A New Method for Ranking triangular Fuzzy numbers

The ranking and comparing of fuzzy numbers have important practical uses, such as in risk analysis problems, decision-making, optimization, forecasting, socioeconomic systems, control and certain other fuzzy application systems. Several methods for ranking fuzzy numbers have been widely-discussed though most of them have shortcomings. In this paper, we present a new method for ranking triangular fuzzy numbers based on their incenter and inradius. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method.

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

[2]  Shichao Zhang,et al.  A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers , 2009, 2009 IEEE International Conference on Granular Computing.

[3]  H. Maeda,et al.  Fuzzy decision analysis in the development of centralized regional energy control systems , 1983 .

[4]  A. Baragar A Survey of Classical and Modern Geometries: With Computer Activities , 2000 .

[5]  R. Yager On a general class of fuzzy connectives , 1980 .

[6]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations , 2008, Expert Syst. Appl..

[7]  Nazirah Ramli,et al.  A COMPARATIVE ANALYSIS OF CENTROID METHODS IN RANKING FUZZY NUMBERS , 2009 .

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

[9]  Shyi-Ming Chen,et al.  A new method for analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers , 2009, 2009 International Conference on Machine Learning and Cybernetics.

[10]  R. Nelsen Heron's Formula via Proofs without Words , 2001 .

[11]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on ranking fuzzy numbers using alpha-cuts, belief features and signal/noise ratios , 2009, Expert Syst. Appl..

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

[13]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers , 2007, Applied Intelligence.

[14]  A. Ungar Barycentric calculus in euclidean and hyperbolic geometry: a comparative introduction , 2010 .

[15]  Ramesh Jain,et al.  DECISION MAKING IN THE PRESENCE OF FUZZY VARIABLES , 1976 .

[16]  B. Agard,et al.  Please Scroll down for Article International Journal of Production Research Improved Fuzzy Ranking Procedure for Decision Making in Product Design Improved Fuzzy Ranking Procedure for Decision Making in Product Design , 2022 .

[17]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads , 2009, Expert Syst. Appl..