Ranking Triangular Fuzzy Numbers Using Fuzzy Set Inclusion Index

In this paper, an original ranking operator is introduced for Triangular Fuzzy Numbers. The purpose is to elaborate fast and efficient algorithms dealing with complicated operations and big data in fuzzy decision-making. The proposed ranking operator takes advantage of the topological relationship of two triangles, besides the Inclusion Index concept — which is an index indicating the Degree of Inclusion in the MIN of two Fuzzy Numbers, a way to approach the ”strongly included in”. Consequently, the ranking result can mostly be deduced directly, allowing an efficient ranking process.

[1]  B. Asady,et al.  RANKING FUZZY NUMBERS BY DISTANCE MINIMIZATION , 2007 .

[2]  László T. Kóczy,et al.  Approximate reasoning by linear rule interpolation and general approximation , 1993, Int. J. Approx. Reason..

[3]  Saeid Abbasbandy,et al.  Ranking of fuzzy numbers by sign distance , 2006, Inf. Sci..

[4]  Sylvie Galichet,et al.  MIN and MAX Operators for Fuzzy Intervals and Their Potential Use in Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

[5]  Tofigh Allahviranloo,et al.  An approach for ranking of fuzzy numbers , 2012, Expert Syst. Appl..

[6]  Ronald R. Yager,et al.  Ranking Fuzzy Numbers Using a-Weighted Valuations , 2000, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[7]  T. Chu,et al.  Ranking fuzzy numbers with an area between the centroid point and original point , 2002 .

[8]  Ching-Hsue Cheng,et al.  A new approach for ranking fuzzy numbers by distance method , 1998, Fuzzy Sets Syst..

[9]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

[10]  Gloria Bordogna,et al.  Fuzzy inclusion in database and information retrieval query interpretation , 1996, SAC '96.

[11]  Wen-June Wang,et al.  A simple computation of MIN and MAX operations for fuzzy numbers , 2002, Fuzzy Sets Syst..

[12]  Ying-Ming Wang,et al.  Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets , 2009, Comput. Ind. Eng..

[13]  Azedine Boulmakoul,et al.  An overview of a multiagent-based simulation system for dynamic management of risk related to Dangerous Goods Transport , 2013, 2013 IEEE International Systems Conference (SysCon).

[14]  A. Boulmakoul.  Generalized path-finding algorithms on semirings and the fuzzy shortest path problem , 2004 .

[15]  Etienne E. Kerre,et al.  Reasonable properties for the ordering of fuzzy quantities (II) , 2001, Fuzzy Sets Syst..

[16]  Jee-Hyong Lee,et al.  A method for ranking fuzzy numbers and its application to decision-making , 1999, IEEE Trans. Fuzzy Syst..

[17]  Shan-Huo Chen.  Ranking fuzzy numbers with maximizing set and minimizing set , 1985 .

[18]  Hsuan-Shih Lee,et al.  The revised method of ranking fuzzy numbers with an area between the centroid and original points , 2008, Comput. Math. Appl..

[19]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[20]  F. Choobineh,et al.  An index for ordering fuzzy numbers , 1993 .

[21]  R. Yager,et al.  On ranking fuzzy numbers using valuations , 1999 .

[22]  Jian-Bo Yang,et al.  On the centroids of fuzzy numbers , 2006, Fuzzy Sets Syst..

[23]  Azedine Boulmakoul,et al.  Fuzzy graphs modelling for HazMat telegeomonitoring , 2006, Eur. J. Oper. Res..

[24]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[25]  Ying Luo,et al.  Area ranking of fuzzy numbers based on positive and negative ideal points , 2009, Comput. Math. Appl..

[26]  Jing-Shing Yao,et al.  Ranking fuzzy numbers based on decomposition principle and signed distance , 2000, Fuzzy Sets Syst..

[27]  Ching-Hsue Cheng,et al.  Evaluating weapon systems using ranking fuzzy numbers , 1999, Fuzzy Sets Syst..

[28]  R. Sacile,et al.  A decentralised control model for the risk-based management of dangerous good transport flows on road , 2012, 2012 IEEE International Systems Conference SysCon 2012.

[29]  Shuo-Yan Chou,et al.  A revised method for ranking fuzzy numbers using maximizing set and minimizing set , 2011, Comput. Ind. Eng..

[30]  Saeid Abbasbandy,et al.  A new approach for ranking of trapezoidal fuzzy numbers , 2009, Comput. Math. Appl..