Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Introduction Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

2. Fuzzy Qualitative Trigonometry

verfasst von : Honghai Liu, Zhaojie Ju, Xiaofei Ji, Chee Seng Chan, Mehdi Khoury

Erschienen in: Human Motion Sensing and Recognition

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This Chapter presents a fuzzy qualitative representation of conventional trigonometry with the goal of bridging the gap between symbolic cognitive functions and numerical sensing and control tasks in the domain of physical systems, especially in intelligent robotics. Fuzzy qualitative coordinates are defined by replacing a unit circle with a fuzzy qualitative circle; a Cartesian translation and orientation are defined by their normalised fuzzy partitions. Conventional trigonometric functions, rules and the extensions to triangles in Euclidean space are converted into their counterparts in fuzzy qualitative coordinates using fuzzy logic and qualitative reasoning techniques. This approach provides a promising representation transformation interface to analyse general trigonometry-related physical systems from an artificial intelligence perspective. Fuzzy qualitative trigonometry has been implemented as a MATLAB toolbox named XTRIG in terms of 4-tuple fuzzy numbers. Examples are given throughout the chapter to demonstrate the characteristics of fuzzy qualitative trigonometry.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Introduction
Nächstes Kapitel Fuzzy Qualitative Robot Kinematics
Literatur
1.
P. Bourseau, K. Bousson, J.I. Dormoy, J.M. Evrard, F. Guerrin, L. Leyval, O. Lhomme, B. Lucas, A. Missier, J. Montmain, N. Piera, N. Rakoto-Ravalontsalama, M. Steyer, J.P. Tomasena, I. Trave-Massuyes, M. Vescovi, S. Xanthakis, and B. Yannou. qualitative reasoning: a survey of techniques and applications. AI communications, 8(3/4):119–193, 1995.
2.
B. Kuipers. Qualitative reasoning. MIT Press, 1994.
3.
D. Berleant. Qualitative and quantitative simulation: bridging the gap. Artificial Intelligence Journal, 95(2):215–255, 1997.
4.
A.F. Blackwell. Spatial reasoning for robots: a qualitative approach. Master Thesis, Victoria University of Wellington, 1988.
5.
Q. Shen and R. Leitch. Fuzzy qualitative simulation. IEEE Transactions on Systems, Man, and Cybernetics, 23(4):1038–1061, 1993.
6.
G. M. Coghill. Mycroft: A Framework for Constraint-Based Fuzzy Qualitative Reasoning. PhD thesis, Heriot-Watt University, 1996.
7.
K.D. Forbus, P. Nielsen, and B. Faltings. Qualitative kinematics: A framework. Proceedings of the International Joint Conference on Artificial Intelligence, pages 430–435, 1987.
8.
P.E. Nielsen. A qualitative approach to rigid body mechanics. University of Illinois at Urbana-Champaign, PhD thesis, 1988.
9.
B. Faltings. A symbolic approach to qualitative kinematics. Artificial Intelligence, 56(2–3):139–170, 1992.
10.
L. Magdalena and F. Monasterio-Huelin. A fuzzy logic controller with learning through the evolution of its knowledge base. International Journal of Approximate Reasoning, 16(3):335–358, 1997.
11.
J.J. Buckley and E. Eslami. An introduction to fuzzy logic and fuzzy sets. Springer-Verlag, 2002.
12.
J. Liu. A method of spatial reasoning based on qualitative trigonometry. Artificial Intelligence, 98(1-2):137–168, 1998.
13.
E. Smith and J. Eloff. Cognitive fuzzy modelling for enhanced risk assessment in a health care institution. IEEE Intelligent Systems, 15(2):69–75, 2000.
14.
J.W.T. Lee, D.S. Yeung, and E.C.C. Tsang. Ordinal fuzzy sets. IEEE transactions on Fuzzy Systems, 10(6):767–778, 2002.
15.
A.H. Ali, D. Dubois, and H. Prade. Qualitative reasoning based on fuzzy relative orders of magnitude. IEEE transactions on Fuzzy Systems, 11(1):9–23, 2003.
16.
Y. Li and S. Li. A fuzzy sets theoretic approach to approximate spatial reasoning. IEEE transactions on Fuzzy Systems, 12(6):745–754, 2004.
