Abstract
An automatic subdivision of the lithologic series into units is difficult because of the complexity of available geological information. Classical algorithms usually are based on the assumption that all values of the considered features are given in the numerical form. It is convenient to simplify the analytical process, but it is connected with associate error. Features described in other forms seem to bring us more information about objects. For example, the subject concerns linguistic form — words or sentences from natural or artificial languages, or new forms of describing of data — that is fuzzy sets. We assume that the geological environment is represented by a given set of features, and three forms of describing of data are allowed: numerical, linguistic, and a fuzzy one. Every sample is characterized by a vector. We introduce distances for the considered types of characters and unify their values by transformation to the unit interval. It enables us to determine a simple formula to calculate distances between samples and as a result an algorithm for subdivision of the investigated lithologic series. The algorithm was programmed in FORTRAN IV language for engineering geology problems.
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
Bezdek, J.C., 1981, Pattern recognition with fuzzy objective function algorithms: Plenum Press, New York and London, 256 p.
Bugayets, A.N., Zhaumitov, B.Zh., Lobova, O.Y., and Maximienko, L.A., 1979, The software for solving problems of ore deposits: Hornicka Pribram ve Vede a Technice, Pribram, p. 715-721.
Full, W.E., Ehrlich, R.E., and Bezdek, J.C., 1982, FUZZY QMODEL — a new approach for linear unmixing: Jour. Math. Geology, v. 14, no. 3, p. 259–270.
Fung, L.W., and Fu, K.S., 1975, Axiomatic approach to rational decision making in a fuzzy environment, in Fuzzy sets and their application to cognitive and decision processes: Academic Press, New York, p. 227–256.
Oden, G.C., 1977, Fuzziness in semantic memory: Memory & Cognition Jour., v. 5, no. 2, p. 198–204.
Rao, S.V.L.N., and Prasad, J., 1982, Definition of kriging in terms of fuzzy logic: Jour. Math. Geology, v. 14, no. 1, p. 37–42.
Sneath, P.H.A., and Sokal, R.R., 1973, Numerical taxonomy: W.H. Freeman and Co., San Francisco, 572 p.
Tanaka, K., and Mizumoto, M., 1975, Fuzzy programs and their execution, in Fuzzy sets and their application to cognitive and decision processes: Academic Press, New York, p. 41–76.
Yager, R.R., 1979, On the measure of fuzziness and negation. Part 1: Membership in the unit interval: Rept. RRY 79-016, Sch. of Business Administration, New Rochelle, New York, 15 p.
Zadeh, L.A., 1965, Fuzzy sets: Inform, and Control, v. 8, no. 3, p. 338–353.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Plenum Press, New York
About this chapter
Cite this chapter
Kacewicz, M. (1988). Application of Fuzzy Sets to the Subdivision of Geological Units. In: Merriam, D.F. (eds) Current Trends in Geomathematics. Computer Applications in the Earth Sciences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7044-4_4
Download citation
DOI: https://doi.org/10.1007/978-1-4684-7044-4_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-7046-8
Online ISBN: 978-1-4684-7044-4
eBook Packages: Springer Book Archive