Axiomatic Fuzzy Set Theory And Its Applications (studies In Fuzziness And Soft Computing)
by Witold Pedrycz /
2009 / English / PDF
8.4 MB Download
It is well known that “fuzziness”—informationgranulesand fuzzy sets
as one of its formal manifestations— is one of important
characteristics of human cognitionandcomprehensionofreality. Fuzzy
phenomena existinnature and are encountered quite vividly within
human society. The notion of a fuzzy set has been introduced by L.
A. , Zadeh in 1965 in order to formalize human concepts, in
connection with the representation of human natural language and
computing with words. Fuzzy sets and fuzzy logic are used for mod-
ing imprecise modes of reasoning that play a pivotal role in the
remarkable human abilities to make rational decisions in an
environment a?ected by - certainty and imprecision. A growing
number of applications of fuzzy sets originated from the
“empirical-semantic” approach. From this perspective, we were
focused on some practical interpretations of fuzzy sets rather than
being oriented towards investigations of the underlying
mathematical str- tures of fuzzy sets themselves. For instance, in
the context of control theory where fuzzy sets have played an
interesting and practically relevant function, the practical facet
of fuzzy sets has been stressed quite signi?cantly. However, fuzzy
sets can be sought as an abstract concept with all formal
underpinnings stemming from this more formal perspective. In the
context of applications, it is worth underlying that membership
functions do not convey the same meaning at the operational level
when being cast in various contexts.
It is well known that “fuzziness”—informationgranulesand fuzzy sets
as one of its formal manifestations— is one of important
characteristics of human cognitionandcomprehensionofreality. Fuzzy
phenomena existinnature and are encountered quite vividly within
human society. The notion of a fuzzy set has been introduced by L.
A. , Zadeh in 1965 in order to formalize human concepts, in
connection with the representation of human natural language and
computing with words. Fuzzy sets and fuzzy logic are used for mod-
ing imprecise modes of reasoning that play a pivotal role in the
remarkable human abilities to make rational decisions in an
environment a?ected by - certainty and imprecision. A growing
number of applications of fuzzy sets originated from the
“empirical-semantic” approach. From this perspective, we were
focused on some practical interpretations of fuzzy sets rather than
being oriented towards investigations of the underlying
mathematical str- tures of fuzzy sets themselves. For instance, in
the context of control theory where fuzzy sets have played an
interesting and practically relevant function, the practical facet
of fuzzy sets has been stressed quite signi?cantly. However, fuzzy
sets can be sought as an abstract concept with all formal
underpinnings stemming from this more formal perspective. In the
context of applications, it is worth underlying that membership
functions do not convey the same meaning at the operational level
when being cast in various contexts.