FUZZY WEIGHTED AVERAGE - Analytical Solution

Pim van den Broek, Joost Noppen

Abstract

An algorithm is presented for the computation of analytical expressions for the extremal values of the α-cuts of the fuzzy weighted average, for triangular or trapeizoidal weights and attributes. Also, an algorithm for the computation of the inverses of these expressions is given, providing exact membership functions of the fuzzy weighted average. Up to now, only algorithms exist for the computation of the extremal values of the α-cuts for a fixed value of α. To illustrate the power of our algorithms, they are applied to several examples from the literature, providing exact membership functions in each case.

References

  1. Chiao, K-P. (2000). Direct Fuzzy Weighted Average Algorithm for Fuzzy Multiple Attributes Decision Making, Tamsui Oxford Journal of Mathematical Sciences, 16, 311-327.
  2. Dong W.M., & Wong F.S. (1987). Fuzzy Weighted Averages and Implementation of the Extension Principle, Fuzzy Sets and Systems, 21, 183-199.
  3. Guh, Y.-Y., & Hon, C.-C., & Lee, E.S. (2001). Fuzzy Weighted Average: The Linear Programming Approach via Charnes and Cooper's Rule, Fuzzy Sets and Systems, 117, 157-160.
  4. Guh, Y.-Y., & Hon, C.-C., & Wang, K.-M., & Lee E.S. (1996). Fuzzy Weighted Average: A Max-Min Paired Elimination Method, Computers Math. Applic., 32, 115-123.
  5. Guu, S.-M. (2002). Fuzzy Weighted Average Revisited, Fuzzy Sets and Systems, 126, 411-414.
  6. Kao, C., & Liu, S.-L. (2001). Fractional Approach to Fuzzy Weighted Average, Fuzzy Sets and Systems, 120, 435-444
  7. Lee, D.H., & Park, D. (1997). An Efficient Algorithm for Fuzzy Weighted Average, Fuzzy Sets and Systems, 87, 39-45
  8. Liou, Y.-C., & Guu, S.-M. (2002). Linear-time Algorithm for the Fuzzy Weighted Average Method, Journal of the Chinese Institute of Industrial Engineers, 19, 7-12
  9. Liou, T.-S., & Wang, M.-J. (1992). Fuzzy Weighted Average: An Improved Algorithm, Fuzzy Sets and Systems, 49, 307-315
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Paper Citation


in Harvard Style

van den Broek P. and Noppen J. (2009). FUZZY WEIGHTED AVERAGE - Analytical Solution . In Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICFC, (IJCCI 2009) ISBN 978-989-674-014-6, pages 31-38. DOI: 10.5220/0002318900310038


in Bibtex Style

@conference{icfc09,
author={Pim van den Broek and Joost Noppen},
title={FUZZY WEIGHTED AVERAGE - Analytical Solution},
booktitle={Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICFC, (IJCCI 2009)},
year={2009},
pages={31-38},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002318900310038},
isbn={978-989-674-014-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICFC, (IJCCI 2009)
TI - FUZZY WEIGHTED AVERAGE - Analytical Solution
SN - 978-989-674-014-6
AU - van den Broek P.
AU - Noppen J.
PY - 2009
SP - 31
EP - 38
DO - 10.5220/0002318900310038