MCDM by Normalized Euclidean Distance in Intuitionistic Multi-Fuzzy Sets

R.Muthuraj; S.Balamurugan

doi:https://doi.org/10.14445/22315373/IJMTT-V35P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 35 | Number 1 | Year 2016 | Article Id. IJMTT-V35P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V35P503

MCDM by Normalized Euclidean Distance in Intuitionistic Multi-Fuzzy Sets

R.Muthuraj, S.Balamurugan

Citation :

R.Muthuraj, S.Balamurugan, "MCDM by Normalized Euclidean Distance in Intuitionistic Multi-Fuzzy Sets," International Journal of Mathematics Trends and Technology (IJMTT), vol. 35, no. 1, pp. 19-23, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V35P503

Abstract

In this paper we propose an efficient approach for multi-criteria decision making (MCDM) based on intuitionistic multi-fuzzy sets (IMFS). Intuitionistic multi-fuzzy set of an universe set is very useful in providing a flexible model to elaborate uncertainty and vagueness involved in decision making. In this paper we used the concept of IMFS and proposed its application in the field of determining the best mechanism under the satisfaction of rider’s aptitude by using Normalized Euclidean Distance method to measure the distance between the each mechanism of heavy motor vehicle (HMV) and each rider’s aptitude with respect to multi-criteria respectively. Finally, optimal determination is obtained by looking for the smallest distance between each rider’s aptitude and each HMV’s mechanism.

Keywords

Fuzzy set, Intuitionistic fuzzy set (IFS), Intuitionistic multi-fuzzy set (IMFS), Normalized Euclidean Distance.

