2017.10.1.2

  • Castiello C, Fanelli AM, Lucarelli M, Mencar C (2019) Interpretable fuzzy partitioning of classified data with variable granularity. Appl Soft Comput 74:567–582. https://doi.org/10.1016/j.asoc.2018.10.040

  • Castro-Lopez A, Alonso JM (2019) Modeling human perceptions in e-commerce applications: a case study on business-to-consumers websites in the textile and fashion sector. In: Applying fuzzy logic for the digital economy and society. Fuzzy management methods. Springer (2019). https://doi.org/10.1007/978-3-030-03368-2_6

  • Chen MY (2002) Establishing interpretable fuzzy models from numeric data. In: IEEE world congress on intelligent control and automation, pp 1857–1861 (2002)

    Google Scholar 

  • Cheong F (2008) A hierarchical fuzzy system with high input dimensions for forecasting foreign exchange rates. Int J Artif Intell Soft Comput 1(1):15–24. https://doi.org/10.1504/IJAISC.2008.021261

    Article  Google Scholar 

  • Conde-Clemente P, Alonso JM, Trivino G (2017) rLDCP: R package for text generation from data. In: IEEE international conference on fuzzy systems (FUZZ-IEEE), pp 1–6 (2017). https://doi.org/10.1109/FUZZ-IEEE.2017.8015487

  • Conde-Clemente P, Alonso JM, Trivino G (2018) Toward automatic generation of linguistic advice for saving energy at home. Soft Comput 22(2):345–359. https://doi.org/10.1007/s00500-016-2430-5

    Article  Google Scholar 

  • Cordón O, Herrera F, Hoffmann F, Magdalena L (2001) Genetic fuzzy systems: evolutionary tuning and learning of fuzzy knowledge bases. World Scientific

    Google Scholar 

  • El-Sappagh S, Alonso JM, Ali F, Ali A, Jang JH, KwakK S (2018) An ontology-based interpretable fuzzy decision support system for diabetes diagnosis. IEEE Access 6:37371–37394. https://doi.org/10.1109/ACCESS.2018.2852004

    Article  Google Scholar 

  • Fernandez-Delgado M, Cernadas E, Barro S, Amorim D (2014) Do we need hundreds of classifiers to solve real world classification problems? J Mach Learn Res 15(1):3133–3181

    MathSciNet  MATH  Google Scholar 

  • Gadaras I, Mikhailov L (2009) An interpretable fuzzy rule-based classification methodology for medical diagnosis. Artif Intell Med 47(1):25–41. https://doi.org/10.1016/j.artmed.2009.05.003

    Article  Google Scholar 

  • Gatt A, Krahmer E (2018) Survey of the state of the art in natural language generation: core tasks, applications and evaluation. J Artif Intell Res 61:65–170. https://doi.org/10.1613/jair.5477

    Article  MathSciNet  MATH  Google Scholar 

  • Gatt A, Reiter E (2009) SimpleNLG: a realisation engine for practical applications. European workshop on natural language generation (ENLG). Greece, Athens, pp 90–93

    Google Scholar 

  • Ghandar A, Michalewicz Z, Zurbruegg R (2012) Enhancing profitability through interpretability in algorithmic trading with a multiobjective evolutionary fuzzy system. In: Coello C, Cutello V, Deb K, Forrest S, Nicosia G, Pavone M (eds) Parallel problem solving from nature-PPSN XII. Lecture notes in computer science, vol 7492. Springer, Berlin, Heidelberg, pp 42–51 (2012). https://doi.org/10.1007/978-3-642-32964-7_5

  • Glorennec PY (1999) Algorithmes d’apprentissage pour systemes d’inference floue. Hermes, Paris

    MATH  Google Scholar 

  • Guillaume S, Charnomordic B (2004) Generating an interpretable family of fuzzy partitions from data. IEEE Trans Fuzzy Syst 12(3):324–335. https://doi.org/10.1109/TFUZZ.2004.825979

  • Guillaume S, Charnomordic B (2010) Interpretable fuzzy inference systems for cooperation of expert knowledge and data in agricultural applications using FisPro. In: IEEE International conference on fuzzy systems (FUZZ-IEEE), pp 2019-2026, Barcelona (2010). https://doi.org/10.1109/FUZZY.2010.5584673

  • Guillaume S, Charnomordic B (2011) Learning interpretable fuzzy inference systems with FisPro. Inform Sci 181(20):4409–4427. https://doi.org/10.1016/j.ins.2011.03.025

    Article  Google Scholar 

  • Hartigan JA, Wong MA (1979) A k-means clustering algorithm. Appl Stat 28:100–108

    Article  Google Scholar 

  • Hühn J, Hüllermeier E (2009) FURIA: an algorithm for unordered fuzzy rule induction. Data Mining Knowl Discov 19(3):293–319. https://doi.org/10.1007/s10618-009-0131-8

    Article  MathSciNet  Google Scholar 

  • Ichihashi H, Shirai T, Nagasaka K, Miyoshi T (1996) Neuro-fuzzy ID3: a method of inducing fuzzy decision trees with linear programming for maximizing entropy and an algebraic method for incremental learning. Fuzzy Sets Syst 81(1):157–167. https://doi.org/10.1016/0165-0114(95)00247-2

    Article  MathSciNet  Google Scholar 

  • Kohonen T (1986) Learning vector quantization for pattern recognition. Helsinki University of Technology, Finland, Technical report

    Google Scholar 

  • Kohonen T (2001) Self-organizing maps, 3rd edn. Springer, Berlin

    Google Scholar 

  • Kumar A (2005) Interpretability and mean-square error performance of fuzzy inference systems for data mining. Intell Syst Account Financ Manag 13(4):185–196. https://doi.org/10.1002/isaf.263

