A Novel Triangular Fuzzy Analytic Hierarchy Process

Triangular fuzzy multiplicative preference relation (TFMPR) is a widely used preference representation framework in the fuzzy analytic hierarchy process (FAHP). In this article, we develop a triangular fuzzy multiplication-based equation to characterize transitivity among original fuzzy assessments...

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Published inIEEE transactions on fuzzy systems Vol. 29; no. 7; pp. 2032 - 2046
Main Author Wang, Zhou-Jing
Format Journal Article
LanguageEnglish
Published New York IEEE 01.07.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Acceptability
Analytic hierarchy process
Analytical models
Biological system modeling
Computational modeling
Consistency
Eigenvectors
Exact solutions
fuzzy analytic hierarchy process (FAHP)
geometric consistency index (GCI)
Indexes
Lagrange multiplier
Least squares
Linguistics
logarithmic least square
Mathematical analysis
Mathematical model
Multiplication
triangular fuzzy multiplicative preference relation (TFMPR)
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Abstract Triangular fuzzy multiplicative preference relation (TFMPR) is a widely used preference representation framework in the fuzzy analytic hierarchy process (FAHP). In this article, we develop a triangular fuzzy multiplication-based equation to characterize transitivity among original fuzzy assessments in a consistent TFMPR. A geometric consistency index is then proposed to measure the inconsistency of TFMPRs. By capturing row fuzziness proportionalities and the difference between the row increasing and decreasing part fuzziness indices, this article establishes two logarithmic least square models to find normalized fuzzy weights from two kinds of TFMPRs. The two logarithmic least square models are further integrated into one whose analytic solution is found by the method of Lagrange multipliers. A novel method is put forward to check the acceptability of TFMPRs by both examining acceptable consistency and acceptable fuzziness. This article devises a parametric defuzzification approach to obtain the real-valued weights of criteria for aggregating the local normalized fuzzy weights into the global fuzzy weights in the triangular FAHP. A comparative analysis of the proposed model with existing fuzzy eigenvector methods and fuzzy average methods is carried out by a numerical example with four TFMPRs to clarify its validity and merits. An outstanding teacher award selection problem is provided to show the practicality of the proposed triangular FAHP.
AbstractList Triangular fuzzy multiplicative preference relation (TFMPR) is a widely used preference representation framework in the fuzzy analytic hierarchy process (FAHP). In this article, we develop a triangular fuzzy multiplication-based equation to characterize transitivity among original fuzzy assessments in a consistent TFMPR. A geometric consistency index is then proposed to measure the inconsistency of TFMPRs. By capturing row fuzziness proportionalities and the difference between the row increasing and decreasing part fuzziness indices, this article establishes two logarithmic least square models to find normalized fuzzy weights from two kinds of TFMPRs. The two logarithmic least square models are further integrated into one whose analytic solution is found by the method of Lagrange multipliers. A novel method is put forward to check the acceptability of TFMPRs by both examining acceptable consistency and acceptable fuzziness. This article devises a parametric defuzzification approach to obtain the real-valued weights of criteria for aggregating the local normalized fuzzy weights into the global fuzzy weights in the triangular FAHP. A comparative analysis of the proposed model with existing fuzzy eigenvector methods and fuzzy average methods is carried out by a numerical example with four TFMPRs to clarify its validity and merits. An outstanding teacher award selection problem is provided to show the practicality of the proposed triangular FAHP.
Author Wang, Zhou-Jing
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  organization: School of Information, Zhejiang University of Finance and Economics, Hangzhou, China
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Cites_doi 10.1109/TFUZZ.2016.2646749
10.1016/0377-2217(95)00300-2
10.1007/s10479-016-2166-8
10.1007/s40815-017-0333-y
10.1007/s40815-019-00711-0
