The fuzzy set theory is capable to capture this uncertainty through the membership functions of these parameters. However, ordinary fuzzy sets are criticized for having one single membership value for each certain parameter value. To remove this criticism, type-2 fuzzy sets were proposed. In this ...
An evolutionary architecture was proposed to generate the rule base and to optimize the membership functions of a type-2 Fuzzy Classification System The proposed architecture is composed of three stages. In the first stage of the architecture, a Genetic Algorithm generates the rule base of the ...
interval type-2 fuzzy set defined on with MF , where and are the lower and upper MFs of , respectively [3]. What is the aggregation of these interval type-2 fuzzy sets through ? Recall that is originally defined as a function of points; hence, in order to address this question,...
In this paper we propose a new evaluation/defuzzification formula for an Interval Type-2 Fuzzy Quantity (IT2 FQ), that is an Interval Type-2 Fuzzy Set (IT2 FS) defined by two Type-1 Fuzzy Quantities (T1 FQs) having membership functions that may be neither convex nor normal. We start ...
While excessive arithmetic operations are needed with type-2 fuzzy sets with respect to type-1's, type-2 fuzzy sets generalize type-1 fuzzy sets and systems so that more uncertainty for defining membership functions can be handled. A type-2 fuzzy set lets us incorporate the uncertainty of ...
In this paper, an interval type-2 fuzzy logic system is designed and compared with a type-I fuzzy logic system. To compare performance of a type-I fuzzy logic system with the type-2 fuzzy logic system, we apply type-I fuzzy logic system and type-2 system to modeling the noised data....
For an interval type-2 fuzzy set, the volume measure is equivalent to the area of the footprint of uncertainty of the set. Experiments show that though the two measures give different results, there is considerable commonality between them. The concept of {\it invariance under vertical ...
As the fuzzy set is actually a precise constant function, it can't accurately describe the uncertainty of the language. While the determining of type-2 fuzzy set(T2FS) membership function is provided with a certain degree of freedom, which is convenient to facilitate the calculation. Meanwhile,...
Deluca, A., Termini, S.: A definition of a nonprobabilistic entropy in the setting of fuzzy set theory. Information and Control 20, 301–312 (1972) CrossRef Tizhoosh, H.: Image thresholding using type-2 fuzzy sets. Pattern Recognition 38, 2363–2372 (2005) CrossRef Pal, N., ...
This tutorial paper demonstrates how the Wavy Slice Representation Theorem (RT) for a general type-2 fuzzy set (T2 FS), when specialized to an interval T2 FS (IT2 FS), can be used as the starting point to solve many diverse problems that involve IT2 FSs. The problems considered are: ...