    Article  Google Scholar 

  • Mamdani EH, Assilian S (1975) An experiment in linguistic synthesis with a fuzzy logic controller. Int J Man-Mach Stud 7:1–13

    Article  Google Scholar 

  • MathWorks: Fuzzy logic toolbox. Design and simulate fuzzy logic systems (2019). https://www.mathworks.com/products/fuzzy-logic.html

  • Mencar C, Castiello C, Cannone R, Fanelli A (2011) Design of fuzzy rule-based classifiers with semantic cointension. Inform Sci 181(20):4361–4377. https://doi.org/10.1016/j.ins.2011.02.014

    Article  Google Scholar 

  • Mucientes M, Casillas J (2007) Quick design of fuzzy controllers with good interpretability in mobile robotics. IEEE Trans Fuzzy Syst 15(4):636–651. https://doi.org/10.1109/TFUZZ.2006.889889

    Article  Google Scholar 

  • Pancho DP, Alonso JM, Cordón O, Quirin A, Magdalena L (2013a) FINGRAMS: visual representations of fuzzy rule-based inference for expert analysis of comprehensibility. IEEE Trans Fuzzy Syst 21(6):1133–1149. https://doi.org/10.1109/TFUZZ.2013.2245130

  • Pancho DP, Alonso JM, Magdalena L (2013b) Quest for interpretability-accuracy trade-off supported by fingrams into the fuzzy modeling tool GUAJE. Int J Comput Intell Syst 6:46–60. https://doi.org/10.1080/18756891.2013.818189

  • Pulkkinen P, Hytonen J, Koivisto H (2008) Developing a bioaerosol detector using hybrid genetic fuzzy systems. Eng Appl Artif Intell 21(8):1330–1346. https://doi.org/10.1016/j.engappai.2008.01.006

    Article  Google Scholar 

  • Ramos-Soto A, Janeiro-Gallardo J, Bugarín A (2017) Adapting SimpleNLG to Spanish. In: International conference on natural language generation (INLG). ACL, pp 142–146. https://doi.org/10.18653/v1/W17-3521

  • Rehse JR, Mehdiyev N, Fettke P (2019) Towards explainable process predictions for industry 4.0 in the DFKI-Smart-Lego-Factory. KI-Künstliche Intelligenz 33(2):181–187 (2019). https://doi.org/10.1007/s13218-019-00586-1

  • Reiter E, Dale R (2000) Building natural language generation systems. Cambridge University Press

    Google Scholar 

  • Riid A, Rustern E (2007) Interpretability of fuzzy systems and its application to process control. In: IEEE international conference on fuzzy systems (FUZZ-IEEE), pp 1–6 (2007). https://doi.org/10.1109/FUZZY.2007.4295370

  • Schoeman W (2016) Why AI is the future of growth. Technical report, Accenture

    Google Scholar 

  • Solis FJ, Wets RJB (1981) Minimization by random search techniques. Math Oper Res 6(1):19–30

    Article  MathSciNet  Google Scholar 

  • Soto-Hidalgo JM, Alonso JM, Acampora G, Alcala-Fdez J (2018) JFML: A Java library to design fuzzy logic systems according to the IEEE Std 1855–2016. IEEE Access 6:54952–54964. https://doi.org/10.1109/ACCESS.2018.2872777

    Article  Google Scholar 

  • Trivino G, Sugeno M (2013) Towards linguistic descriptions of phenomena. Int J Approx Reason 54(1):22–34

    Article  Google Scholar 

  • Troiano L, Rodríguez-Muñiz LJ, Ranilla J, Díaz I (2012) Interpretability of fuzzy association rules as means of discovering threats to privacy. Int J Comput Math 89(3):325–333

    Article  Google Scholar 

  • Vanbroekhoven E, Adriaenssens V, Debaets B (2007) Interpretability-preserving genetic optimization of linguistic terms in fuzzy models for fuzzy ordered classification: an ecological case study. Int J Approx Reason 44(1):65–90. https://doi.org/10.1016/j.ijar.2006.03.003

    Article  MathSciNet  Google Scholar 

  • Wang LX, Mendel JM (1992) Generating fuzzy rules by learning from examples. IEEE Trans Syst Man Cybern 22(6):1414–1427

    Google Scholar 

  • Witten IH, Frank E, Hall MA, Pal CJ (2016) Data mining: practical machine learning tools and techniques. Morgan Kaufmann

    Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inform. Control 8:338–353

    Article  MathSciNet  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inform Sci 8:199–249

    Article  MathSciNet  Google Scholar 

  • Zadeh LA (1999) From computing with numbers to computing with words-from manipulation of measurements to manipulation of perceptions. IEEE Trans Circ Syst I: Fundamental Theory Appl 46(1):105–119

    Article  MathSciNet  Google Scholar 

  • Zadeh LA (2001) A new direction in AI: toward a computational theory of perceptions. Artif Intell Mag 22(1):73–84

    MATH  Google Scholar 

  • Zadeh LA (2011) A note on Z-numbers. Inform Sci 181(14):2923–2932. https://doi.org/10.1016/j.ins.2011.02.022

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jose Maria Alonso Moral .

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Alonso Moral, J.M., Castiello, C., Magdalena, L., Mencar, C. (2021). Design and Validation of an Explainable Fuzzy Beer Style Classifier. In: Explainable Fuzzy Systems. Studies in Computational Intelligence, vol 970. Springer, Cham. https://doi.org/10.1007/978-3-030-71098-9_6

Download citation

Publish with us

Policies and ethics