On the normalization of interval and fuzzy weights

Ying Ming Wang; T. M S Elhag

doi:10.1016/j.fss.2006.06.008

On the normalization of interval and fuzzy weights

Ying Ming Wang, T. M S Elhag

Research output: Contribution to journal › Article › peer-review

Abstract

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. © 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	2456-2471
Number of pages	15
Journal	Fuzzy Sets and Systems
Volume	157
Issue number	18
DOIs	https://doi.org/10.1016/j.fss.2006.06.008
Publication status	Published - 16 Sept 2006

Keywords

Fuzzy weights
Interval weights
Multiple criteria decision making
Normalization

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10.1016/j.fss.2006.06.008

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abstract = "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. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",

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AB - 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. © 2006 Elsevier B.V. All rights reserved.

KW - Fuzzy weights

KW - Interval weights

KW - Multiple criteria decision making

KW - Normalization

U2 - 10.1016/j.fss.2006.06.008

DO - 10.1016/j.fss.2006.06.008

M3 - Article

VL - 157

SP - 2456

EP - 2471

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

IS - 18

ER -

On the normalization of interval and fuzzy weights

Abstract

Keywords

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