Abstract
The purpose of this paper is to critically examine the use of fuzzy arithmetic in dealing with fuzzy systems. It is argued that the well-known overestimation and other questionable results of standard fuzzy arithmetic have one common cause: constraints regarding linguistic variables involved are not taken into account. A general formulation of constrained fuzzy arithmetic – a nonstandard fuzzy arithmetic that takes into account these constraints – is presented and its basic characteristics are examined. More specific characteristics of constrained fuzzy arithmetic are then investigated for some common types of constraints.
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Klir, G., Pan, Y. Constrained fuzzy arithmetic: Basic questions and some answers. Soft Computing 2, 100–108 (1998). https://doi.org/10.1007/s005000050038
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DOI: https://doi.org/10.1007/s005000050038