Novel and Different Definitions for Fuzzy Union and Intersection Operations
This paper presents three new methodologies for the
basic operations, which aim at finding new ways of computing union
(maximum) and intersection (minimum) membership values by
taking into effect the entire membership values in a fuzzy set. The
new methodologies are conceptually simple and easy from the
application point of view and are illustrated with a variety of
problems such as Cartesian product of two fuzzy sets, max –min
composition of two fuzzy sets in different product spaces and an
application of an inverted pendulum to determine the impact of the
new methodologies. The results clearly indicate a difference based on
the nature of the fuzzy sets under consideration and hence will be
highly useful in quite a few applications where different values have
significant impact on the behavior of the system.
[1] George J.Klir and B. O Yuan, "Fuzzy sets, Fuzzy logic and Fuzzy
systems-Selected papers by Lotfi A. Zadeh," 1996. World Scientific
Publication Co Pvt Ltd
[2] E.Cox, "The Fuzzy Systems Handbook," Second Edition, AP
Professional, New York (1998).
[3] Timothy J.Ross, "Fuzzy Logic with Engineering Applications",
McGraw Hill.1997
[4] Witold Pedrycz and Fernando Gomide, "An Introduction to Fuzzy sets-
Analysis and Design," 1998.
[5] Zimmerman H.J, "Fuzzy set theory and its applications," Second
Edition, Kluwer academic publishers
[6] B.Kovalerchuk and V.Taliansky, "Comparison of empirical and
computed values of fuzzy conjunction," Fuzzy sets and systems,
46:49-53, 1992.
[7] U.Thole, H.J.Zimerman, and P.Zysno, "On the suitability of minimum
and product operators for the intersection of fuzzy sets," Fuzzy sets and
systems, 2:167-180, 1979.
[8] H.J.Zimmerman and P.Zysno, "Latent connectives in human decision
making," Fuzzy sets and systems, 4:37-51, 1980.
[9] Harald Dyckhoff and Witold Pedrycz, "Generalized means as model of
compensative connectives," Fuzzy sets and systems, 14:143-154,
1984.
[10] Masaharu Mizumoto, "Pictorial representation of fuzzy connectives,
parti: cases of t-norms, t-co norms and averaging operators," Fuzzy sets
and systems 31:217-242, 1989.
[1] George J.Klir and B. O Yuan, "Fuzzy sets, Fuzzy logic and Fuzzy
systems-Selected papers by Lotfi A. Zadeh," 1996. World Scientific
Publication Co Pvt Ltd
[2] E.Cox, "The Fuzzy Systems Handbook," Second Edition, AP
Professional, New York (1998).
[3] Timothy J.Ross, "Fuzzy Logic with Engineering Applications",
McGraw Hill.1997
[4] Witold Pedrycz and Fernando Gomide, "An Introduction to Fuzzy sets-
Analysis and Design," 1998.
[5] Zimmerman H.J, "Fuzzy set theory and its applications," Second
Edition, Kluwer academic publishers
[6] B.Kovalerchuk and V.Taliansky, "Comparison of empirical and
computed values of fuzzy conjunction," Fuzzy sets and systems,
46:49-53, 1992.
[7] U.Thole, H.J.Zimerman, and P.Zysno, "On the suitability of minimum
and product operators for the intersection of fuzzy sets," Fuzzy sets and
systems, 2:167-180, 1979.
[8] H.J.Zimmerman and P.Zysno, "Latent connectives in human decision
making," Fuzzy sets and systems, 4:37-51, 1980.
[9] Harald Dyckhoff and Witold Pedrycz, "Generalized means as model of
compensative connectives," Fuzzy sets and systems, 14:143-154,
1984.
[10] Masaharu Mizumoto, "Pictorial representation of fuzzy connectives,
parti: cases of t-norms, t-co norms and averaging operators," Fuzzy sets
and systems 31:217-242, 1989.
@article{"International Journal of Information, Control and Computer Sciences:57218", author = "Aarthi Chandramohan and M. V. C. Rao", title = "Novel and Different Definitions for Fuzzy Union and Intersection Operations", abstract = "This paper presents three new methodologies for the
basic operations, which aim at finding new ways of computing union
(maximum) and intersection (minimum) membership values by
taking into effect the entire membership values in a fuzzy set. The
new methodologies are conceptually simple and easy from the
application point of view and are illustrated with a variety of
problems such as Cartesian product of two fuzzy sets, max –min
composition of two fuzzy sets in different product spaces and an
application of an inverted pendulum to determine the impact of the
new methodologies. The results clearly indicate a difference based on
the nature of the fuzzy sets under consideration and hence will be
highly useful in quite a few applications where different values have
significant impact on the behavior of the system.", keywords = "Centroid, fuzzy set operations, intersection,
triangular norms , triangular S-norms, union.", volume = "2", number = "5", pages = "1523-7", }