Title :
How to make sure that "≈100"+1 is ≈100 in fuzzy arithmetic: solution and its (inevitable) drawbacks
Author :
Kreinovich, Vladik ; Nguyen, Hung T. ; Pedrycz, Witold
Author_Institution :
Texas Univ., El Paso, TX, USA
Abstract :
From the common-sense viewpoint, if a person who weighs around 100 kilograms gains one more kilogram, his weight is still around 100 kilograms. Alas, not so in traditional fuzzy arithmetic. In this paper, we propose a modification of fuzzy arithmetic which does have this property. We gain the desired property, but there is no free lunch - we have to lose two important properties of the traditional fuzzy arithmetic: first, addition is no longer always associative; second, addition is no longer always easily computable
Keywords :
arithmetic; common-sense reasoning; computability; fuzzy set theory; addition; approximation; associativity; common-sense viewpoint; computability; fuzzy arithmetic; Arithmetic; Fuzzy sets; Shape;
Conference_Titel :
IFSA World Congress and 20th NAFIPS International Conference, 2001. Joint 9th
Conference_Location :
Vancouver, BC
Print_ISBN :
0-7803-7078-3
DOI :
10.1109/NAFIPS.2001.943799
