CLC number: O212.5
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2019-02-15
Cited: 0
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Renato A. Krohling, André G. C. Pacheco, Guilherme A. dos Santos. TODIM and TOPSIS with Z-numbers[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(2): 283-291.
@article{title="TODIM and TOPSIS with Z-numbers",
author="Renato A. Krohling, André G. C. Pacheco, Guilherme A. dos Santos",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="20",
number="2",
pages="283-291",
year="2019",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1700434"
}
%0 Journal Article
%T TODIM and TOPSIS with Z-numbers
%A Renato A. Krohling
%A André G. C. Pacheco
%A Guilherme A. dos Santos
%J Frontiers of Information Technology & Electronic Engineering
%V 20
%N 2
%P 283-291
%@ 2095-9184
%D 2019
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1700434
TY - JOUR
T1 - TODIM and TOPSIS with Z-numbers
A1 - Renato A. Krohling
A1 - André G. C. Pacheco
A1 - Guilherme A. dos Santos
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 20
IS - 2
SP - 283
EP - 291
%@ 2095-9184
Y1 - 2019
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1700434
Abstract: In this paper, we present an approach that can handle z-numbers in the context of multi-criteria decision-making problems. The concept of z-number as an ordered pair Z=(A, B) of fuzzy numbers A and B is used, where A is a linguistic value of a variable of interest and B is a linguistic value of the probability measure of A. As human beings, we communicate with each other by means of natural language using sentences like “the journey from home to university most likely takes about half an hour.” The z-numbers are converted to fuzzy numbers. Then the Z-TODIM and Z-TOPSIS are presented as a direct extension of the fuzzy TODIM and fuzzy TOPSIS, respectively. The proposed methods are applied to two case studies and compared with the standard approach using crisp values. The results obtained show the feasibility of the approach.
[1]Aliev RA, Alizadeh AV, Huseynov OH, 2015. The arithmetic of discrete Z-numbers. Inform Sci, 290:134-155.
[2]Aliev RA, Huseynov OH, Zeinalova LM, 2016. The arithmetic of continuous Z-numbers. Inform Sci, 373:441-460.
[3]Atanassov KT, 1986. Intuitionistic fuzzy sets. Fuzzy Set Syst, 20(1):87-96.
[4]Azadeh A, Saberi M, Atashbar NZ, et al., 2013. Z-AHP: a Z-number extension of fuzzy analytical hierarchy process. Proc 7th IEEE Int Conf on Digital Ecosystems and Technologies, p.141-147.
[5]Chen CT, 2000. Extensions of the TOPSIS for group decision- making under fuzzy environment. Fuzzy Set Syst, 114(1): 1-9.
[6]Chen TY, Tsao CY, 2008. The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Set Syst, 159(11):1410-1428.
[7]Dubois D, Prade H, 1980. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, USA.
[8]Dymova L, Sevastjanov P, Tikhonenko A, 2013. A direct interval extension of TOPSIS method. Expert Syst Appl, 40(12):4841-4847.
[9]Fan ZP, Zhang X, Chen FD, et al., 2013. Extended TODIM method for hybrid multiple attribute decision making problems. Knowl-Based Syst, 42:40-48.
[10]Gomes LFAM, Lima MMPP, 1992. TODIM: basics and application to multicriteria ranking of projects with environmental impacts. Found Comput Decis Sci, 16(4): 113-127.
[11]Gomes LFAM, Rangel LAD, 2009. An application of the TODIM method to the multicriteria rental evaluation of residential properties. Eur J Oper Res, 193(1):204-211.
[12]Hwang CL, Yoon K, 1981. Multiple Attributes Decision Making Methods and Applications. Springer, Berlin, Germany.
[13]Jahanshahloo GR, Lotfi FH, Davoodi AR, 2009. Extension of TOPSIS for decision-making problems with interval data: interval efficiency. Math Comput Model, 49(5-6):1137- 1142.
[14]Kang BY, Wei DJ, Li Y, et al., 2012a. Decision making using Z-numbers under uncertain environment. J Inform Comput Sci, 8(7):2807-2814.
[15]Kang BY, Wei DJ, Li Y, et al., 2012b. A method of converting Z-number to classical fuzzy number. J Inform Comput Sci, 9(3):703-709.
[16]Krohling RA, Campanharo VC, 2011. Fuzzy TOPSIS for group decision making: a case study for accidents with oil spill in the sea. Expert Syst Appl, 38(4):4190-4197.
[17]Krohling RA, de Souza TTM, 2012. Combining prospect theory and fuzzy numbers to multi-criteria decision making. Expert Syst Appl, 39(13):11487-11493.
