Abstract
This paper reports some novel approach on linguistic logic with our intention to realize CWW, Computing With Words, via a simple example which consists of only five words. As a by product, this simple example of the linguistic logical system may serve as a mathematical model which modeling the degree of truthfulness in daily usage. The five words set of a linguistic variable modeling the degree of truthfulness are; true, nearly true, undecided, nearly false and false. We subjectively choose trapezoidal fuzzy numbers as our linguistic truth values in order to model our linguistic logic system. Firstly, some natural operations and linguistic logic operators are defined to suit our objective of developing a closed linguistic variable set. Then the computation of linguistic truth values for this linguistic logical system is developed in order to facilitate us to perform the linguistic inferences. Properties of these natural operations can be derived accordingly. It is perhaps quite rewarding to see numerous linguistic truth relations defined on a single linguistic truth set and linguistic implications ended up with numerous linguistic truth tables. In addition, the linguistic inferences of generalized modus ponens and generalized tollens determined by linguistic compositional rules based on the linguistic truth relation and some natural operations are introduced. The simple examples of the linguistic inferences of the various generalized tautologies are illustrated. Finally, we have proved via a simple dictionary that a closed and self consistent linguistic logical system indeed can be constructed and it is possible to move a chunk of information as modeled by a fuzzy set to a higher level according to the theory of semiotics. These results have shown some promise in realizing the appealing theory of CWW.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Carlsson, C., Fedrizzi, M., Fuller, R.: Fuzzy logic in management, p. 41. Kluwer Academic Publishers, Dordrecht (2004)
Chen, S.H., Hsieh, C.H.: Graded mean integration representation of generalized fuzzy number. In: Proceedings of the sixth Conference of Chinese Fuzzy Sets and Systems (CD-ROM: filename: 031.wdl), p. 31 (1998)
Chen, S.H., Hsieh, C.H.: Ranking generalized fuzzy number with graded mean integration representation. In: Proceedings of the Eighth International Conference of Fuzzy Sets and Systems Association World Congress, vol. 2, pp. 551–555 (1999)
Chen, S.H., Hsieh, C.H.: Representation, Ranking, Distance, and Similarity of L-R type Fuzzy Number and Application. Australian Journal of Intelligent Information Processing Systems 6(4), 217–229 (2000)
Hsieh, C.H., Chen, S.H.: Similarity of generalized fuzzy number with graded mean integration representation. In: Proceedings of the Eighth International Conference of Fuzzy Sets and Systems Association World Congress, vol. 2, pp. 899–902 (1999)
Hsieh, C.H.: The natural operations of linguistic logic. New Mathematics and Natural Computations 4(1), 77–86 (2008)
Hintikka, J., Suppes, P.: Aspects of inductive logic. North-Holland Publ. Co., Amsterdam (1996)
Kaufmann, A., Gupta, M.M.: Introduction to fuzzy arithmetic theory and applications. Int. Thomson Computer Press, USA (1991)
Klir, G.J., Yuan, B.: Fuzzy sets and fuzzy logic—Theory and applications. Prentice-Hall Inc., Englewood Cliffs (1995)
Łukasiewicz, J.: Aristotle’s syllogistic. Clarendon Press, Oxford (1951)
Lawry, J., G. Shanahan, J., L. Ralescu, A. (eds.): Modelling with Words. LNCS (LNAI), vol. 2873. Springer, Heidelberg (2003)
Rescher, N.: Many-valued logic. McGraw-Hill, New York (1969)
Wang, P.P. (ed.): Advances in Fuzzy Theory and Technology (USA) III, 3 (1997)
Wang, P.P.: Computing with Words. John Wiley & Sons, Inc., Chichester (2001)
Zadeh, L.A.: Fuzzy logic-Computing with word. IEEE Trans. Fuzzy Syst. 4, 103–111 (1996)
Zadeh, L.A.: Fuzzy logic and approximate reasoning. In: Klir, G.J., Yuan, B. (eds.) Fuzzy sets and fuzzy logic—Theory and applications, World Scientific Publishing Co. Pte. Ltd., Singapore (1996)
Zadeh, L.A.: What is truth? BISC Group Seminar & Discussion, BISC, University of California at Berkeley. Berkeley Initiative in Soft Computing, June 2 (2009)
Zimmermann, H.J.: Fuzzy set theory and its applications, 2nd edn. Kluwer Academic Publishers, Dordrecht (1991)
Ching, H.: Translated by Sister Mary Lelia Makra. St. John’s University Press, New York (1961)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, P.P., Hsieh, C.H. (2010). Modeling the Degree of Truthfulness. In: Cao, By., Wang, Gj., Chen, Sl., Guo, Sz. (eds) Quantitative Logic and Soft Computing 2010. Advances in Intelligent and Soft Computing, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15660-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-15660-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15659-5
Online ISBN: 978-3-642-15660-1
eBook Packages: EngineeringEngineering (R0)