T-Normas, T-Conormas, Complementos e Implicações Intervalares

Authors

  • A. Takahashi
  • B.R.C Bedregal

DOI:

https://doi.org/10.5540/tema.2006.07.01.0139

Abstract

A lógica fuzzy modela matematicamente a imprecisão da linguagem natural, utilizando graus de pertinências (valores entre 0 e 1), contudo, nem sempre é simples especificar com precisão esses graus de pertinências. Existem infinitas formas de generalizar o comportamento dos conectivos lógicos clássicos (álgebra booleana) para valores no conjunto [0, 1]. As t-normas, t-conormas, implicações e complementos são operações sobre [0, 1] satisfazendo certas propriedades que generalizam os conectivos lógicos de conjunção, disjunção, implicação e negação, respectivamente, de forma a preservar algumas das propriedades da lógica clássica desses conectivos. Este trabalho consiste em introduzir uma generalização de t-norma, t-conorma, implicação e complemento, para o conjunto I = {[a, b] : 0 a b 1}, chamados de t-norma intervalar, t-conorma intervalar, implicação intervalar e complemento intervalar, de tal modo que, formas canônicas de se obter t-conorma intervalar, implicação intervalar e complemento intervalar a partir de uma t-norma intervalar sejam preservados.

References

[1] M.S. Aguiar, A.C.R. Costa e G.P. Dimuro, ICTM: An interval tessellationbased model for reliable topographic segmentation. Numerical Algorithms, 36 (2004), 1-10.

M. Baczynski, Residual implications revisited. notes on the Smets-Magrez. Fuzzy Sets and Systems, 145, No. 2 (2004), 267-277.

L.V. Barboza, G.P. Dimuro e R.H.S. Reiser, Power flow with load uncertainty. TEMA - Tendências em Matemática Aplicada e Computacional, 5 (2004), 27-36.

G. Bojadziev e M. Bojadziev, “Fuzzy Sets, Fuzzy Logic, Applications”, volume 5. World Scientific, 1995.

H. Bustince, P. Burilo e F. Soria, Automorphism, negations and implication operators. Fuzzy Sets and Systems, 134 (2003), 209-229.

D. Dubois e H. Prade, Random sets and fuzzy interval analysis. Fuzzy Sets and Systems, 42 (1991), 87-101.

J.C. Fodor, On fuzzy implication operators. Fuzzy Sets and Systems, 42 (1991), 293-300.

M. Gehrke, C. Walker e E. Walker, Algebraic aspects of fuzzy sets and fuzzy logic. Proceedings of Workshop on Current Trends and Develoments in Fuzzy Logic, pp. 101-170, 1999.

R. Horcik e M. Navara, Validation sets in fuzzy logics. Kybernetika, 38 No. 3 (2002), 319-326.

L.J. Kohout e E. Kim, Characterization ofinterval fuzzy logic systems of connectives by group transformation. Reliable Computing, 10 (2004), 299-334.

V. Kreinovich e M. Mukaidono, Interval (pairs of fuzzy values), triples, etc.: Can we thus get an arbitrary ordering? Proceedings of the 9th IEEE International Conference on Fuzzy Systems. San Antonio, Texas, 1 (2000), 234-238.

U.B. Kulisch e W.L. Miranker, “Computer Arithmetic Theory and Pratice”, Academic Press, San Diego, 1981.

J.M. Leski, Insensitive learning techniques for approximate reasoning system. Int. J. Computational Cognition, 1, No. 1 (2003), 21-77.

A. Lyra, B.R.C. Bedregal, R. Callejas-Bedregal e A.D. Doria Neto, The interval digital images processing. WSEAS Transactions on Circuits and Systems, 3, No. 2 (2004), 229-233.

R.J. Marks-II, “Fuzzy logic technology and applications”, chapter Preface by L.A. Zadeh. IEEE Technical Activities Board, 1994.

K. Menger, Statistical metrics. Proc. Nat. Acad., pp. 535-537, 1942.

R.E. Moore, Methods and Applications of Interval Arithmetic. PhD thesis, Studies in Applied Mathematics - SIAM, 1979.

B. Schweizer e A. Sklar, Associative functions and statistical triangle inequalities. Publicationes Mathematicae Debrecen, pp. 168-186, 1961.

M.M.M.T. Silveira e B.R.C. Bedregal, A method of inference and defuzzyfication fuzzy interval. Proceeding of the IASTED International Conference on Artificial Intelligence e Applications, pp. 242-247, 2001.

L.H. Tsoukalas e R.E. Uhrig, Fuzzy e Neural Approaches in Engineering. Wiley Interscience, 1997.

I.B. Turksen, Interval valued fuzzy sets based on normal forms. Fuzzy Sets and Systems, 20 (1986), 191-210.

L.A. Zadeh, Fuzzy sets. Proc. Nat. Acad., pp. 535-537, 1942.

Q. Zuo, Description of strictly monotonic interval AND/OR operations. APIC’S Proceedings: International Workshop on Applications of Interval Computations, pp. 232-235, 1995.

Published

2006-06-01

How to Cite

Takahashi, A., & Bedregal, B. (2006). T-Normas, T-Conormas, Complementos e Implicações Intervalares. Trends in Computational and Applied Mathematics, 7(1), 139–148. https://doi.org/10.5540/tema.2006.07.01.0139

Issue

Section

Original Article