Rough membership functions: a tool for reasoning with uncertainty

Z. Pawlak; A. Skowron

Banach Center Publications (1993)

  • Volume: 28, Issue: 1, page 135-150
  • ISSN: 0137-6934

Abstract

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A variety of numerical approaches for reasoning with uncertainty have been investigated in the literature. We propose rough membership functions, rm-functions for short, as a basis for such reasoning. These functions have values in the interval [0,1] and are computable on the basis of the observable information about the objects rather than on the objects themselves. We investigate properties of the rm-functions. In particular, we show that our approach is intensional with respect to the class of all information systems [P91]. As a consequence we point out some differences between the rm-functions and the fuzzy membership functions [Z65], e.g. the rm-function values for X ∪ Y (X ∩ Y) cannot be computed in general by applying the operation max(min) to the rm-function values for X and Y.

How to cite

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Pawlak, Z., and Skowron, A.. "Rough membership functions: a tool for reasoning with uncertainty." Banach Center Publications 28.1 (1993): 135-150. <http://eudml.org/doc/262811>.

@article{Pawlak1993,
abstract = {A variety of numerical approaches for reasoning with uncertainty have been investigated in the literature. We propose rough membership functions, rm-functions for short, as a basis for such reasoning. These functions have values in the interval [0,1] and are computable on the basis of the observable information about the objects rather than on the objects themselves. We investigate properties of the rm-functions. In particular, we show that our approach is intensional with respect to the class of all information systems [P91]. As a consequence we point out some differences between the rm-functions and the fuzzy membership functions [Z65], e.g. the rm-function values for X ∪ Y (X ∩ Y) cannot be computed in general by applying the operation max(min) to the rm-function values for X and Y.},
author = {Pawlak, Z., Skowron, A.},
journal = {Banach Center Publications},
keywords = {evidence theory; rough sets; reasoning with incomplete information; fuzzy sets; reasoning with uncertainty; rough membership functions; information systems; fuzzy membership functions},
language = {eng},
number = {1},
pages = {135-150},
title = {Rough membership functions: a tool for reasoning with uncertainty},
url = {http://eudml.org/doc/262811},
volume = {28},
year = {1993},
}

TY - JOUR
AU - Pawlak, Z.
AU - Skowron, A.
TI - Rough membership functions: a tool for reasoning with uncertainty
JO - Banach Center Publications
PY - 1993
VL - 28
IS - 1
SP - 135
EP - 150
AB - A variety of numerical approaches for reasoning with uncertainty have been investigated in the literature. We propose rough membership functions, rm-functions for short, as a basis for such reasoning. These functions have values in the interval [0,1] and are computable on the basis of the observable information about the objects rather than on the objects themselves. We investigate properties of the rm-functions. In particular, we show that our approach is intensional with respect to the class of all information systems [P91]. As a consequence we point out some differences between the rm-functions and the fuzzy membership functions [Z65], e.g. the rm-function values for X ∪ Y (X ∩ Y) cannot be computed in general by applying the operation max(min) to the rm-function values for X and Y.
LA - eng
KW - evidence theory; rough sets; reasoning with incomplete information; fuzzy sets; reasoning with uncertainty; rough membership functions; information systems; fuzzy membership functions
UR - http://eudml.org/doc/262811
ER -

References

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  1. [DP80] D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, 1980. Zbl0444.94049
  2. [P91] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer, 1991. Zbl0758.68054
  3. [PS91] Z. Pawlak and A. Skowron, Rough membership functions, ICS Research Report 10/91, Warsaw Univ. of Technology. Zbl0794.03045
  4. [Sc82] D. Scott, Domains for denotational semantics, a corrected and expanded version of a paper presented at ICALP 82, Aarhus, Denmark, 1982. 
  5. [Sh76] G. Shafer, A Mathematical Theory of Evidence, Princeton Univ. Press, 1976. 
  6. [S91] A. Skowron, The rough set theory as a basis for the evidence theory, ICS Research Report 2/91, 53 pp. 
  7. [Sk91] A. Skowron, Numerical uncertainty measures, lecture delivered at the S. Banach Mathematical Center during the semester 'Algebraic Methods in Logic and their Computer Science Applications', Warszawa, November 1991. 
  8. [SG91] A. Skowron and J. Grzymała-Busse, From the rough set theory to the evidence theory, ICS Research Report 8/91, 49 pp. 
  9. [Z65] L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353. Zbl0139.24606

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