Abstract
Using words rather than numbers to convey vague information as part of uncertain reasoning is a sophisticated human activity. The theory of fuzzy sets is now a popular tool for computing with words[12] which attempts to formally capture this human reasoning process[3–4] Furthermore, linguistic modeling based on fuzzy IF-THEN rules [6–8] has achieved promising results in many application areas. However, the currently proposed interpretations of the membership function in fuzzy set theory are not consistent with the truth-functional calculus of fuzzy logic[9]. Alternatively, from the philosophical viewpoint of the epistemic stance, Lawry proposed a functional (but non-truth functional) calculus, label semantics, for computing with words[10,11]. In this framework, the meaning of linguistic labels is encoded by mass functions which represent the subjective probabilities that a given set of labels is appropriate to describe a given instance. Label semantics is a powerful new tool for modelling with vague concepts, the possible applications of which include knowledge fusion[12], decision tree learning[13], linguistic rule induction[14], and collective decision making[15,16].
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References
Zadeh L. A.: Fuzzy logic = computing with words, IEEE Transaction on Fuzzy Systems. 4(2): pp. 103–111. (1996).
Zadeh L. A.: From computing with numbers to computing with words — from manipulation of measurements to manipulation of perceptions, IEEE Trans. Circuits Systems I 45(1), pp. 105–119. (1999).
Zadeh L. A.: The concept of linguistic variable and its application to approximate reasoning, part I, Information Sciences 8(3), pp. 199–249. (1975).
Zadeh L. A.: The concept of linguistic variable and its application to approximate reasoning, part II, Information Sciences 8(4), pp. 301–357. (1975).
Zadeh L. A.: The concept of linguistic variable and its application to approximate reasoning, part III, Information Sciences 9(1), pp. 43–80. (1975).
Takagi T., Sugeno M.: Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst., Man, Cybernetics, 15, pp. 116–132. (1985).
Lee C.: Fuzzy logic in control systems: part I, IEEE Trans. Syst., Man, Cybernetics, 20(2), pp. 404–419. (1990).
Lee C.: Fuzzy logic in control systems: part II, IEEE Trans. Syst., Man, Cybernetics, 20(2), pp. 419–435. (1990).
Dubois D., Prade H. £ºThe three semantics of fuzzy sets, Fuzzy Sets and Systems, 90, pp. 141–150. (1997).
Lawry J.: Modelling and Reasoning with Vague Concepts, Springer. (2006).
Lawry J.: Appropriateness measures: an uncertainty model for vague concepts. Synthese, 161(2), pp. 255–269. (2008).
Lawry L., Hall J. W., Bovey R.: Fusion of expert and learnt knowledge in a framework of fuzzy labels, Journal of Approximate Reasoning, 36: pp. 151–198. (2004).
Qin Z., Lawry J.: Decision tree learning with fuzzy labels, Information Sciences, 172/1–2: pp. 91–129. (2005).
Qin Z., Lawry J.: LFOIL: Linguistic rule induction in the label semantics framework. Fuzzy Sets and Systems 159(4): pp. 435–448. (2008).
Tang Y., Zheng J.: Linguistic modelling based on semantic similarity relation among linguistic labels, Fuzzy Sets and Systems 157(12), pp. 1662–1673. (2006).
Tang Y.: A collective decision model involving vague concepts and linguistic expressions, IEEE Trans. Syst., Man, Cybernetics B, 38(2), pp. 421–428. (2008).
Lawry J., Tang Y.: Relating prototype theory and label semantics, in: Dubois D., Lubiano M. A., Prade H., Gil M. A., Grzegorzewski P., Hryniewicz O.(Eds.), Soft Methods for Handling Variability and Imprecision, pp. 35–42. (2008).
Lawry J., Tang Y.: Uncertainty modeling for vague concepts: A prototype theory approach. Artificial Intelligence, 173, pp. 1539–1558. (2009).
Lawry J.: A framework for linguistic modelling, Artificial Intelligence, 155: pp. 1–39. (2004).
Goodman I., Nguyen H.: Uncertainty Model for Knowledge Based Systems, North Holland. (1985).
Nguyen H.: On modeling of linguistic information using random sets, Information Sciences 34, pp. 265–274. (1984).
Williamson T.: Vagueness, Routledge. (1994).
de Finetti B.: Fondamenti logici del ragionamento probabilistico, Bollettino dell’ Unione Matemztica Italiana 9, pp. 258–261. (1930).
Ramsey F. P.: The Foundations of Mathematics, and other Logical Essays, Kegan Paul, Trench, Trubner and Company Ltd, London. (1931).
Smets P., Kennes R.: The transferable belief model, Artificial Intelligence, 66, pp. 191–234.(1994).
Mamdani E., Assilian S.: An experiment in linguistic synthesis with a fuzzy logic controller, International Journal of Man-Machine Studies 7(1), pp. 1–13. (1975).
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© 2014 Zhejiang University Press, Hangzhou and Springer-Verlag Berlin Heidelberg
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Qin, Z., Tang, Y. (2014). A Prototype Theory Interpretation of Label Semantics. In: Uncertainty Modeling for Data Mining. Advanced Topics in Science and Technology in China. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41251-6_9
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