A prototype-based rule inference system incorporating linear functions.

*(English)*Zbl 1207.68392Summary: A calculus of appropriateness measures of linguistic expressions is proposed, which is based on the prototype theory and random set theory interpretation of vague concepts. A prototype-based rule inference system is then introduced to incorporate linguistic labels in the rule antecedents and linear functions in the consequents of rules. A rule learning algorithm is developed by combining a new clustering algorithm and a conjugate gradient algorithm. The proposed prototype-based inference system is then applied to a number of benchmark prediction problems including a nonlinear two-dimensional surface, the Mackey-Glass time series and the sunspot time-series. Results suggest that the proposed model is very robust and can perform well in high-dimensional noisy data.

##### MSC:

68T37 | Reasoning under uncertainty in the context of artificial intelligence |

##### Keywords:

prototype theory; appropriateness measures; prototype-based rules; random set theory; rule learning; clustering algorithm; fuzzy set theory
PDF
BibTeX
XML
Cite

\textit{Y. Tang} and \textit{J. Lawry}, Fuzzy Sets Syst. 161, No. 21, 2831--2853 (2010; Zbl 1207.68392)

Full Text:
DOI

##### References:

[1] | Zadeh, L., The concept of linguistic variable and its application to approximate reasoning, part I, Inf. sci., 8, 3, 199-249, (1975) · Zbl 0397.68071 |

[2] | Zadeh, L., The concept of linguistic variable and its application to approximate reasoning, part II, Inf. sci., 8, 4, 301-357, (1975) · Zbl 0404.68074 |

[3] | Zadeh, L., The concept of linguistic variable and its application to approximate reasoning, part III, Inf. sci., 9, 1, 43-80, (1975) · Zbl 0404.68075 |

[4] | Zadeh, L., Fuzzy logic=computing with words, IEEE trans. fuzzy syst., 4, 2, 103-111, (1996) |

[5] | Zadeh, L., From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions, IEEE trans. circuits syst. I, 45, 1, 105-119, (1999) · Zbl 0954.68513 |

[6] | Mamdani, E.; Assilian, S., An experiment in linguistic synthesis with a fuzzy logic controller, Int. J. man – machine stud., 7, 1, 1-13, (1975) · Zbl 0301.68076 |

[7] | Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE trans. syst. man cybern., 15, 116-132, (1985) · Zbl 0576.93021 |

[8] | Lee, C., Fuzzy logic in control systems: part I, IEEE trans. syst. man cybern., 20, 2, 404-419, (1990) |

[9] | Lee, C., Fuzzy logic in control systems: part II, IEEE trans. syst. man cybern., 20, 2, 419-435, (1990) · Zbl 0707.93037 |

[10] | Dubois, D.; Prade, H., The three semantics of fuzzy sets, Fuzzy sets and systems, 90, 141-150, (1997) · Zbl 0919.04006 |

[11] | Lawry, J., A methodology for computing with words, Int. J. approx. reasoning, 28, 51-89, (2001) · Zbl 0991.68109 |

[12] | Lawry, J., A framework for linguistic modelling, Artif. intell., 155, 1-39, (2004) · Zbl 1085.68695 |

[13] | Lawry, J., Modelling and reasoning with vague concepts, (2006), Springer New York · Zbl 1092.68095 |

[14] | Lawry, J., Appropriateness measures: an uncertainty model for vague concepts, Synthese, 161, 2, 255-269, (2008) · Zbl 1140.68066 |

[15] | Tang, Y.; Lawry, J., Linguistic modelling and information coarsening based on prototype theory and label semantics, Int. J. approx. reasoning, 50, 8, 1177-1198, (2009) · Zbl 1191.68699 |

[16] | Lawry, J.; Hall, J.; Bovey, R., Fusion of expert and learnt knowledge in a framework of fuzzy labels, Int. J. approx. reasoning, 36, 151-198, (2004) |

[17] | Qin, Z.; Lawry, J., Decision tree learning with fuzzy labels, Inf. sci., 172, 1-2, 91-129, (2005) · Zbl 1087.68094 |

[18] | Qin, Z.; Lawry, J., LFOIL: linguistic rule induction in the label semantics framework, Fuzzy sets and systems, 159, 4, 435-448, (2008) · Zbl 1176.68164 |

[19] | Tang, Y.; Zheng, J., Linguistic modelling based on semantic similarity relation among linguistic labels, Fuzzy sets and systems, 157, 12, 1662-1673, (2006) · Zbl 1101.68886 |

[20] | Tang, Y., A collective decision model involving vague concepts and linguistic expressions, IEEE trans. syst. man cybern. B, 38, 2, 421-428, (2008) |

[21] | Lawry, J.; Tang, Y., Relating prototype theory and label semantics, (), 35-42 |

[22] | Lawry, J.; Tang, Y., Uncertainty modelling for vague concepts: a prototype theory approach, Artif. intell., 173, 1539-1558, (2009) · Zbl 1185.68710 |

[23] | Rosch, E., Cognitive representations of semantic categories, J. exp. psychol. general, 104, 3, 192-233, (1975) |

[24] | Rosch, E., Natural categories, Cogn. psychol., 4, 3, 328-350, (1973) |

[25] | Goodman, I.; Nguyen, H., Uncertainty model for knowledge based systems, (1985), North-Holland New York |

[26] | Goodman, I.R., Fuzzy sets as equivalence classes of random sets, (), 327-342 |

[27] | Nguyen, H., On modeling of linguistic information using random sets, Inf. sci., 34, 265-274, (1984) · Zbl 0557.68066 |

[28] | Jang, J.-S.R., Anfis: adaptive-network-based fuzzy inference systems, IEEE trans. syst. man cybern., 23, 3, 665-685, (1993) |

[29] | Bezdek, J., Pattern recognition with fuzzy objective function algorithms, (1981), Plenum Press New York · Zbl 0503.68069 |

[30] | Setnes, M., Supervised fuzzy clustering for rule extraction, IEEE trans. fuzzy syst., 8, 4, 416-424, (2000) |

[31] | Hagan, M.; Demuth, H.; Beale, M., Neural network design, (1996), PWS Publishing Boston, MA |

[32] | Kim, D.; Kim, C., Forecasting time series with genetic fuzzy predictor ensemble, IEEE trans. fuzzy syst., 5, 523-535, (1997) |

[33] | Russo, M., Genetic fuzzy learning, IEEE trans. evol. comput., 4, 3, 259-273, (2000) |

[34] | Tang, Y.; Xu, Y., Application of fuzzy naive Bayes and a real-valued genetic algorithm in identification of fuzzy model, Inf. sci., 169, 3-4, 205-226, (2005) |

[35] | R. Hyndman, M. Akram, Time series data library \(\langle\)http://www-personal.buseco.monash.edu.au/hyndman/TSDL/index.htm⟩. |

[36] | N.J. Randon, Fuzzy and random set based induction algorithms, Ph.D. Thesis, University of Bristol, 2004. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.