Abstract
Fuzzy set is commonly explored to deal with uncertainty generally involved in decision-making process. Moreover, ranking of fuzzy numbers plays efficient role in the process in order to adopt appropriate action by a decision-maker in any real-world problems under uncertain environment. A few numbers of ranking approaches have been encountered in last few decades. However, it is observed that the existing approaches are more often situation dependent and have lots of drawbacks. In this regard, this paper presents a straightforward general approach based on the concept of the exponential area of the input fuzzy numbers. The outputs produced by this present approach are more efficient in comparison to the other ranking approaches and successfully work in all situations. The efficiency of the approach has been showcased by comparing with existing recent approaches. Furthermore, the ranking approach has been successfully applied in medical investigation problem and observed that the results obtained by the approach corroborate the analytical result and human intuition as well.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Zadeh, L.A.: Fuzzy sets. Inf. Control. 8, 338–356 (1965)
Fortemps, P., Roubens, M.: Ranking and defuzzification methods based on area compensation. Fuzzy Sets Syst. 82(3), 319–330 (1996)
Wang, Y.J., Lee, H.S.: The revised method of ranking fuzzy numbers with an area between the centroid and original points. Comput. Math. Appl. 55(9), 2033–2042 (2008)
Nejad, A.M., Mashinchi, M.: Ranking fuzzy numbers based on the areas on the left and the right sides of fuzzy number. Comput. Math. Appl. 61(2), 431–442 (2011)
Yu, V.F., Chi, H.T.X., Dat, L.Q., Phuc, P.N.K., Shen, C.W.: Ranking generalized fuzzy numbers in fuzzy decision making based on the left and right transfer coefficients and areas. Appl. Math. Modell. 37(16–17), 8106–8117 (2013)
Wang, Z.X., Liu, Y.J., Fan, Z.P., Feng, B.: Ranking L-R fuzzy number based on deviation degree. Inf. Sci. 179(13), 2070–2077 (2009)
Asady, B.: The revised method of ranking L-R fuzzy number based on deviation degree. Expert Syst. Appl. 37(7), 5056–5060 (2010)
Hajjari, T., Abbasbandy, S.: A note on the revised method of ranking L-R fuzzy number based on deviation degree. Expert Syst. Appl. 38(10), 13491–13492 (2011)
Yu, V.F., Chi, H.T.X., Shen, C.W.: Ranking fuzzy numbers based on epsilon-deviation degree. Appl. Soft Comput. 13(8), 3621–3627 (2013)
Chu, T.C., Tsao, C.T.: Ranking fuzzy numbers with an area between the centroid point and original point. Comput. Math. Appl. 43(1–2), 111–117 (2002)
Wang, Y.M., Yang, J.B., Xu, D.L., Chin, K.S.: On the centroids of fuzzy numbers. Fuzzy Sets Syst. 157(7), 919–926 (2006)
Cheng, C.H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst. 95(3), 307–317 (1998)
Abbasbandy, S., Asady, B.: Ranking of fuzzy numbers by sign distance. Inf. Sci. 176(16), 2405–2416 (2006)
Asady, B., Zendehnam, A.: Ranking fuzzy numbers by distance minimization. Appl. Math. Modell. 31(11), 2589–2598 (2007)
Liou, T.S., Wang, M.J.J.: Ranking fuzzy numbers with integral value. Fuzzy Sets Syst. 50(3), 247–255 (1992)
Chen, C.C., Tang, H.C.: Ranking nonnormal p-norm trapezoidal fuzzy numbers with integral value. Comput. Math. Appl. 56(9), 2340–2346 (2008)
Yu, V.F., Dat, L.Q.: An improved ranking method for fuzzy numbers with integral values. Appl. Soft Comput. 14(Part C), 603–608 (2014)
Kim, K., Park, K.S.: Ranking fuzzy numbers with index of optimism. Fuzzy Sets Syst. 35(2), 143–150 (1990)
Choobineh, F., Li, H.: An index for ordering fuzzy numbers. Fuzzy Sets Syst. 54(3), 287–294 (1993)
Garcia, M.S., Lamata, M.T.: A modification of the index of liou and wang for ranking fuzzy numbers. Int. J. Uncert. Fuzziness Knowledge-Based Syst. 15(04), 411–424 (2007)
Kumar, A., Singh, P., Kaur, A., Kaur, P.: A new approach for ranking nonnormal p-norm trapezoidal fuzzy numbers. Comput. Math. Appl. 61(4), 881–887 (2011)
Chutia, R., Gogoi, R., Datta, D.: Ranking p-norm generalised fuzzy numbers with different left height and right height using integral values. Math. Sci. 9(1), 1–9 (2015)
Chen, S.J., Chen, S.M.: Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Appl. Intell. 26(1), 1–11 (2007)
Chen, S.M., Chen, J.H.: Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Syst. Appl. 36(3, Part 2), 6833–6842 (2009)
Chen, S.M., Sanguansat, K.: Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers. Expert Syst. Appl. 38(3), 2163–2171 (2011)
Abbasbandy, S., Hajjari, T.: A new approach for ranking of trapezoidal fuzzy numbers. Comput. Math. Appl. 57(3), 413–419 (2009)
Dutta, P., Dash S.R.: Medical decision making via the arithmetic of generalized triangular fuzzy numbers. Open Cybern. Syst. J. 12(1) (2018)
Dutta, P., Boruah, H., Ali, T.: Fuzzy arithmetic with and without using \(\alpha \)-cut method: a comparative study. Int. J. Latest Trends Comput. 2(1), 99–107 (2011)
Yager, R.R.: Ranking fuzzy subsets over the unit interval. In: 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes, January, pp. 1435–1437 (1978)
Nasseri, S.H., Zadeh, M.M., Kardoost, M., Behmanesh, E.: Ranking fuzzy quantities based on the angle of the reference functions. Appl. Math. Modell. 37(22), 9230–9241 (2013)
Rezvani, S.: Ranking generalized exponential trapezoidal fuzzy numbers based on variance. Appl. Math. Computat. 262, 191–198 (2015)
Chutia, R., Chutia, B.: A new method of ranking parametric form of fuzzy numbers using value and ambiguity. Appl. Soft Comput. 52, 1154–1168 (2017)
Chen, S.M., Munif, A., Chen, G.S., Liu, V., Kuo, B.C.: Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. Expert Syst. Appl. 39(7), 6320–6334 (2012)
Zadeh, L.A.: Biological application of the theory of fuzzy sets and systems. In: Proctor, L.D. (ed.) Biocybernetics of the Central Nervous System, pp. 199–212. Little Brown, Boston, MA (1969)
Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control. 30, 38–48 (1976)
Sanchez, E.: Medical diagnosis and composite fuzzy relations. In: Gupta, M.M., Ragade, R.K., Yager, R.R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 437–444. North-Holland, Amsterdam (1979)
Çelik, Y., Yamak, S.: Fuzzy soft set theory applied to medical diagnosis using fuzzy arithmetic operations. J. Inequalities Appl. pp. 1–9 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Dutta, P. (2020). A Straightforward Advanced Ranking Approach of Fuzzy Numbers. In: Satapathy, S., Bhateja, V., Mohanty, J., Udgata, S. (eds) Smart Intelligent Computing and Applications . Smart Innovation, Systems and Technologies, vol 159. Springer, Singapore. https://doi.org/10.1007/978-981-13-9282-5_45
Download citation
DOI: https://doi.org/10.1007/978-981-13-9282-5_45
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-9281-8
Online ISBN: 978-981-13-9282-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)