Finite cut-based approximation of fuzzy sets and its evolutionary optimization

Authors:
Adam Pedrycz;Fangyan Dong;Kaoru Hirota
Affiliations:
Department of Computational Intelligence and Intelligent Informatics, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, ...;Department of Computational Intelligence and Intelligent Informatics, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, ...;Department of Computational Intelligence and Intelligent Informatics, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, ...
Venue:
Fuzzy Sets and Systems
Year:
2009

Citing 14
Cited 2

Vertex method for computing functions of fuzzy variables

Fuzzy Sets and Systems
The particle swarm optimization algorithm: convergence analysis and parameter selection

Information Processing Letters
Threshold selection using fuzzy set theory

Pattern Recognition Letters
Toward a generalized theory of uncertainty (GTU): an outline

Information Sciences—Informatics and Computer Science: An International Journal
Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization

Computers and Operations Research
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)

Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Image thresholding using restricted equivalence functions and maximizing the measures of similarity

Fuzzy Sets and Systems
Relationship between restricted dissimilarity functions, restricted equivalence functions and normal EN-functions: Image thresholding invariant

Pattern Recognition Letters
Differential evolution and particle swarm optimisation in partitional clustering

Computational Statistics & Data Analysis
Practical inference with systems of gradual implicative rules

IEEE Transactions on Fuzzy Systems
Greenhouse air temperature predictive control using the particle swarm optimisation algorithm

Computers and Electronics in Agriculture
A study of particle swarm optimization particle trajectories

Information Sciences: an International Journal
Infrared image segmentation with 2-D maximum entropy method based on particle swarm optimization (PSO)

Pattern Recognition Letters
Shadowed sets: representing and processing fuzzy sets

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Risk evaluation through decision-support architectures in threat assessment and countering terrorism

Applied Soft Computing
Granular representation and granular computing with fuzzy sets

Fuzzy Sets and Systems

Quantified Score

Hi-index	0.20

Visualization

Abstract

Given the representation theorem, it is well known that any fuzzy set can be represented by an infinite family of its @a-cuts. While there have been a lot of theoretical investigations along this line, a surprisingly limited attention has been paid to the optimization of the representation (approximation) of fuzzy sets by some finite, usually quite limited, family of their @a-cuts. In this study, we formulate a problem of the best approximation of a fuzzy set by a finite number of its @a-cuts. Being concise, the task is formulated as follows: for a given fuzzy set and a prescribed finite number of a-cuts, optimize the values of the corresponding thresholds (a-cuts), so that the obtained finite representation as a nested set of intervals approximates the original fuzzy set to the highest possible extent. While for several (say, 2 or 3) threshold values detailed paper-and-pencil derivations could be accomplished thus leading to the construction of an analytic solution, in general, we need to resort to some optimization procedures. Considering the requirements of the resulting optimization problem formulated with this regard, we use here a certain biologically inspired optimization technique known as particle swarm optimization (PSO). In the paper, we elaborate on some categories of important and commonly encountered problems in which the capabilities of fuzzy sets are fully exploited, including decision-making and data analysis (supported by means of fuzzy clustering). The study includes a series of detailed numeric experiments that illustrate the performance of the PSO and demonstrate the effectiveness of the solutions developed through such optimization.