Abstract
From logic and algebra point of view, Computing with words is discussed in this paper. By analyzing the semantically ordering relation of linguistic variable Truth, orderings on linguistic hedges H and atomic evaluating syntagm Tr = {true, false} are obtained, respectively. Let H be finite chain, then Lukasiewicz product algebra of T = H×Tr of Truth is obtained, and term-set T(X) of Truth is embedded into an algebra Γ of type Δ = { ∨ , ∧ , ′,→ L }. In some cases, Γ can be applied in linguistic decision directly, also as truth domain of logic statements. Different with other truth domain, here truth values are linguistic terms rather than numerals (or symbolic).
Keywords
- Fuzzy Logic
- Linguistic Term
- Algebraic Property
- Information Granulation
- Implication Algebra
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Zadeh, L.A.: Fuzzy logic = computing with words. Fuzzy Systems 4, 103–111 (1996)
Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in houman reasoning and fuzzy logic. Fuzzy Sets and Systems 90, 103–111 (1997)
Novák, V., Perfilieva, I., Močkoř, J.: Mathematical principles of fuzzy logic. Kluwer Academic Publishers, Dordrecht (1999)
Novák, V.: Antonyms and linguistic quantifiers in fuzzy logic. Fuzzy Sets and Systems 124, 335–351 (2001)
Dvořák, A., Novák, V.: Fromal theories and linguistic descriptions. Fuzzy Sets and Systems 143, 169–188 (2004)
Wang, P.P.: Computing with words. John Wiley and Sons, Chichester (2001)
Trillas, E.: On the use of words and fuzzy sets. Information Sciences 176, 1463–1487 (2006)
Herrera, F., Herrera-Viedma, E.: Aggregation operators for linguistic weighted information. IEEE Trans. System, Man, Cybernet. - Part A: Systems Humans 27, 646–656 (1997)
Herrera, F., Lopez, E., Rodriguez, M.A.: A linguistic decision model for promotion mix management solved with genetic algorithms. Fuzzy Sets and Systems 131, 47–61 (2002)
Pei, Z., Du, Y., Yi, L., Xu, Y.: Obtaining a complex linguistic data summaries from database based on a new linguistic aggregation operator. In: Cabestany, J., Prieto, A.G., Sandoval, F. (eds.) IWANN 2005. LNCS, vol. 3512, pp. 771–778. Springer, Heidelberg (2005)
Ho, N.C., Khang, T.D., Huynh, V.N.: An algebraic approach to linguistic hedges in Zadeh’s fuzzy logic. Fuzzy Sets and Systems 129, 229–254 (2002)
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Pei, Z. (2007). The Algebraic Properties of Linguistic Value “Truth” and Its Reasoning. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_43
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DOI: https://doi.org/10.1007/978-3-540-72950-1_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72917-4
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