Abstract
The structure of logical and/or pseudo-logical formula is introduced. The structure of logical formula is its characteristic invariant to its functional realization ({0,1}-valued, many-valued and/or [0,1]-valued logical function). The Boolean algebra is defined on the set of all n-ary logical structures. The fundamental principle of structural functionality is introduced. A logical discrete Choquet integral is defined as [0,1]-valued logical and pseudo-logical function for AND operator defined as min function.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
G. Choquet, Theory of capacities, Ann. Inst. Fourier 5 (1953) 131–295.
D. Dubois, H. Prade, Possibility Theory, Plenum Press, New York, 1988.
S. Gottwald, A Treatise on Many - Valued Logic, Research Studies Press, UK, (2001)
G. Klir, T. Folger, Fuzzy Sets, Uncertainty, and Information, Prentice-Hall, Englewood Cliffs, NJ. 1988.
P.Hajek, Metamatematics of Fuzzy Logic, Kluwer, (1998)
T. Murofushi, M. Sugeno, An interpretation of fuzzy measure and the Choquet integral as an integral with respect to fuzzy measure, Fuzzy Sets and Systems 29 (1989) 201–227.
D. Radojevic, Logical interpretation of discrete Choquet integral defined by general measure, International Journal of Uncertainty, Fuzzines and Knowledge-Based Systems, Vol. 7, No. 6 (1999) 577–588.
D. Radojevic, Logical measure of continual logical function, 8th Int. Conf. IPMU–Information Processing and Management of Uncertainty in Knowledge-based Systems, Madrid, (2000) 574–581.
D. Radojevic, The logical representation of discrete Choquet integral, JORBEL–The Belgian Journal of Operations Research, Statistics and Computer Science, Vol. 38 (2–3), (1998), 67–89.
D. Radojevic, [0,1]-valued logic: a natural generalization of Boolean logic, YU-JOR - Yugoslav Journal of Operational Research Vol 10, Number 2,(2000) 85–216
M. Sugeno, Theory of fuzzy integrals and its applications, Thesis, Tokyo Institute of Technology, 1974.
L.A. Zadeh, Similarity Relations and Fuzzy Orderings, Information Sciences, 3 (1971) 177–200.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Radojević, D. (2002). Logical Measure — Structure of Logical Formula. In: Bouchon-Meunier, B., Gutiérrez-Ríos, J., Magdalena, L., Yager, R.R. (eds) Technologies for Constructing Intelligent Systems 2. Studies in Fuzziness and Soft Computing, vol 90. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1796-6_33
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1796-6_33
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2504-6
Online ISBN: 978-3-7908-1796-6
eBook Packages: Springer Book Archive