NDLI: An Optimization of ac-cuts of Fuzzy Sets Through Particle Swarm Optimization

Content Provider	IEEE Xplore Digital Library
Author	Pedrycz, A. Reformat, M.
Copyright Year	2006
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Alberta Univ., Edmonton, Alta. (Pedrycz, A.; Reformat, M.)
Abstract	Given the representation theorem, it is well-known that any fuzzy set can be represented by its infinite family of alpha-cuts. While there have been a lot of theoretical investigations along this line, a surprisingly limited attention was paid to the optimization of the representation (approximation) of fuzzy sets by some finite, usually quite limited, family of their alpha-cuts. In this study, we formulate a problem of the best approximation of a fuzzy set by a finite number of its alpha-cuts. Being concise, the task is formulated as follows: for a given fuzzy set A and a certain finite number of "n" alpha-cuts, optimize the values of these cuts (thresholds), $alpha_{1}$ < $alpha_{2}$ < ... < $alpha_{n}$ where $alpha_{i}$ isin (0,1] so that this finite alpha-cut representation of A approximates the original fuzzy set A to the highest possible extent. While for several (say, 2 or 3) threshold values detailed paper-and-pencil derivations could be easily completed 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
Starting Page	57
Ending Page	62
File Size	2995352
Page Count	6
File Format	PDF
ISBN	1424403626
DOI	10.1109/NAFIPS.2006.365859
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-06-03
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fuzzy sets Particle swarm optimization Data analysis Biological materials Data structures Decision making Vehicles
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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