10.1016/j.tourman.2019.103961
10.1016/j.inffus.2013.04.002
10.1109/TFUZZ.2018.2856125
10.1016/S0165-0114(83)80082-7
10.1016/j.ins.2015.03.074
10.1016/j.ejor.2017.05.041
10.1504/IJISM.2014.064353
10.1016/j.knosys.2018.09.015
10.1016/j.cie.2017.07.002
10.1016/S0377-2217(02)00255-2
10.1016/j.ejor.2005.10.057
10.1016/j.fss.2006.06.008
10.1016/j.fss.2017.02.004
10.1007/s13369-019- 04053-9
10.1016/j.fss.2011.06.003
10.1007/s40815-016-0150-8
10.1016/j.ins.2014.12.061
10.1016/j.ejor.2015.03.010
10.1016/0165-0114(85)90090-9
10.1057/jors.2013.135
10.1016/j.eswa.2016.08.064
10.3846/tede.2019.11412
10.1016/j.ejor.2013.10.019
10.1016/j.amc.2006.02.026
10.1109/TFUZZ.2012.2226893
10.1007/s10479-013-1413-5
10.1109/TFUZZ.2018.2852307
10.1016/0022-2496(85)90002-1
10.1016/j.ejor.2013.10.039
10.1016/j.fss.2016.03.006
10.1016/j.fss.2006.08.010
10.1109/TFUZZ.2017.2788881
10.1109/TFUZZ.2017.2697403
10.1016/S0165-0114(99)00155-4
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References ref35
ref13
ref34
ref12
ref37
ref15
ref36
ref14
ref31
ref30
ref33
ref11
ref32
ref10
krej?í (ref29) 2017; 315
ref2
ref39
ref17
ref38
ref16
saaty (ref4) 1980
ref19
ref18
ref24
ref23
ref26
brunelli (ref1) 2014
ref25
ref20
ref41
ref22
ref21
ref28
ref27
ref8
ref7
ref9
ref3
ref6
ref5
ref40
References_xml – ident: ref33
  doi: 10.1109/TFUZZ.2016.2646749
– ident: ref36
  doi: 10.1016/0377-2217(95)00300-2
– ident: ref18
  doi: 10.1007/s10479-016-2166-8
– ident: ref38
  doi: 10.1007/s40815-017-0333-y
– ident: ref20
  doi: 10.1007/s40815-019-00711-0
– year: 1980
  ident: ref4
  publication-title: The Analytic Hierarchy Process Planning Priority Setting Resource Allocation
– ident: ref8
  doi: 10.1016/j.tourman.2019.103961
– ident: ref40
  doi: 10.1016/j.inffus.2013.04.002
– ident: ref6
  doi: 10.1109/TFUZZ.2018.2856125
– ident: ref9
  doi: 10.1016/S0165-0114(83)80082-7
– ident: ref26
  doi: 10.1016/j.ins.2015.03.074
– ident: ref2
  doi: 10.1016/j.ejor.2017.05.041
– ident: ref28
  doi: 10.1504/IJISM.2014.064353
– ident: ref31
  doi: 10.1016/j.knosys.2018.09.015
– ident: ref21
  doi: 10.1016/j.cie.2017.07.002
– ident: ref13
  doi: 10.1016/S0377-2217(02)00255-2
– ident: ref14
  doi: 10.1016/j.ejor.2005.10.057
– year: 2014
  ident: ref1
  publication-title: Introduction to the Analytic Hierarchy Process
– ident: ref39
  doi: 10.1016/j.fss.2006.06.008
– ident: ref24
  doi: 10.1016/j.fss.2017.02.004
– ident: ref12
  doi: 10.1007/s13369-019- 04053-9
– ident: ref5
  doi: 10.1016/j.fss.2011.06.003
– ident: ref25
  doi: 10.1007/s40815-016-0150-8
– ident: ref32
  doi: 10.1016/j.ins.2014.12.061
– ident: ref17
  doi: 10.1016/j.ejor.2015.03.010
– ident: ref10
  doi: 10.1016/0165-0114(85)90090-9
– ident: ref19
  doi: 10.1057/jors.2013.135
– ident: ref11
  doi: 10.1016/j.eswa.2016.08.064
– ident: ref7
  doi: 10.3846/tede.2019.11412
– ident: ref16
  doi: 10.1016/j.ejor.2013.10.019
– ident: ref30
  doi: 10.1016/j.amc.2006.02.026
– ident: ref34
  doi: 10.1109/TFUZZ.2012.2226893
– ident: ref15
  doi: 10.1007/s10479-013-1413-5
– ident: ref22
  doi: 10.1109/TFUZZ.2018.2852307
– ident: ref35
  doi: 10.1016/0022-2496(85)90002-1
– ident: ref23
  doi: 10.1016/j.ejor.2013.10.039
– volume: 315
  start-page: 26
  year: 2017
  ident: ref29
  article-title: Fuzzy eigenvector method for obtaining normalized fuzzy weights from fuzzy pairwise comparison matrices
  publication-title: Fuzzy Sets Syst
  doi: 10.1016/j.fss.2016.03.006
– ident: ref37
  doi: 10.1016/j.fss.2006.08.010
– ident: ref3
  doi: 10.1109/TFUZZ.2017.2788881
– ident: ref41
  doi: 10.1109/TFUZZ.2017.2697403
– ident: ref27
  doi: 10.1016/S0165-0114(99)00155-4
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Snippet Triangular fuzzy multiplicative preference relation (TFMPR) is a widely used preference representation framework in the fuzzy analytic hierarchy process...
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SubjectTerms Acceptability
Analytic hierarchy process
Analytical models
Biological system modeling
Computational modeling
Consistency
Eigenvectors
Exact solutions
fuzzy analytic hierarchy process (FAHP)
geometric consistency index (GCI)
Indexes
Lagrange multiplier
Least squares
Linguistics
logarithmic least square
Mathematical analysis
Mathematical model
Multiplication
triangular fuzzy multiplicative preference relation (TFMPR)
Title A Novel Triangular Fuzzy Analytic Hierarchy Process
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