1Mathematical Analysis
We present some materials from mathematical analysis, which will be used throughout this book. More detailed arguments can be found in any mathematical analysis monograph.
1.1 Infimum and Supremum
Let 
be a subset of 
. The upper and lower bounds of 
are defined below.
- We say that
is an upper bound of 
when there exists a real number 
satisfying 
for every 
. In this case, we also say that 
is bounded above by 
. - We say that is a lower bound of when there exists a real ...
Get Mathematical Foundations of Fuzzy Sets now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
