Elementary fuzzy calculus. (English) Zbl 0626.26014

Goetschel, Roy jun.; Voxman, William

Fuzzy Sets Syst. 18, 31-43 (1986).

An extension of the Hausdorff distance is used in definitions of limit properties of fuzzy valued functions. In particular, the derivative and the definite integral of such functions are obtained with properties modelled on real analysis. The paper explains some assumptions introduced by D. Dubois and H. Prade in their consideration of fuzzy differential calculus (cf. [Fuzzy sets and systems. Theory and applications. New York etc.: Academic Press (1980; Zbl 0444.94049), pp. 106–119].

Reviewer: J.Drewniak

MSC:

26E50	Fuzzy real analysis
03E72	Theory of fuzzy sets, etc.

Keywords:

fuzzy number; fuzzy function; derivative; definite integral; fuzzy differential calculus

Citations:

Zbl 0444.94049

References:

[1]	Dubois, D., Modêles mathématiques de l’imprécis et de l’incertain en vue d’applications aux techniques d’aide à la décision, (Thèse de doctorat d’Etat (1983), Université P. Sabatier: Université P. Sabatier Toulouse) · Zbl 0546.94036
[2]	Dubois, D.; Prade, H., Operations on fuzzy numbers, Internat. J. of Systems Sci., 9, 613-626 (1978) · Zbl 0383.94045
[3]	Dubois, D.; Prade, H., Towards fuzzy differential calculus, Part 3: Differentiation, Fuzzy Sets and Systems, 8, 225-235 (1982) · Zbl 0499.28009
[4]	Goetschel, R.; Voxman, W., Topological properties of fuzzy numbers, Fuzzy Sets and Systems, 9, 87-99 (1983) · Zbl 0521.54001
[5]	Goetschel, R.; Voxman, W., Eigen fuzzy number sets, Fuzzy Sets and Systems, 16, 75-85 (1985) · Zbl 0581.04007
[6]	Rizzi, M., Sélection et classement d’actions en avenir incertain, Document du LAMSADE No. 14 (1981)