Fundamentals of a mathematical theory of fuzzy sets

Jindřich Spal

Aplikace matematiky (1982)

  • Volume: 27, Issue: 5, page 326-340
  • ISSN: 0862-7940

Abstract

top
Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.

How to cite

top

Spal, Jindřich. "Fundamentals of a mathematical theory of fuzzy sets." Aplikace matematiky 27.5 (1982): 326-340. <http://eudml.org/doc/15255>.

@article{Spal1982,
abstract = {Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.},
author = {Spal, Jindřich},
journal = {Aplikace matematiky},
keywords = {fuzzy sets; fuzzy relations; informational entropy; random variable; fuzzy sets; fuzzy relations; informational entropy; random variable},
language = {eng},
number = {5},
pages = {326-340},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Fundamentals of a mathematical theory of fuzzy sets},
url = {http://eudml.org/doc/15255},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Spal, Jindřich
TI - Fundamentals of a mathematical theory of fuzzy sets
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 5
SP - 326
EP - 340
AB - Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.
LA - eng
KW - fuzzy sets; fuzzy relations; informational entropy; random variable; fuzzy sets; fuzzy relations; informational entropy; random variable
UR - http://eudml.org/doc/15255
ER -

References

top
  1. L. A. Zadeh, 10.1016/S0019-9958(65)90241-X, Information and Control 8, 1965, pp. 338 - 353. (1965) Zbl0139.24606MR0219427DOI10.1016/S0019-9958(65)90241-X
  2. Fuzzy množiny a možnosti jejich uplatnění při řešení systémových úloh, (Fuzzy sets and the possibilities of their aplication in solving problems about systems) (Proceedings of a conference). Dům techniky ČsVTS, Praha, 1980. (1980) 
  3. A. Kaufmann, Introduction ä Ia théorie des sous-ensembles flous, Masson, Paris, 1973. (1973) 
  4. B. Kumrner B. Straube, Eine Einführung in die Theorie unscharfer Mengen, Wiss. Zeitschr. der Techn. Universität, Dresden, 26, 1977, No. 2, pp. 363 - 369. (1977) MR0446772
  5. M. Peschel, Modellbildung für Signale und Systeme, VEB Verlag Technik., Berlin 1978. (1978) 
  6. J. A. Goguen, 10.1016/0022-247X(67)90189-8, J. Math. Anal. Appl., 18, 1967, pp. 145-174. (1967) Zbl0145.24404MR0224391DOI10.1016/0022-247X(67)90189-8
  7. J. Spal, Informácia a riadenie, (Information and control) Transactions of the 10th Symposium of the Slovak Cybernetic Society, Slovak Academy of Sciences, Bratislava, 1980. (1980) 
  8. J. Spal, Neostrá klasifikácia, (Fuzzy classification). Informačné systémy, 9, 1980, No. 5, pp. 413-429. (1980) 

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.