Generalized Discrete Fuzzy Number and Application in Risk Evaluation

In this paper, the definition of generalized discrete fuzzy numbers is introduced, and a representation theorem of such fuzzy numbers is obtained. Based on the representation theorem, it is shown that the usual addition and multiplication which are defined by Zadeh’s extension principle do not preserve the closeness of the operation, and a new addition operation and a new multiplication operation are defined, which not only preserve the closeness of the operation, but also are easy to calculate. Then some weak orders on the generalized discrete fuzzy number space are defined, and their properties are investigated. At last, a practical example is given to show the application of the algorithmic version to rank uncertain or imprecise discrete quantity.

[1]  Enrique Herrera-Viedma,et al.  A new linguistic computational model based on discrete fuzzy numbers for computing with words , 2014, Inf. Sci..

[2]  Shyi-Ming Chen,et al.  New methods for students' evaluation using fuzzy sets , 1999, Fuzzy Sets Syst..

[3]  Florin Ionescu,et al.  Fuzzy Voronoi diagram for disjoint fuzzy numbers of dimension two , 2014, J. Intell. Fuzzy Syst..

[4]  William Voxman,et al.  Canonical representations of discrete fuzzy numbers , 2001, Fuzzy Sets Syst..

[5]  Joan Torrens,et al.  Aggregation of subjective evaluations based on discrete fuzzy numbers , 2012, Fuzzy Sets Syst..

[6]  Joan Torrens,et al.  Aggregation functions on the set of discrete fuzzy numbers defined from a pair of discrete aggregations , 2014, Fuzzy Sets Syst..

[7]  Marek Gagolewski,et al.  Nearest piecewise linear approximation of fuzzy numbers , 2013, Fuzzy Sets Syst..

[8]  Jaume Casasnovas,et al.  Maximum and Minimum of Discrete Fuzzy Numbers , 2007, CCIA.

[9]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[10]  Ta-Chung Chu,et al.  Ordering Alternatives under Fuzzy Multiple Criteria Decision Making via a Fuzzy Number Dominance Based Ranking Approach , 2013 .

[11]  Dug Hun Hong.  The law of large numbers and renewal process for T-related weighted fuzzy numbers on R0 , 2013, Inf. Sci..

[12]  Jaume Casasnovas,et al.  Lattice Properties of Discrete Fuzzy Numbers under Extended Min and Max , 2009, IFSA/EUSFLAT Conf..

[13]  Shyi-Ming Chen,et al.  Evaluating Students' Answerscripts Using Fuzzy Numbers Associated With Degrees of Confidence , 2008, IEEE Trans. Fuzzy Syst..

[14]  Abdul Rahman M. Alamoud,et al.  A novel VLSI architecture for a fuzzy inference processor using Gaussian-shaped membership function , 2013, J. Intell. Fuzzy Syst..

[15]  Joan Torrens,et al.  Residual implications on the set of discrete fuzzy numbers , 2013, Inf. Sci..

[16]  Jaume Casasnovas,et al.  Discrete Fuzzy Numbers Defined on a Subset of Natural Numbers , 2007, IFSA.

[17]  T.Y.T. Chan.  Fast naive euclidean concept learning , 2002, IEEE International Conference on Systems, Man and Cybernetics.

[18]  Jaume Casasnovas,et al.  Extension of discrete t-norms and t-conorms to discrete fuzzy numbers , 2011, Fuzzy Sets Syst..

[19]  Lotfi A. Zadeh,et al.  On Fuzzy Mapping and Control , 1996, IEEE Trans. Syst. Man Cybern..

[20]  Shuo-Yan Chou,et al.  An Improved Ranking Method for Fuzzy Numbers Based on the Centroid-Index , 2012 .

[21]  Peng Shi,et al.  Representation of Uncertain Multichannel Digital Signal Spaces and Study of Pattern Recognition Based on Metrics and Difference Values on Fuzzy $n$ -Cell Number Spaces , 2009, IEEE Transactions on Fuzzy Systems.

[22]  Jaume Casasnovas,et al.  On the addition of discrete fuzzy numbers , 2006 .

[23]  Peng Shi,et al.  Fuzzy $n$-Ellipsoid Numbers and Representations of Uncertain Multichannel Digital Information , 2014, IEEE Transactions on Fuzzy Systems.

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

[25]  D. Dubois,et al.  Towards fuzzy differential calculus part 1: Integration of fuzzy mappings , 1982 .

[26]  Juan Moreno García,et al.  Fuzzy numbers from raw discrete data using linear regression , 2013, Inf. Sci..

[27]  Liangjian Hu,et al.  Perturbation analysis of fuzzy linear systems , 2010, Inf. Sci..

[28]  Jiang-Xia Nan,et al.  Intuitionistic Fuzzy Programming Models for Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers , 2014 .