17.
Chee Seng Chan, George M Coghill, and Honghai Liu. Recent advances in fuzzy qualitative reasoning. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 19(03):417–422, 2011.
18.
Scott Friedman and Ann Kate Lockwood. Qualitative reasoning: Everyday, pervasive, and moving forwarda report on qr-15. AI Magazine, 37(2):95–96, 2016.
19.
R. Fuller. On fuzzy reasoning schemes. The state of the art of information systems application in 2007, TUCS General Publications, Carlsson (eds),C., 16:85–112, 1999.
20.
B.S. Chen, Yang Y.S., B.K. Lee, and Lee T.H. Fuzzy adaptive predictive flow control of atm network traffic. IEEE Transactions on Fuzzy Systems, 11(4):568–581, 2003.
21.
M. Setnes and H. Roubos. Ga-fuzzy modelling and classification: complexity and performance. IEEE Transactions on Fuzzy Systems, 8(5):35–44, 2000.
22.
E. Pedrycz and M. Reformat. Evolutionary fuzzy modelling. IEEE Transactions on Fuzzy Systems, 11(5):652–655, 2003.
23.
A. Fernández, M. del Jesus, and F. Herrera. Hierarchical fuzzy rule based classification systems with genetic rule selection for imbalanced data-sets. International Journal of Approximate Reasoning, 50(3):561–577, 2009.
24.
M. Antonelli, P. Ducange, B. Lazzerini, and F. Marcelloni. Learning concurrently partition granularities and rule bases of mamdani fuzzy systems in a multi-objective evolutionary framework. International Journal of Approximate Reasoning, 50(7):1066–1080, 2009.
25.
Andrea GB Tettamanzi and Marco Tomassini. Soft computing: integrating evolutionary, neural, and fuzzy systems. Springer Science & Business Media, 2013.
26.
E.C.C. Tsang, X.Z. Wang, and D.S. Yeung. Improving learning accuracy of fuzzy decision trees by hybrid neural networks. IEEE transactions on Fuzzy Systems, 8(5):601–614, 2000.
27.
P. Pulkkinen and H. Koivisto. Fuzzy classifier identification using decision tree and multiobjective evolutionary algorithms. International Journal of Approximate Reasoning, 48(2):526–543, 2008.
28.
P. Vuorimaa, T. Jukarainen, and E. Karpanoja. A neuro-fuzzy system for chemical agent detection. IEEE transactions on Fuzzy Systems, 3(4):415–424, 1995.
29.
A. Ciaramella, R. Tagliaferri, W. Pedrycz, and A. Di Nola. Fuzzy relational neural network. International Journal of Approximate Reasoning, 41(2):146–163, 2006.
30.
L. Hung and H. Chung. Decoupled sliding-mode with fuzzy-neural network controller for nonlinear systems. International Journal of Approximate Reasoning, 46(1):74–97, 2007.
31.
Ronald R Yager and Lotfi A Zadeh. An introduction to fuzzy logic applications in intelligent systems, volume 165. Springer Science & Business Media, 2012.
32.
Guillermo Bosque, Inés del Campo, and Javier Echanobe. Fuzzy systems, neural networks and neuro-fuzzy systems: a vision on their hardware implementation and platforms over two decades. Engineering Applications of Artificial Intelligence, 32:283–331, 2014.
33.
D. Schwartz. A system for reasoning with imprecise linguistic information. International Journal of Approximate Reasoning, 5(5):463–488, 1991.
34.
H. Kwan and Y. Cai. A fuzzy neural network and its application to pattern recognition. IEEE Transactions on Fuzzy Systems, 2(3):185–193, 1994.
35.
M. Ghalia and P. Wang. Intelligent system to support judgmental business forecasting: the case of estimating hotel room demand. In Computational Intelligence in Economics and Finance, pages 59–92. Springer, 2004.
36.
S.M. Bae, S.C. Park, and S.H. Ha. Fuzzy web ad selector based on web usage mining. IEEE Intelligent Systems, 18(6):62–69, 2003.
37.
J. Casillas, F. Herrera, R. Pérez, M. del Jesus, and P. Villar. Special issue on genetic fuzzy systems and the interpretability–accuracy trade-off. International Journal of Approximate Reasoning, 44(1):1–3, 2007.
38.
D.S. Weld and J. de Kleer (eds). Reading in qualitative reasoning about physical systems. Morgan Kaufman, San Mateo, CA, 1990.