[18]Krohling RA, Pacheco AGC, Siviero ALT, 2013. IF-TODIM: an intuitionistic fuzzy TODIM for decision making. Knowl-Based Syst, 53:142-146.
[19]Li J, Wang JQ, 2017. Multi-criteria outranking methods with hesitant probabilistic fuzzy sets. Cogn Comput, 9(5): 611-625.
[20]Lourenzutti R, Krohling RA, 2013. A study of TODIM in a intuitionistic fuzzy and random environment. Expert Syst Appl, 40(16):6459-6468.
[21]Lourenzutti R, Krohling RA, 2014. The Hellinger distance in multicriteria decision making: an illustration to the TOPSIS and TODIM methods. Expert Syst Appl, 41(9): 4414-4421.
[22]Lourenzutti R, Krohling RA, 2016. A generalized TOPSIS method for group decision making with heterogeneous information in a dynamic environment. Inform Sci, 330: 1-18.
[23]Lourenzutti R, Krohling RA, Reformat MZ, 2017. Choquet based TOPSIS and TODIM for dynamic and heterogeneous decision making with criteria interaction. Inform Sci, 408:41-69.
[24]Mahdavi I, Mahdavi-Amiri N, Heidarzade A, et al., 2008. Designing a model of fuzzy TOPSIS in multiple criteria decision making. Appl Math Comput, 206(2):607-617.
[25]Park JH, Park IY, Kwun YC, et al., 2011. Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment. Appl Math Model, 35(5):2544-2556.
[26]Patel P, Rahimi S, Khorasani E, 2015. Applied Z-numbers. Proc Annual Conf of the North American Fuzzy Information Processing Society held jointly with 5th World Conf on Soft Computing, p.1-6.
[27]Peng HG, Wang JQ, 2017. Hesitant uncertain linguistic Z-numbers and their application in multi-criteria group decision-making problems. Int J Fuzzy Syst, 19(5):1300- 1316.
[28]Peng HG, Zhang HY, Wang JQ, 2018. Probability multi- valued neutrosophic sets and its application in multi- criteria group decision-making problems. Neur Comput Appl, 30(2):563-583.
[29]Wang J, Liu SY, Zhang J, 2005. An extension of TOPSIS for fuzzy MCDM based on vague set theory. J Syst Sci Syst Eng, 14(1):73-84.
[30]Wang J, Wang JQ, Zhang HY, et al., 2017. Distance-based multi-criteria group decision-making approaches with multi-hesitant fuzzy linguistic information. Int J Inform Technol Dec Mak, 16(4):1069-1099.
[31]Wang JG, Wang RQ, 2008. Hybrid random multi-criteria decision-making approach with incomplete certain information. Proc Chinese Control and Decision Conf, p.1444-1448.
[32]Wang TC, Lee HD, 2009. Developing a fuzzy TOPSIS approach based on subjective weights and objective weights. Expert Syst Appl, 36(5):8980-8985.
[33]Xiao ZQ, 2014. Application of Z-numbers in multi-criteria decision making. Proc Int Conf on Informative and Cybernetics for Computational Social Systems, p.91-95.
[34]Xiong WT, Qi H, 2010. A extended TOPSIS method for the stochastic multi-criteria decision making problem through interval estimation. Proc 2nd Int Workshop on Intelligent Systems and Applications, p.1-4.
[35]Ye F, 2010. An extended TOPSIS method with interval-valued intuitionistic fuzzy numbers for virtual enterprise partner selection. Expert Syst Appl, 37(10):7050-7055.
[36]Yu SM, Wang J, Wang JQ, 2018. An extended TODIM approach with intuitionistic linguistic numbers. Int Trans Oper Res, 25(3):781-805.
[37]Yue ZL, 2014. TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting. Inform Sci, 277: 141-153.
[38]Zadeh LA, 1965. Fuzzy sets. Inform Contr, 8(3):338-353.
[39]Zadeh LA, 2011. A note on Z-numbers. Inform Sci, 181(14): 2923-2932.
[40]Zhang HY, Peng HG, Wang J, et al., 2017. An extended out-ranking approach for multi-criteria decision-making problems with linguistic intuitionistic fuzzy numbers. Appl Soft Comput, 59:462-474.
[41]Zhang XL, Xu ZS, 2014. The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowl-Based Syst, 61:48-58.
[42]Zhou H, Wang JQ, Zhang HY, 2017. Stochastic multicriteria decision-making approach based on SMAA-ELECTRE with extended gray numbers. Int Trans Oper Res, in press.
[43]Zimmermann HJ, 1991. Fuzzy Set Theory and Its Applications. Kluwer Academic P ublishers, Boston, USA.
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