Interpolation with function space representation of membership functions

Yeung Yam, Man Lung Wong, P. Baranyi

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

This paper generalizes a previous Cartesian approach for interpolating fuzzy rules comprised of membership functions with finite number of characteristic points. Instead of representing membership functions as points in Cartesian spaces, they now become elements in the space of square, integrable function. Interpolation is thus conducted between the antecedent and consequent function spaces. The generalized representation allows an extended class of membership functions satisfying two monotonicity conditions to be accommodated in the interpolation process. They include the popular bell-shaped membership functions, which were not possible before with the Cartesian representation. The work also extends the similarity triangle-based interpolation technique from the previous Cartesian representation to the new representation. Ensuing issues on computational complexity and nonunique conclusion are discussed. Other concepts such as spanning set and extensibility functions are also presented under the generalized framework. Examples to illustrate the extended approach and to compare with the Cartesian approach are given.

Original languageEnglish
Pages (from-to)398-411
Number of pages14
JournalIEEE Transactions on Fuzzy Systems
Volume14
Issue number3
DOIs
Publication statusPublished - Jun 2006

Fingerprint

Membership functions
Cartesian
Membership Function
Function Space
Interpolation
Interpolate
Fuzzy rules
Computational complexity
Fuzzy Rules
Monotonicity
Triangle
Computational Complexity
Generalise

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Artificial Intelligence

Cite this

Interpolation with function space representation of membership functions. / Yam, Yeung; Wong, Man Lung; Baranyi, P.

In: IEEE Transactions on Fuzzy Systems, Vol. 14, No. 3, 06.2006, p. 398-411.

Research output: Contribution to journalArticle

@article{71fcc6358cfa4cb586a992bc586be714,
title = "Interpolation with function space representation of membership functions",
abstract = "This paper generalizes a previous Cartesian approach for interpolating fuzzy rules comprised of membership functions with finite number of characteristic points. Instead of representing membership functions as points in Cartesian spaces, they now become elements in the space of square, integrable function. Interpolation is thus conducted between the antecedent and consequent function spaces. The generalized representation allows an extended class of membership functions satisfying two monotonicity conditions to be accommodated in the interpolation process. They include the popular bell-shaped membership functions, which were not possible before with the Cartesian representation. The work also extends the similarity triangle-based interpolation technique from the previous Cartesian representation to the new representation. Ensuing issues on computational complexity and nonunique conclusion are discussed. Other concepts such as spanning set and extensibility functions are also presented under the generalized framework. Examples to illustrate the extended approach and to compare with the Cartesian approach are given.",
author = "Yeung Yam and Wong, {Man Lung} and P. Baranyi",
year = "2006",
month = "6",
doi = "10.1109/TFUZZ.2006.876332",
language = "English",
volume = "14",
pages = "398--411",
journal = "IEEE Transactions on Fuzzy Systems",
issn = "1063-6706",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "3",

}

TY - JOUR

T1 - Interpolation with function space representation of membership functions

AU - Yam, Yeung

AU - Wong, Man Lung

AU - Baranyi, P.

PY - 2006/6

Y1 - 2006/6

N2 - This paper generalizes a previous Cartesian approach for interpolating fuzzy rules comprised of membership functions with finite number of characteristic points. Instead of representing membership functions as points in Cartesian spaces, they now become elements in the space of square, integrable function. Interpolation is thus conducted between the antecedent and consequent function spaces. The generalized representation allows an extended class of membership functions satisfying two monotonicity conditions to be accommodated in the interpolation process. They include the popular bell-shaped membership functions, which were not possible before with the Cartesian representation. The work also extends the similarity triangle-based interpolation technique from the previous Cartesian representation to the new representation. Ensuing issues on computational complexity and nonunique conclusion are discussed. Other concepts such as spanning set and extensibility functions are also presented under the generalized framework. Examples to illustrate the extended approach and to compare with the Cartesian approach are given.

AB - This paper generalizes a previous Cartesian approach for interpolating fuzzy rules comprised of membership functions with finite number of characteristic points. Instead of representing membership functions as points in Cartesian spaces, they now become elements in the space of square, integrable function. Interpolation is thus conducted between the antecedent and consequent function spaces. The generalized representation allows an extended class of membership functions satisfying two monotonicity conditions to be accommodated in the interpolation process. They include the popular bell-shaped membership functions, which were not possible before with the Cartesian representation. The work also extends the similarity triangle-based interpolation technique from the previous Cartesian representation to the new representation. Ensuing issues on computational complexity and nonunique conclusion are discussed. Other concepts such as spanning set and extensibility functions are also presented under the generalized framework. Examples to illustrate the extended approach and to compare with the Cartesian approach are given.

UR - http://www.scopus.com/inward/record.url?scp=33745145789&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745145789&partnerID=8YFLogxK

U2 - 10.1109/TFUZZ.2006.876332

DO - 10.1109/TFUZZ.2006.876332

M3 - Article

AN - SCOPUS:33745145789

VL - 14

SP - 398

EP - 411

JO - IEEE Transactions on Fuzzy Systems

JF - IEEE Transactions on Fuzzy Systems

SN - 1063-6706

IS - 3

ER -