zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the extent analysis method for fuzzy AHP and its applications. (English) Zbl 1144.90011
Summary: In a paper by {\it D.Y. Chang} [Eur. J. Oper. Res. 95, No. 3, 649--655 (1996; Zbl 0926.91008)], an extent analysis method on fuzzy AHP was proposed to obtain a crisp priority vector from a triangular fuzzy comparison matrix. It is found that the extent analysis method cannot estimate the true weights from a fuzzy comparison matrix and has led to quite a number of misapplications in the literature. In this paper, we show by examples that the priority vectors determined by the extent analysis method do not represent the relative importance of decision criteria or alternatives and that the misapplication of the extent analysis method to fuzzy AHP problems may lead to a wrong decision to be made and some useful decision information such as decision criteria and fuzzy comparison matrices not to be considered. We show these problems to avoid any possible misapplications in the future.

MSC:
90B50Management decision making, including multiple objectives
WorldCat.org
Full Text: DOI
References:
[1] Bozbura, F. T.; Beskese, A.: Prioritization of organizational capital measurement indicators using fuzzy AHP, International journal of approximate reasoning 44, 124-147 (2007)
[2] Bozbura, F. T.; Beskese, A.; Kahraman, C.: Prioritization of human capital measurement indicators using fuzzy AHP, Expert systems with applications 32, 1100-1112 (2007)
[3] Bozda&gbreve, C. E.; ; Kahraman, C.; Ruan, D.: Fuzzy group decision making for selection among computer integrated manufacturing systems, Computers in industry 51, 13-29 (2003)
[4] Buckley, J. J.: Fuzzy hierarchical analysis, Fuzzy sets and systems 17, 233-247 (1985) · Zbl 0602.90002 · doi:10.1016/0165-0114(85)90090-9
[5] Büyüközkan, G.: Multi-criteria decision making for e-marketplace selection, Internet research 14, No. 2, 139-154 (2004)
[6] Büyüközkan, G.; Ertay, T.; Kahraman, C.; Ruan, D.: Determining the importance weights for the design requirements in the house of quality using the fuzzy analytic network approach, International journal of intelligent systems 19, 443-461 (2004) · Zbl 1101.68837 · doi:10.1002/int.20006
[7] Büyüközkan, G.; Kahraman, C.; Ruan, D.: A fuzzy multi-criteria decision approach for software development strategy selection, International journal of general systems 33, 259-280 (2004) · Zbl 1093.68567 · doi:10.1080/03081070310001633581
[8] Chan, F. T. S.; Kumar, N.: Global supplier development considering risk factors using fuzzy extended AHP-based approach, Omega 35, 417-431 (2007)
[9] Chang, D. Y.: Applications of the extent analysis method on fuzzy AHP, European journal of operational research 95, 649-655 (1996) · Zbl 0926.91008 · doi:10.1016/0377-2217(95)00300-2
[10] Csutora, R.; Buckley, J. J.: Fuzzy hierarchical analysis: the lamda-MAX method, Fuzzy sets and systems 120, 181-195 (2001) · Zbl 0994.90078 · doi:10.1016/S0165-0114(99)00155-4
[11] Ertay, T.; Büyüközkan, G.; Kahraman, C.; Ruan, D.: Quality function deployment implementation based on analytic network process with linguistic data: an application in automotive industry, Journal of intelligent and fuzzy systems 16, 221-232 (2005)
[12] Erensal, Y. C.; Öncan, T.; Demircan, M. L.: Determining key capabilities in technology management using fuzzy analytic hierarchy process: A case study of Turkey, Information sciences 176, 2755-2770 (2006)
[13] Kahraman, C.; Cebeci, U.; Ruan, D.: Multi-attribute comparison of catering service companies using fuzzy AHP: the case of Turkey, International journal of production economics 87, 171-184 (2004)
[14] Kahraman, C.; Cebeci, U.; Ulukan, Z.: Multi-criteria supplier selection using fuzzy AHP, Logistics information management 16, No. 6, 382-394 (2003)
[15] Kahraman, C.; Ertay, T.; Büyüközkan, G.: A fuzzy optimization model for QFD planning process using analytic network approach, European journal of operational research 171, 390-411 (2006) · Zbl 1090.90016 · doi:10.1016/j.ejor.2004.09.016
[16] Kahraman, C.; Ruan, D.; Do&gbreve, I.; An: Fuzzy group decision-making for facility location selection, Information sciences 157, 135-153 (2003) · Zbl 1049.90038
[17] Kulak, O.; Kahraman, C.: Fuzzy multi-attribute selection among transportation companies using axiomatic design and analytic hierarchy process, Information sciences 170, 191-210 (2005) · Zbl 1074.90507 · doi:10.1016/j.ins.2004.02.021
[18] Kwong, C. K.; Bai, H.: Determining the importance weights for the customer requirements in QFD using a fuzzy AHP with an extent analysis approach, IIE transactions 35, 619-626 (2003)
[19] Mikhailov, L.: Deriving priorities from fuzzy pairwise comparison judgments, Fuzzy sets and systems 134, 365-385 (2003) · Zbl 1031.90073 · doi:10.1016/S0165-0114(02)00383-4
[20] Saaty, T. L.: Multicriteria decision making: the analytic hierarchy process, (1988)
[21] Tang, Y. C.; Beynon, M.: Application and development of a fuzzy analytic hierarchy process within a capital investment study, Journal of economics and management 1, 207-230 (2005)
[22] Tolga, E.; Demircan, M. L.; Kahraman, C.: Operating system selection using fuzzy replacement analysis and analytic hierarchy process, International journal of production economics 97, 89-117 (2005)
[23] Tüysüz, F.; Kahraman, C.: Project risk evaluation using a fuzzy analytic hierarchy process: an application to information technology projects, International journal of intelligent systems 21, No. 6, 559-584 (2006) · Zbl 1104.68753 · doi:10.1002/int.20148
[24] Vaidya, O. S.; Kumar, S.: Analytic hierarchy process: an overview of applications, European journal of operational research 169, 1-29 (2006) · Zbl 1077.90542 · doi:10.1016/j.ejor.2004.04.028
[25] Van Laarhoven, P. J. M.; Pedrycz, W.: A fuzzy extension of saaty’s priority theory, Fuzzy sets and systems 11, 229-241 (1983) · Zbl 0528.90054 · doi:10.1016/S0165-0114(83)80083-9
[26] Xu, R.: Fuzzy least-squares priority method in the analytic hierarchy process, Fuzzy sets and systems 112, 359-404 (2000) · Zbl 0961.90138 · doi:10.1016/S0165-0114(97)00376-X
[27] Van Laarhoven, P. J. M.; Pedrycz, W.: A fuzzy extension of saaty’s priority theory, Fuzzy sets and systems 11, 229-241 (1983) · Zbl 0528.90054 · doi:10.1016/S0165-0114(83)80083-9
[28] Wang, Y. M.; Elhag, T. M. S.: On the normalization of interval and fuzzy weights, Fuzzy sets and systems 157, 2456-2471 (2006) · Zbl 1171.68764 · doi:10.1016/j.fss.2006.06.008
[29] Wang, Y. M.; Elhag, T. M. S.; Hua, Z. S.: A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process, Fuzzy sets and systems 157, 3055-3071 (2006) · Zbl 1114.90492 · doi:10.1016/j.fss.2006.08.010
[30] Zhu, K. J.; Jing, Y.; Chang, D. Y.: A discussion on extent analysis method and application of fuzzy AHP, European journal of operational research 116, 450-456 (1999) · Zbl 1009.90514 · doi:10.1016/S0377-2217(98)00331-2