A Composition of Fuzzy Sets

• Authors: Vitaly I. Levin
• Languages of publication: EN

Abstracts

EN

A new operation on fuzzy sets - the r-composition of n-sets - is introduced. The particular cases of this operation are logical conjunction (r = 1) or disjunction (r = n). In the general case (1 < r < n), this operation is purely fuzzy and has no analogs among the operations on fuzzy sets. The operation of r-composition is applied to the solution of control problems under uncertainty.

Keywords

EN

fussy sets; logical operations; composition; uncertainty; control problems

• Publisher: Sciendo
• Journal: Studia Humana
• Year: 2015
• Volume: 4
• Issue: 4
• Pages: 39-46

Dates

published

2015-12-01

online

2016-02-12

Contributors

author

Vitaly I. Levin

• Mathematics Department, Penza State Technological University 1-a, Baidukov pr., Penza, 440039, Russia

References

• 1. Bellman, R.E., Zadeh, L.A., “Decision Making in Fuzzy Environment”, Management Science, 4, Vol. 17, 1970.[Crossref]
• 2. Dubois, D., Prade, H., Fuzzy Sets and Systems: Theory and Applications, New York: Academic Press, 1980.
• 3. Zimmermann, H.J., Fuzzy Sets, Decision Making and Expert Systems, Kluwer Academic, 1986.
• 4. Yager, R.R., “Connectives and Quantifiers in Fuzzy Sets”, Fuzzy Sets and Systems, Vol. 40, 1991.
• 5. Zadeh, L., The Concept of Linguistic Variable and Its Application to Approximate Reasoning, New York: Elsevier, 1973.
• 6. Levin, V.I., Structural-Logical Methods of Analysis of Complex Systems. Moscow: Nauka, 1987 [in Russian].

Identifiers

DOI

10.1515/sh-2015-0024