A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process

Ying Ming Wang; T. M S Elhag; Zhongsheng Hua

doi:10.1016/j.fss.2006.08.010

A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process

Ying Ming Wang, T. M S Elhag, Zhongsheng Hua

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

Abstract

This paper revisits the fuzzy logarithmic least squares method (LLSM) in the analytic hierarchy process and points out its incorrectness in the normalization of local fuzzy weights, infeasibility in deriving the local fuzzy weights of a fuzzy comparison matrix when the lower bound value of a non-normalized fuzzy weight turns out to be greater than its upper bound value, uncertainty of local fuzzy weights for incomplete fuzzy comparison matrices, and unreality of global fuzzy weights. A modified fuzzy LLSM, which is formulated as a constrained nonlinear optimization model, is therefore suggested to tackle all these problems. A numerical example is examined to show the applicability of the modified fuzzy LLSM and its advantages. © 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	3055-3071
Number of pages	16
Journal	Fuzzy Sets and Systems
Volume	157
Issue number	23
DOIs	https://doi.org/10.1016/j.fss.2006.08.010
Publication status	Published - 1 Dec 2006

Keywords

Fuzzy analytic hierarchy process
Fuzzy comparison matrix
Fuzzy weights
Normalization

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10.1016/j.fss.2006.08.010

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title = "A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process",

abstract = "This paper revisits the fuzzy logarithmic least squares method (LLSM) in the analytic hierarchy process and points out its incorrectness in the normalization of local fuzzy weights, infeasibility in deriving the local fuzzy weights of a fuzzy comparison matrix when the lower bound value of a non-normalized fuzzy weight turns out to be greater than its upper bound value, uncertainty of local fuzzy weights for incomplete fuzzy comparison matrices, and unreality of global fuzzy weights. A modified fuzzy LLSM, which is formulated as a constrained nonlinear optimization model, is therefore suggested to tackle all these problems. A numerical example is examined to show the applicability of the modified fuzzy LLSM and its advantages. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",

keywords = "Fuzzy analytic hierarchy process, Fuzzy comparison matrix, Fuzzy weights, Normalization",

author = "Wang, {Ying Ming} and Elhag, {T. M S} and Zhongsheng Hua",

year = "2006",

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AU - Elhag, T. M S

AU - Hua, Zhongsheng

PY - 2006/12/1

Y1 - 2006/12/1

N2 - This paper revisits the fuzzy logarithmic least squares method (LLSM) in the analytic hierarchy process and points out its incorrectness in the normalization of local fuzzy weights, infeasibility in deriving the local fuzzy weights of a fuzzy comparison matrix when the lower bound value of a non-normalized fuzzy weight turns out to be greater than its upper bound value, uncertainty of local fuzzy weights for incomplete fuzzy comparison matrices, and unreality of global fuzzy weights. A modified fuzzy LLSM, which is formulated as a constrained nonlinear optimization model, is therefore suggested to tackle all these problems. A numerical example is examined to show the applicability of the modified fuzzy LLSM and its advantages. © 2006 Elsevier B.V. All rights reserved.

AB - This paper revisits the fuzzy logarithmic least squares method (LLSM) in the analytic hierarchy process and points out its incorrectness in the normalization of local fuzzy weights, infeasibility in deriving the local fuzzy weights of a fuzzy comparison matrix when the lower bound value of a non-normalized fuzzy weight turns out to be greater than its upper bound value, uncertainty of local fuzzy weights for incomplete fuzzy comparison matrices, and unreality of global fuzzy weights. A modified fuzzy LLSM, which is formulated as a constrained nonlinear optimization model, is therefore suggested to tackle all these problems. A numerical example is examined to show the applicability of the modified fuzzy LLSM and its advantages. © 2006 Elsevier B.V. All rights reserved.

KW - Fuzzy analytic hierarchy process

KW - Fuzzy comparison matrix

KW - Fuzzy weights

KW - Normalization

U2 - 10.1016/j.fss.2006.08.010

DO - 10.1016/j.fss.2006.08.010

M3 - Article

VL - 157

SP - 3055

EP - 3071

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

IS - 23

ER -

A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process

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Keywords

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