A Novel Approach to Type-Reduction and Design of Interval Type-2 Fuzzy Logic Systems

Abstract

Fuzzy logic systems, unlike black-box models, are known as transparent artificial intelligence systems that have explainable rules of reasoning. Type 2 fuzzy systems extend the field of application to tasks that require the introduction of uncertainty in the rules, e.g. for handling corrupted data. Most practical implementations use interval type-2 sets and process interval membership grades. The key role in the design of type-2 interval fuzzy logic systems is played by the type-2 inference defuzzification method. In type-2 systems this generally takes place in two steps: type-reduction first, then standard defuzzification. The only precise type-reduction method is the iterative method known as Karnik-Mendel (KM) algorithm with its enhancement modifications. The known non-iterative methods deliver only an approximation of the boundaries of a type-reduced set and, in special cases, they diminish the profits that result from the use of type-2 fuzzy logic systems. In this paper, we propose a novel type-reduction method based on a smooth approximation of maximum/minimum, and we call this method a smooth type-reduction. Replacing the iterative KM algorithm by the smooth type-reduction, we obtain a structure of an adaptive interval type-2 fuzzy logic which is non-iterative and as close to an approximation of the KM algorithm as we like.

Ranking of Alternatives Described by Atanassov’s Intuitionistic Fuzzy Sets – Reconciling Some Misunderstandings

“…Sometimes the concept of the hesitation margin is just indispensable, for example, for a proper definition of the Hausdorff distance [40] or attribute selection [37,41,42]. Research on IFSs belongs to a broad trend of research on generalized uncertain fuzzy systems, such as type-2 fuzzy logic systems [43,44] or fuzzy-rough systems [45], which deal with data uncertainty occurring due to lack of data, class overlap or the presence of noise in the data (cf. [46,47,48]).…”