39.
B.C. Williams and J. de Kleer (eds). Special issue on qualitative reasoning about physical systems. Artificial Intelligence, 51(1–3), 1991.
40.
Q. Shen and R. Leitch. Combining qualitative simulation and fuzzy sets. Recent advances in qualitative physics, pages 83–100, 1993.
41.
B. Bredeweg and P. Struss (eds). Special issues on qualitative reasoning. AI Magzine, 2003.
42.
P. Nayak and B. Williams. A model-based approach to reactive self-configuring systems. AAAI-96, pages 971–978, 1996.
43.
Hidde De Jong, Jean-Luc Gouzé, Céline Hernandez, Michel Page, Tewfik Sari, and Johannes Geiselmann. Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bulletin of Mathematical Biology, 66(2):301–340, 2004.
44.
G.M. Coghill, S.M. Garrett, and R.D. King. Learning qualitative metabolic models. In European Conference on Artificial Intelligence (ECAI’04), 2004.
45.
H. Liu, G.M. Coghill, and D.J. Brown. Qualitative kinematics of planar robots: Intelligent connection (in press). International Journal of Approximate Reasoning, 2007.
46.
H. Liu, D.J. Brown, and G.M. Coghill. Fuzzy qualitative robot kinematics. IEEE Transactions on Fuzzy Systems, 16(3):802–822, 2008.
47.
H. Liu. A fuzzy qualitative framework for connecting robot qualitative and quantitative representations. IEEE Transactions on Fuzzy Systems, 16(6):1522–1530, 2008.
48.
H. Liu and G.M. Coghill. Fuzzy qualitative trigonometry. Proc. IEEE International Conference on Systems, Man and Cybernetics, Hawaii, USA., 2005.
49.
M. Brady. Artificial intelligence and robotics. Artificial Intelligence, 26:79–121, 1985.
50.
P. Dpherty, G. Lakemeyer, and A.P. Del Pobil. Proceedings of the Fourth International Cognitive Robotics Workshop. CogRob, 2004.
51.
P.P. Bonissone and K.S. Decker. Selecting uncertainty calculi and granularity: An experiment in trading-off precision and complexity. Uncertainty in Artificial Intelligence, pages 217–247, 1986.
52.
T.J. Ross. Fuzzy logic with engineering applications. Jonh Wiley & Sons Ltd, 2004.
53.
J.J. Saade. Mapping convex and normal fuzzy sets. Fuzzy sets and systems, 81:251–256, 1996.
54.
C. Carlsson and R. Fuller. On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems, 122:315–326, 2001.
55.
A. Neumaier. Interval methods for systems of equations. Encyclopedia of mathematics and its applications, Cambridge University Press, 1990.
56.
L.D. Petković and M.S. Petković. Inequalities in circular arithmetic: A survey. In Recent Progress in Inequalities, pages 325–340. Springer, 1998.
57.
S.M. Rump. Fast and parallel interval arithmetic. BIT Numerical Mathematics, 39(3):534–554, 1999.
58.
L.A. Zadeh. The concept of a linguistic variable and its applications to approximate reasoning - i. Information Sciences, 8:199–249, 1975.
59.
L.A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning-ii. Information Sciences, 8(4):301–357, 1975.
60.
L.A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning-iii. Information Sciences, 9(1):43–80, 1975.
61.
T. Calvo, A. Kolesarova, M. Komornikova, and R. Mesiar. Aggregation operators: properties, classes and construction methods. In T. Calvo, G. Mayor, and R. Mesiar, editors, Aggregation Operators. New Trends and Applications, pages 3–104. Physica-Verlag, Heidelberg, New York, 2002.
62.
R.C. Arkin. Behavior-based robotics. MIT press, 1998.
63.
O.C. Jenkins and M.J. Mataric. Performance-derived behavior vocabularies: data-driven acquisition of skills from motion. International Journal of Humanoid Robotics, pages 237–288, 2004.
Metadaten
Titel
Fuzzy Qualitative Trigonometry
verfasst von
Honghai Liu
Zhaojie Ju
Xiaofei Ji
Chee Seng Chan
Mehdi Khoury
Copyright-Jahr
2017
Verlag
Springer Berlin Heidelberg
Buch
Human Motion Sensing and Recognition

Print ISBN: 978-3-662-53690-2

Electronic ISBN: 978-3-662-53692-6

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-662-53692-6_2