MODELING THE DEGREE OF TRUTHFULNESS

Paul P. Wang and Chih Hsun Hsieh ()
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Paul P. Wang: Department of Electrical & Computer Engineering, Pratt School of Engineering, Duke University, Durham, NC, 27708, USA
Chih Hsun Hsieh: Department of Information Management, Aletheia University, 32, Chen-Li street, Tamsui 251, Taipei, Taiwan

New Mathematics and Natural Computation (NMNC), 2010, vol. 06, issue 02, 141-161

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, 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.

Keywords: Linguistic logic; fuzzy number; representation; ordering & ranking of fuzzy sets; natural operators; approximated reasoning; computing with words; fuzzy relation; semiotics; semantics; truthfulness modeling (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S1793005710001712

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