# zbMATH — the first resource for mathematics

Linguistic modelling and information coarsening based on prototype theory and label semantics. (English) Zbl 1191.68699
Summary: The theory of prototypes provides a new semantic interpretation of vague concepts. In particular, the calculus derived from this interpretation results in the same calculus as label semantics proposed by Lawry. In the theory of prototypes, each basic linguistic label $$L$$ has the form ‘about P’, where $$P$$ is a set of prototypes of $$L$$ and the neighborhood size of the underlying concept is described by the word ‘about’ which represents a probability density function $$\delta$$ on $$[0,+\infty$$). In this paper we propose an approach to vague information coarsening based on the theory of prototypes. Moreover, we propose a framework for linguistic modelling within the theory of prototypes, in which the rules are concise and transparent. We then present a linguistic rule induction method from training data based on information coarsening and data clustering. Finally, we apply this linguistic modelling method to some benchmark time series prediction problems, which show that our linguistic modelling and information coarsening methods are potentially powerful tools for linguistic modelling and uncertain reasoning.

##### MSC:
 68T37 Reasoning under uncertainty in the context of artificial intelligence
##### Software:
ANFIS; LFOIL; TDSL; TSDL
Full Text:
##### References:
 [1] Zadeh, L., Fuzzy logic=computing with words, IEEE trans. fuzzy syst., 4, 2, 103-111, (1996) [2] 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 [3] Zadeh, L., The concept of linguistic variable and its application to approximate reasoning, part I, Inform. sci., 8, 3, 199-249, (1975) · Zbl 0397.68071 [4] Zadeh, L., The concept of linguistic variable and its application to approximate reasoning, part II, Inform. sci., 8, 4, 301-357, (1975) · Zbl 0404.68074 [5] Zadeh, L., The concept of linguistic variable and its application to approximate reasoning, part III, Inform. sci., 9, 1, 43-80, (1975) · Zbl 0404.68075 [6] 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 [7] Lee, C., Fuzzy logic in control systems: part I, IEEE trans. syst. man cybern., 20, 2, 404-419, (1990) [8] Lee, C., Fuzzy logic in control systems: part II, IEEE trans. syst. man cybern., 20, 2, 419-435, (1990) · Zbl 0707.93037 [9] Dubois, D.; Prade, H., The three semantics of fuzzy sets, Fuzzy sets syst., 90, 141-150, (1997) · Zbl 0919.04006 [10] Lawry, J., A methodology for computing with words, Int. J. approx. reason., 28, 51-89, (2001) · Zbl 0991.68109 [11] Lawry, J., A framework for linguistic modelling, Artif. intell., 155, 1-39, (2004) · Zbl 1085.68695 [12] Lawry, J., Modelling and reasoning with vague concepts, (2006), Springer · Zbl 1092.68095 [13] Lawry, J., Appropriateness measures: an uncertainty model for vague concepts, Synthese, 161, 255-269, (2008) · Zbl 1140.68066 [14] Lawry, J.; Hall, J.; Bovey, R., Fusion of expert and learnt knowledge in a framework of fuzzy labels, Int. J. approx. reason., 36, 151-198, (2004) [15] Qin, Z.; Lawry, J., Decision tree learning with fuzzy labels, Inform. sci., 172, 1-2, 91-129, (2005) · Zbl 1087.68094 [16] Qin, Z.; Lawry, J., LFOIL: linguistic rule induction in the label semantics framework, Fuzzy sets syst., 159, 4, 435-448, (2008) · Zbl 1176.68164 [17] Tang, Y.; Zheng, J., Linguistic modelling based on semantic similarity relation among linguistic labels, Fuzzy sets syst., 157, 12, 1662-1673, (2006) · Zbl 1101.68886 [18] Tang, Y., A collective decision model involving vague concepts linguistic expressions, IEEE trans. syst. man cybern. B, 38, 2, 421-428, (2008) [19] J. Lawry, Y. Tang, Relating prototype theory and label semantics, in: Proceedings of SMPS08, in press. · Zbl 1191.68699 [20] J. Lawry, Y. Tang, Uncertainty modelling for vague concepts: A prototype theory approach, submitted for publication. · Zbl 1185.68710 [21] Barnes, D.W.; Mack, J.M., An algebraic introduction to mathematical logic, (1975), Springer-Verlag New York, Heidelberg, Berlin · Zbl 0311.02001 [22] Goodman, I.; Nguyen, H., Uncertainty model for knowledge based systems, (1985), North Holland [23] I.R. Goodman, Fuzzy sets as equivalence classes of random sets, in: R. Yager (Ed.), Fuzzy Set and Possibility Theory, 1982, pp. 327-342. [24] Nguyen, H., On modeling of linguistic information using random sets, Inform. sci., 34, 265-274, (1984) · Zbl 0557.68066 [25] Klawonn, F.; Kruse, R., Equality relations as a basis for fuzzy control, Fuzzy sets and systems, 54, 2, 147-156, (1993) · Zbl 0785.93059 [26] Klawonn, F., Fuzzy sets and vague environments, Fuzzy sets syst., 66, 207-221, (1994) · Zbl 0850.93440 [27] F. Klawonn, Similarity based reasoning, in: Proceedings of Third European Congress on Fuzzy and Intelligent Technologies, Aachen, 1995, pp. 34-38. [28] Klawonn, F.; Castro, J.L., Similarity in fuzzy reasoning, Mathware soft comput., 3, 2, 197-228, (1995) · Zbl 0859.04006 [29] Klawonn, F.; Novák, V., The relation between inference and interpolation in the framework of fuzzy systems, Fuzzy sets syst., 81, 3, 331-354, (1996) · Zbl 0891.93053 [30] Smets, P.; Kennes, R., The transferable belief model, Artif. intell., 66, 191-234, (1994) · Zbl 0807.68087 [31] Mamdani, E.; Assilian, S., An experiment in linguistic synthesis with a fuzzy logic controller, Int. J. man Mach. stud., 7, 1, 1-13, (1975) · Zbl 0301.68076 [32] Bezdek, J., Pattern recognition with fuzzy objective function algorithms, (1981), Plenum Press New York · Zbl 0503.68069 [33] Kim, D.; Kim, C., Forecasting time series with genetic fuzzy predictor ensemble, IEEE trans. fuzzy syst., 5, 523-535, (1997) [34] Russo, M., Genetic fuzzy learning, IEEE trans. evol. comput., 4, 3, 259-273, (2000) [35] Tang, Y.; Xu, Y., Application of fuzzy naive Bayes and a real-valued genetic algorithm in identification of fuzzy model, Inform. sci., 169, 3-4, 205-226, (2005) [36] R. Hyndman, M. Akram, Time series data library, . [37] N.J. Randon, Fuzzy and Random Set Based Induction Algorithms, PhD Thesis, University of Bristol, 2004. [38] Rumelhart, D.E.; Hinton, G.E.; Williams, R.J., Learning internal representations by error propagation, (), 318-362 [39] Jang, J.-S.R., Anfis: adaptive-network-based fuzzy inference systems, IEEE trans. syst. man cybern., 23, 3, 665-685, (1993)
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.