By Topic

Interpretable Fuzzy Systems: Analysis of T-norm interpretability

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Kovalerchuk, B. ; Central Washington Univ., Ellensburg, WA, USA

The issues of Interpretable Fuzzy Systems (IFS) spin from the fundamental definitions of the concept of IFS to practical design of such systems. This paper addresses the current issues of formalization of the concept of interpretability, its dimensions, evaluations and design of interpretable Fuzzy Systems, including fuzzy control systems. T-norms and T-conorms are in the core of Fuzzy Systems, therefore we consider the following questions about them. Where is the adequate sphere for T-norms in IFS to be interpretable operations? How to modify the T-norms to satisfy the IFS requirements? What are the alternatives to T-norms and t-conorms in IFS? This analysis of T-norms is done in the context of their interpretation as measurements. We show that the approach used in the representative measurement theory is a source of the interpretability definition, which is in line with Tarsky's definition of interpretability. This approach is used to define a concept of the interpretable fuzzy operations. Next, it is shown that an adequate scope for scalar T-norms is to be compact approximations of 2-D lattice operations. Such lattice operations are an alternative to T-norms and T-conorms in IFS because they have better interpretability. It is shown that such popular T-norms as the minimum and the product operations are similar as approximations of the Pareto optimal set, but quite different in representation of the lattice structure, where the product is preferable because it distorts the lattice structure less.

Published in:

Fuzzy Systems (FUZZ), 2010 IEEE International Conference on

Date of Conference:

18-23 July 2010