Open Access Journal

ISSN : 2456-1304 (Online)

International Journal of Engineering Research in Electronics and Communication Engineering(IJERECE)

Monthly Journal for Electronics and Communication Engineering

Open Access Journal

International Journal of Science Engineering and Management (IJSEM)

Monthly Journal for Science Engineering and Management

ISSN : 2456-1304 (Online)

A New Method for Ranking Fuzzy Numbers Based on Principal Component Analysis

Author : Ayad M. Ramadan 1 Goran Hidayat Kareem 2

Date of Publication :13th September 2022

Abstract: It is difficult to rank fuzzy numbers because of their ambiguous values. A few numbers of ranking techniques have been encountered in last few decades. However, existing techniques are situation-dependent which have drawbacks. In this paper we introduced a statistical technique to rank two types of fuzzy numbers, triangular and trapezoidal fuzzy numbers. This technique is the multi-dimensional scaling, more precisely the principal component analysis. Here, we presented each fuzzy numbers as a row in a matrix, then found the scale points in a low dimensions. The scale points are then reconfigured to have a unique representation. The results from this approach are obtained by comparison to the other ranking methods. The validity has been established by comparison with existing works.

Reference :

    1. Allahviranloo, Tofigh and Saneifard, Rahim (2012) "Defuzzification Method for Ranking Fuzzy Numbers Based on Center of Gravity", Iranian Journal of Fuzzy Systems, Vol. 9, No. 6, pp. 57-67.
    2. Asady, B. and Zendehnam, A. (2007) "Ranking fuzzy numbers by distance minimization", Applied Mathematical Modelling, Vol. 31, Iss. 11, pp. 2589-2598.
    3. Cheng, C. H. (1998) "A new approach for ranking fuzzy numbers by distance method", Fuzzy Sets and Systems, Vol. 95, No. 3, PP. 307– 317.
    4. Chu, Ta-Chung and Tsao, Chung-Tsen (2002) "Ranking fuzzy numbers with an area between the centroid point and original point", Computers & Mathematics with Applications, Vol. 43, Iss. 1, pp. 111–117.
    5. Chen, S. H. and Li, G. C. (2000). "Representation, ranking and distance of fuzzy number with exponential membership function using graded mean integration method".
    6. Chen, Shyi-Ming , Munif, Abdul , Chen, Guey-Shya , Liu, Hsiang-Chuan and Kuo, Bor-Chen (2012). "Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights". Expert Systems with Applications, Vol. 39, No. 7, pp. 6320-6334.
    7. K. Gnanapriya, M. Pachamuthu, and S. Kavitha, (2020) "Fuzzy Ranking Approach for Randomized Block Designs using Median Value", European Journal of Molecular & Clinical Medicine ISSN 2515-8260 Vol. 7, Iss. 3, pp. 582-590.
    8. A. Hari Ganesh and S. Jayakumar, (2014) "Ranking of Fuzzy Numbers using Radius of Gyation of Centeroids", International Journal of Basic and Sciences, Vol. 3, No. 1, PP 17-22.
    9. Jain, R., (1978) "Decision-making in the presence of a fuzzy variable". IEEE Transactions on Systems, Man and Cybernetics, Vol. 6, pp. 698-703.
    10. Joseph Adewumi, (2019) "Understanding thr Role of Eigenvectors and Eigenvalues in PCA Dimensionality Reduction". https://medium.com/@dareyadewumi650/ understanding-the-role-of-eigenvectors-and-eigenvalues-in-p ca-dimensionality-reduction-10186dad0c5c
    11. József Dombia, Tamás Jónásb, (2020) "Ranking trapezoidal fuzzy numbers using a parametric relation pair", Fuzzy Sets and Systems, Vol. 399, pp. 20-43.
    12. Mahesh Kumar (2016) "Principal Component Analysis".https://medium.com/maheshkkumar/principal-com ponent-analysis-2d11043ff324
    13. Nalla Veerraju, V. Lakshmi Prasannam, L. N. P. Kumar Rallabandi, (2020) "Defuzzification Index for Ranking of Fuzzy Numbers on the Basis of Geometric Mean" International of Intelligent Systems and Applications (IJISA), Vol. 12, No. 4, pp. 13-24.
    14. Nasseri, Hadi, F.Taleshian, Alizadeh, Z. and Vahidi, Javad. (2012) "A New Method for Ordering LR Fuzzy Numbers", The Journal of Mathematics and Computer Science, Vol. 4, No. 3, PP. 283-294.
    15. Parandin, N. and Fariborzi, M. A. (2008) "Ranking of Fuzzy Numbers by Distance Method", Journal of Applied Mathematics, Vol. 5, No. 19, pp. 47-55.
    16. Peterfreund, Erez, and Matan Garish. (2021) "Multidimensional scaling of noisy high dimensional data." Applied and Computational Harmonic Analysis Vol. 51, pp. 333-373.
    17. Ramadan, Ayad Mohammed (2021) "Ranking of Fuzzy Numbers by using Scaling Method", Passer Journal, Vol. 3, Iss. 2, pp. 137-143.
    18. Rao, P. Phani Bushan and Shankar, N. Ravi (2011) "Ranking Fuzzy Numbers with a Distance Method using Cricumcenter of Centroids and an Index of Modality", Advances in Fuzzy Systems. Vol. 2011, pp. 1-7.
    19. Rencher, A. C. (2009) "Multivariate Statistical Inference and Applications", Wiley Series in Probability and Statistics.
    20. Rezvani, Salim (2013). "Ranking exponential trapezoidal fuzzy numbers by median value". Journal of Fuzzy Set Valued Analysis, Vol. 2013, pp. 1-9.
    21. N. Rajeswari and W. Ritha, (2021) "Exploration Of Ranking Based On Statistical Beta Distribution For A Heterogeneous Server Imprecise Queue With A Slow Server Threshold", Natural Volatiles & Essential Oils, Vol. 8, No. 4, pp. 9782-9794
    22. Singh, Pushpinder (2010) "A New Approach For Ranking Of Generalized Trapezoidal Fuzzy Numbers", International Journal of Computer and Information Engineering, Vol. 68, pp. 299-302.
    23. Selvam, Parthiban and Gajivaradhan, P. (2016). " A comparative study of two factor ANOVA model under fuzzy environments using trapezoidal fuzzy numbers". Int. J. of Fuzzy Mathematical Archive, Vol. 10, No. 1, pp. 1-25. 
    24. Taheri, Mahmoud and Hesamian, Gholamreza (2017) "Non-parametric Statistical Tests for Fuzzy Observations: Fuzzy Test Statistic Approach" International Journal of Fuzzy Logic and Intelligent Systems, Vol. 17, No. 3, pp. 145-153.
    25. Wang, Ying-Ming and Luo, Ying (2009) "Area ranking of fuzzy numbers based on positive and negative idea points", Computers and Mathematics with Application, Vol. 58, Iss. 9, pp.1769-1779.
    26. Yager, Ronald R. (1981) "A procedure for ordering fuzzy subsets of the unit interval", Information Sciences, Vol. 24, Iss. 2, pp. 143–161
    27. Zadeh, L. A. (1985) "Fuzzy Sets", Information and Control, Vol. 8, No. 3, pp. 338-353

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