Abstract
Linguistic modifiers, defined by Zadeh in fuzzy logic context, are operators that transform a linguistic term to another linguistic term. Akdag and al. extend linguistic modifiers to symbolic multi-valued logic context, and called them Generalized Symbolic Modifiers. In this paper we propose a study which allows deepening the use of Generalized Symbolic Modifiers in soft computing applications. We focus on symbolic modifiers composition, and we give new properties. Then, we study modifiers order relation, based on a lattice that orders all the defined modifiers according to their parameters. Finally, we illustrate the utilities of our propositions, particularly in approximate reasoning based on linguistic modifiers.
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References
Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)
Akdag, H., Glas, M.D., Pacholczyk, D.: A qualitative theory of uncertainty. Fun- dam. Inform. 17(4), 333–362 (1992)
Ginsberg, M.L.: Multivalued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4(3), 265–316 (1988)
Akdag, H., Mellouli, N., Borgi, A.: A symbolic approach of linguistic modifiers. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems, Madrid, 1713–1719 (2000)
Akdag, H., Truck, I., Borgi, A., Mellouli, N.: Linguistic modifiers in a symbolic framework. International Journal of Uncertainty. Fuzziness and Knowledge-Based Systems 9(suppl.), 49–61 (2001)
Khoukhi, F.: Approche logico-symbolique dans le traitement des connaissances incertaines et imprécises dans les systémes á base de connaissances. PhD thesis, Université de Reims, France (1996)
El-Sayed, M., Pacholczyk, D.: Towards a symbolic interpretation of approximate reasoning. Electr. Notes Theor. Comput. Sci. 82(4) (2003)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning - i - ii - iii. Information Sciences 8, 199–249, 8, 301–357, 9, 43–80 (1975)
Truck, I., Akdag, H., Borgi, A.: A symbolic approach for colorimetric alterations. In: Proceedings of the 2nd International Conference in Fuzzy Logic and Technology (EUSFLAT 2001), Leicester, UK, pp. 105–108 (2001)
Truck, I., Borgi, A., Akdag, H.: Generalized modifiers as an interval scale: To- wards adaptive colorimetric alterations. In: Garijo, F.J., Riquelme, J.-C., Toro, M. (eds.) IBERAMIA 2002. LNCS, vol. 2527, pp. 111–120. Springer, Heidelberg (2002)
Truck, I., Akdag, H.: Manipulation of qualitative degrees to handle uncertainty: formal models and applications. Knowledge and Information Systems 9(4), 385–411 (2006)
Kacem, S.B.H., Borgi, A., Ghédira, K.: Generalized modus ponens based on linguistic modifiers in a symbolic multi-valued framework. In: Proceeding of the 38th IEEE International Symposium on Multiple-Valued Logic, Dallas, USA, pp. 150–155 (2008)
Borgi, A., Kacem, S.B.H., Ghédira, K.: Approximate reasoning in a symbolic multi-valued framework. In: Lee, R.Y., Kim, H.K. (eds.) Computer and Information Science. Studies in Computational Intelligence, vol. 131, pp. 203–217. Springer, Heidelberg (2008)
Baldwin, J., Pilsworth, B.: Axiomatic approach to implication for approximate reasoning with fuzzy logic. Fuzzy Sets and Systems 3(2), 193–219 (1980)
Fukami, S., Mizumoto, M., Tanaka, K.: Some considerations of fuzzy conditional inference. Fuzzy Sets and Systems 4(3), 243–273 (1980)
Lascio, H.D., Gisolfi, A., Cortés, U.: Linguistic hedges and the generalized modus ponens. International Journal of Intelligent Systems 14, 981–993 (1999)
Cornelis, C., Kerre, E.E.: Inclusion-based approximate reasoning. In: Alexandrov, V.N., Dongarra, J., Juliano, B.A., Renner, R.S., Tan, C.J.K. (eds.) ICCS-ComputSci 2001. LNCS, vol. 2074, pp. 221–230. Springer, Heidelberg (2001)
Truck, I.: Approches symbolique et oue des modificateurs linguistiques et leur lien avec l’agrégation. PhD thesis, Université de Reims, France (2002)
Zadeh, L.A.: A theory of approximate reasoning. Machine Intelligence 9, 149–194 (1979)
Schwartz, D.G.: A system for reasoning with imprecise linguistic information. Int. J. Approx. Reasoning 5(5), 463–488 (1991)
Chung, H.T., Schwartz, D.G.: A resolution-based system for symbolic approximate reasoning. Int. J. Approx. Reasoning 13(3), 201–246 (1995)
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Kacem, S.B.H., Borgi, A., Tagina, M. (2009). On Some Properties of Generalized Symbolic Modifiers and Their Role in Symbolic Approximate Reasoning. In: Huang, DS., Jo, KH., Lee, HH., Kang, HJ., Bevilacqua, V. (eds) Emerging Intelligent Computing Technology and Applications. With Aspects of Artificial Intelligence. ICIC 2009. Lecture Notes in Computer Science(), vol 5755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04020-7_21
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DOI: https://doi.org/10.1007/978-3-642-04020-7_21
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