On a canonical representation of fuzzy numbers

Abstract Fuzzy numbers, and more generally linguistic values, are approximate assessments, given by experts and accepted by decision-makers when obtaining more accurate values is impossible or unnecessary. To simplify the task of representing and handling fuzzy numbers, several authors have introduced real indices in order to capture the information contained in a fuzzy number. In this paper we propose two parameters, value and ambiguity, for this purpose. We use these parameters to obtain canonical representations and to deal with fuzzy numbers in decision-making problems. Several examples illustrate these ideas.

[1]  G. Bortolan,et al.  The problem of linguistic approximation in clinical decision making , 1988, Int. J. Approx. Reason..

[2]  Ramesh C. Jain.  Tolerance analysis using fuzzy sets , 1976 .

[3]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[4]  B. Hutton.  Normality in fuzzy topological spaces , 1975 .

[5]  P. Yu.  Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives , 1974 .

[6]  M. Vila,et al.  A procedure for ranking fuzzy numbers using fuzzy relations , 1988 .

[7]  D. Dubois,et al.  Fuzzy real algebra: Some results , 1979 .

[8]  Milan Mares,et al.  How to handle fuzzy-quantities? , 1977, Kybernetika.

[9]  E. Sanchez.  Solution of fuzzy equations with extended operations , 1984 .

[10]  L. P..  Cone Convexity , Cone Extreme Points , and Nondominated Solutions in Decision Problems with Multiobjectives 1 , .

[11]  D. Dubois,et al.  Additions of interactive fuzzy numbers , 1981 .

[12]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[13]  Piero P. Bonissone,et al.  Editorial: Reasoning with Uncertainty in Expert Systems , 1985, Int. J. Man Mach. Stud..

[14]  Piero P. Bonissone,et al.  Selecting Uncertainty Calculi and Granularity: An Experiment in Trading-off Precision and Complexity , 1985, UAI.

[15]  R. Yager.  On the lack of inverses in fuzzy arithmetic , 1980 .

[16]  Huibert Kwakernaak,et al.  Rating and ranking of multiple-aspect alternatives using fuzzy sets , 1976, Autom..

[17]  Lotfi A. Zadeh,et al.  Please Scroll down for Article International Journal of General Systems Fuzzy Sets and Systems* Fuzzy Sets and Systems* , 2022 .

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

[19]  A. J. Klein,et al.  Generalizing the L-fuzzy unit interval , 1984 .

[20]  Stephen E. Rodabaugh,et al.  Separation axioms and the fuzzy real lines , 1983 .

[21]  Elie Sanchez.  NON STANDARD FUZZY ARITHMETIC , 1994 .

[22]  Milan Mares,et al.  On fuzzy-quantities with real and integer values , 1977, Kybernetika.

[23]  S. E. Rodabaugh.  Fuzzy addition in the L-fuzzy real line , 1982 .

[24]  E. Czogala,et al.  Associative monotonic operations in fuzzy set theory , 1984 .

[25]  R. Lowen,et al.  On (R (L), o) , 1983 .

[26]  I. M. Hanafy.  δ-COMPACTNESS IN FUZZY TOPOLOGICAL SPACES , 2000 .