Journal
FUZZY SETS AND SYSTEMS
Volume 157, Issue 18, Pages 2456-2471Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.fss.2006.06.008
Keywords
interval weights; fuzzy weights; multiple criteria decision making; normalization
Funding
- Engineering and Physical Sciences Research Council [GR/S66770/01] Funding Source: researchfish
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The normalization of interval and fuzzy weights is often necessary in multiple criteria decision analysis (MCDA) under uncertainty, especially in analytic hierarchy process (AHP) with interval or fuzzy judgements. The existing normalization methods based on interval arithmetic and fuzzy arithmetic are found flawed and need to be revised. This paper presents the correct normalization methods for interval and fuzzy weights and offers relevant theorems in support of them. Numerical examples are examined to show the correctness of the proposed normalization methods and their differences from those existing normalization methods. (C) 2006 Elsevier B.V. All rights reserved.
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