# Mirko Navara presents Principles of inclusion and exclusion for interval-valued fuzzy sets and IF-sets

On 2018-04-19 11:00:00 at G205, Karlovo náměstí 13, Praha 2

The principle of inclusion and exclusion is one of basic tools of classical set

theory. (It has different names; a trivial example is the following: How many

people are there in the world? Sum up the citizens of all states, subtract

those

with double citizenship, add those with triple citizenship, etc.)

Many previous papers have presented its generalizations to fuzzy sets,

interval-valued fuzzy sets, or IF-sets (Atanassov’s intuitionistic fuzzy

sets) with some set operations, where cardinality is replaced by a probability

measure. We clarified which operations satisfy the principle of inclusion and

exclusion.

The material is published in the paper

Principles of inclusion and exclusion for interval-valued fuzzy sets and

Fuzzy Sets and Systems, Volume 324, Pages 60-73

https://www.sciencedirect.com/science/article/pii/S0165011416303402/pdfft?md5=5488ade44b2967ddd27694063e4cbe06&pid=1-s2.0-S0165011416303402-main.pdf

theory. (It has different names; a trivial example is the following: How many

people are there in the world? Sum up the citizens of all states, subtract

those

with double citizenship, add those with triple citizenship, etc.)

Many previous papers have presented its generalizations to fuzzy sets,

interval-valued fuzzy sets, or IF-sets (Atanassov’s intuitionistic fuzzy

sets) with some set operations, where cardinality is replaced by a probability

measure. We clarified which operations satisfy the principle of inclusion and

exclusion.

The material is published in the paper

Principles of inclusion and exclusion for interval-valued fuzzy sets and

Fuzzy Sets and Systems, Volume 324, Pages 60-73

https://www.sciencedirect.com/science/article/pii/S0165011416303402/pdfft?md5=5488ade44b2967ddd27694063e4cbe06&pid=1-s2.0-S0165011416303402-main.pdf