IFSA 2007 World Congress

Cancun, Mexico, June 18-21, 2007

SPECIAL SESSION 5SS

Intuitionistic fuzzy sets some related approaches and applications

ORGANIZERS: E. Szmidt and J. Kacprzyk

Systems Research Institute

Polish Academy of Sciences

Ul. Newelska 6, 01-447 Warsaw, Poland

e-mails: [email-masked] , [email-masked]

SCOPE: For several centuries (starting from the mid-seventeenth century) uncertainty was identified and expressed in terms of probability theory only. Uncertainty was a synonym of randomness. This situation was challenged in the 1960s by other theories, distinct from probability theory, characterizing different aspects of uncertain situations. Uncertainty started to be perceived as a multidimensional concept manifesting one of its dimensions as randomness. Other dimensions turned out equally important from the point of view of representing and processing information. The most visible of the theories, dealing with different aspects of uncertainty, is Zadeh’s theory of fuzzy sets.

Many extensions of the conventional theory of fuzzy sets have appeared over the years. Among those extensions, Atanassov's theory of intuitionistic fuzzy sets plays an important role, and has gained popularity in recent years. Basically, it introduces, for each element of a universe of discourse, a degree of membership and a degree of non-membership, both from the unit interval, but which do not sum up to 1 as in the conventional fuzzy sets. The idea of making use of positive and (independently given) negative information lying in the core of intuitionistic fuzzy sets is natural in real life, and as an obvious consequence, is well-known in psychology. It also attracted attention of the scientists in soft computing. It would be difficult to deal with machine learning (making use of examples and counter-examples), modeling of preferences or voting without taking into account positive and (independently given) negative data.

Intuitionistic fuzzy sets making use of both membership and non-membership values can represent more adequately the situations when, for instance, decision makers abstain from expressing their testimonies, some assessments can not be classified but also can not be discarded, etc. Therefore, intuitionistic fuzzy sets provide a richer apparatus to grasp imprecision than the conventional fuzzy sets.

CONTACT INFORMATION:

Eulalia Szmidt

Systems Research Institute

Polish Academy of Sciences

Ul. Newelska 6, 01-447 Warsaw

Poland

E-mail: [email-masked]

Janusz Kacprzyk

Systems Research Institute

Polish Academy of Sciences

Ul. Newelska 6, 01-447 Warsaw

Poland

E-mail: [email-masked]

URL: http://www.ibspan.waw.pl/~kacprzyk