A new method for computing continuous functions with fuzzy variable

M. Z. Ahmad, Mohammad Khatim Hasan, B. de Baets

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

This study proposes a new method for computing f(U) where f is a real continuous function and U is a fuzzy interval. The computation of f(U) is performed by incorporating optimisation technique into Zadeh's extension principle. By discretising α up to n finite numbers, a set of n closed and bounded intervals is obtained. Here, the computation of f on closed and bounded intervals is the same idea of solving unconstrained optimisation problems. For every finite numbers of α, if the function to be optimised is unimodal, the authors apply Brent's method. One of the main advantages of using this method is that it does not require the calculation of derivative. In case where f is reduced to monotone or to a straight line, the optimal solutions are obtained at the endpoints of intervals. This new strategy gives better results and requires only few function evaluations. An example is provided to illustrate the effectiveness of the proposed method.

Original languageEnglish
Pages (from-to)1143-1149
Number of pages7
JournalJournal of Applied Sciences
Volume11
Issue number7
DOIs
Publication statusPublished - 2011

Fingerprint

Fuzzy Variable
Continuous Function
Computing
Interval
Fuzzy Intervals
Closed
Extension Principle
Unconstrained Optimization
Evaluation Function
Straight Line
Optimization Techniques
Monotone
Optimal Solution
Optimization Problem
Derivative

Keywords

  • Discretisation
  • Fuzzy interval
  • Fuzzy set
  • Optimisation
  • Zadeh's extension principle

ASJC Scopus subject areas

  • General

Cite this

A new method for computing continuous functions with fuzzy variable. / Ahmad, M. Z.; Hasan, Mohammad Khatim; de Baets, B.

In: Journal of Applied Sciences, Vol. 11, No. 7, 2011, p. 1143-1149.

Research output: Contribution to journalArticle

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