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By Zarko Mijajlovic

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The zero error occurs for the triangular fuzzy sets with Y:z overlap between successive membership functions). , 1993), the process of converting numeric data into the format accepted by the inference engine is called Juzzijication. This is the name used for the encoding mechanism. The decoding is referred to as a defuzzijication scheme. One may also envision also a mixed form of information granules, namely they may originate from different formal environments of information granulation. DJA AID Digital world Analog world Figure 6.

A. (1997), Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets and Systems, 90,111-117. Zadeh, L. , Kacprzyk, J. (1999), Computing with Words in Information/Intelligent Systems, vol. 1-2, Physica-Verlag, Heidelberg. 2 SETS AND INTERVALS The chapter on set theory and interval analysis fulfils a dual role in this book. It provides a backdrop against which a more general representation of the world, using fuzzy sets, rough sets, shadowed sets, etc.

If we now consider an operator op acting on specific sets A 1 and B h that are subsets of the corresponding sets A and B, the result of applying this operator will, in general be a set that have a complex topology even if the operands are hyperboxes. Consequently we are often interested in the enclosure of the operator op, denoted as [op], that is defined as an operator producing an enclosure of the results set obtained with operator op itself. ([CD that contains C 1• So, by the above definition the enclosure operator [op] always generates a set that contains the set generated by the operator op itself.

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