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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.