References

[1] Atanassov K: Intuitionistic fuzzy sets, Springer Physica, Heidelberg (1999)
[2] Atanassov K: New operations defined over the intuitionistic fuzzy sets, Fuzzy Set. Syst., 61, 137–142 (1994)
[3] Atanassov KT: Intuitionistic fuzzy sets, Fuzzy Set. Syst, 20, 87–96 (1986)
[4] Atanassov K, Pasi G, Yager R: Intuitionistic fuzzy interpretations of multi-person multicriteria decision making, Proc. of 2002 First Intern. IEEE Symposium Intell. Syst, 1, 115–119 (2002)
[5] Blizard W.D.: Multiset theory, Notre Dame J. Formal Logic, 30(1), 36–66 (1989)
[6] De S.K., Biswas R, Roy A.R.: An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Set. Syst., 117(2),209–213 (2001)
[7] Dey S.K., Biswas R, Roy A.R.: Some operations on intuitionistic fuzzy sets, Fuzzy Set. Syst., 114, 477–484 (2000)
[8] Ejegwa P.A., Akubo A.J., Joshua O.M., Intuitionistic fuzzy set and its application in career determination via normalized Euclidean distance method, European Scientific Journal, vol.10, iss.15, pp.529-536 (May 2014)
[9] Goguen J.A.: L-fuzzy sets, J. Math. Anal. Appl., 18, 145– 174 (1967)
[10] Li D.F.: Multi attribute decision making models and methods using intuitionistic fuzzy sets. J. Comput. Syst. Sci.,70, 73–85 (2005)
[11] Li D., Cheng C., New Similarity measures of Intuitionistic fuzzy sets and application to pattern recognition, PatternRecognition Letters, 23, 221-225 (2002)
[12] Liang Z., Shi P., Similarity measures on Intuitionistic fuzzy sets, Pattern Recognition Letters, 24, 2687-2693 (2003)
[13] Lin L., Yuan X.H., Xia Z.Q.: Multi criteria fuzzy decisionmaking methods based on intuitionistic fuzzy sets, J. Comput.Syst. Sci., 73, 84–88 (2007)
[14] Liu H.W., Wang G.J.: Multi-criteria decision-making methods based on intuitionistic fuzzy sets, Eur. J. Oper. Res.,179, 220–233 (2007)
[15] Muthuraj R. and Balamurugan S., “Multi-fuzzy group and its Level subgroups”, Gen. Math. Notes, Vol. 17, No. 1, pp.74-81 (July 2013)
[16] Muthuraj R. and Balamurugan S., “Multi-anti fuzzy group and its Lower level subgroups”, Int. Journal of Engineering Research and Applications, Vol. 3, Issue 6, , pp.1498-1501 (Nov-Dec 2013)
[17] Muthuraj R. and Balamurugan S., “Some Characterization of multi-fuzzy and multi-anti fuzzy subgroup”, SVRM science journal, Volume1, Issue1, pp.36-46 (Oct-Dec 2013)
[18] Muthuraj R. and Balamurugan S., “Some Characterization of Normal Multi-fuzzy and Normal Multi-anti fuzzy Subgroup”, IOSR Journal of Mathematics (IOSR-JM), Volume 10, Issue 1 Ver. IV. , pp. 116-122 (Feb. 2014)
[19] Muthuraj R. and Balamurugan S., “Some Characterization of Multi-fuzzy group”, International Journal of Innovative Research and Development, vol.3, issue2, pp.243-257 (Feb. 2014)
[20] Muthuraj R. and Balamurugan .S, “Some Characterization of Multi-anti fuzzy group”, Researchjournali’s Journal of Mathematics, vol.1, issue1, pp.1-25 (March 2014)
[21] Muthuraj R. and Balamurugan .S, “Correspondence Theorem for normal multi-anti fuzzy subgroups”, Discovery, 21(68), pp.113-117 (July 2014)
[22] Muthuraj R. and Balamurugan S., “A Study On Multi- Fuzzy Cosets”, Journal of Uncertain Systems (Communicated)
[23] Muthuraj R. and Balamurugan S., “A Study on Intuitionistic Multi-Fuzzy Subgroups”, Intl. Jour. of Applications of Fuzzy Sets and Artificial Intelligence, Vol. 4 ,153 – 172 ( 2014)
[24] Muthuraj R. and Balamurugan S., “A Study on Intuitionistic Multi-Anti Fuzzy Subgroups”, Applied Mathematics and Sciences:An International Journal(MathSJ), (Accepted for August 2014 issue)
[25] Muthuraj R. and Balamurugan S., “Correspondence Theorem for Normal Multi-fuzzy Subgroups”, SSRG International Journal of Mathematics Trends and Technology (IJMTT), ISSN: 2231-5373, pp.1-3 (special issues 2014).
[26] Rajarajeswari P. and Uma N., On Distance and Similarity Measures of Intuitionistic Fuzzy Multi Set, IOSR Journalof Mathematics (IOSR-JM) Vol. 5, Issue 4 , 19-23 (Jan. - Feb. 2013)
[27] Rajarajeswari P. and Uma N., Hausdroff Similarity measures for Intuitionistic Fuzzy Multi Sets and Its Application in Medical diagnosis, International Journal of Mathematical Archive-4(9), 106-111 (2013)
[28] Shinoj T.K. and Sunil Jacob John, Intuitionistic Fuzzy Multisets and its Application in Medical Diagnosis, World Academy of Science, Engineering and Technology, Vol. 61 (2012)
[29] Sabu Sebastian and Ramakrishnan.T.V., Multi-fuzzy sets, International Mathematical Forum, 50, 2471-2476 (2010)
[30] Szmidt E., Kacprzyk J., Remarks on some applications of Intuitionistic fuzzy sets in decision making, Notes on IFS, 2, 22-31 ,(1996)
[31] Szmidt E., Kacprzyk J., On measuring distances between Intuitionistic fuzzy sets, Notes on IFS, Vol. 3, 1- 13 (1997)
[32] Szmidt E., Kacprzyk J., Distances between Intuitionistic fuzzy sets. Fuzzy Sets System, 114, 505-518 (2000)
[33] Xu Z.: Intuitionistic preference relations and their application in group decision making, Inform. Sci.,177, 23- 63.
[34] Yager R.R.: On the theory of bags, Int. J. Gen. Syst., 13, 23–37 (1986)
[35] Yanhong L., Olson D., Qin Z., Similarity between Intuitionistic Fuzzy sets : Comparative Analysis, PatternRecognition Letters, 28- 2, 278-285 (2007)
[36] Zadeh L.A.: Fuzzy sets. Inf. Control, 8, 338–356 (1965).