Type-2 fuzzy sets made simple

By Jerry M. Mendel, Robert Ivor John. IEEE transactions on fuzzy systems, 2002

2,645 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/173e283422111cb1381c03e64544717c6c2346fe

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Citations in the corpus

Image thresholding using type II fuzzy sets (2005, background): “There are different sources of uncertainties in type I fuzzy sets (see[29]): the meanings of the words that are used, measurements may be noisy, the data that are used to tune the parameters of type I fuzzy sets may also be noisy.”
Interval Type-2 Fuzzy Logic Systems Made Simple (2006, background): “This representation, which makes very heavy use of embedded IT2 FSs (Definition 8), was first presented in [19] for an arbitrary T2 FS, and is the bedrock for the rest of this paper.”
A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots (2004, background): “…functions of type-2 fuzzy sets are three dimensional and include a footprint of uncertainty, it is the new third dimension of type-2 fuzzy sets and the footprint of uncertainty that provide additional degrees of freedom that make it possible to directly model and handle uncertainties [17], [18].”
Type-2 FLCs: A New Generation of Fuzzy Controllers (2007, background): “❏ Each input and output will be represented by a large number of type-1 fuzzy sets, which are embedded in the type-2 fuzzy sets [25], [26].”
A Historical Account of Types of Fuzzy Sets and Their Relationships (2016, background): “From the ideas given by Karnik and Mendel [80] in 1998, Mendel and John [93] provide in 2002 the following definition.”
Optimization of Interval Type-2 Fuzzy Logic Controllers for a Perturbed Autonomous Wheeled Mobile Robot Using Genetic Algorithms (2009, methodology): “Doing this for all x 2 X, we create a three-dimensional membership function – a type-2 membership function – that characterizes a type-2 fuzzy set [31,33].”
Uncertainty measures for interval type-2 fuzzy sets (2007, background): “Mendel and John [49] have presented a Representation Theorem for a general T2 FS, which when specialized to an IT2 FS can be expressed as: Representation Theorem for an IT2 FS: Assume that primary variable x of an IT2 FS e A is sampled at N values, x 1 ; x 2 ; . . . ; x N , and at each of these…”
Pythagorean fuzzy subsets (2013, methodology): “In order to enhance the capability of fuzzy sets to capture and model user provided membership information researchers have introduced non-standard second order fuzzy sets such as intuitionistic [1, 2] and intervalvalued [3, 4].”
Toward General Type-2 Fuzzy Logic Systems Based on zSlices (2010, background): “Several publications have shown that interval type-2 FLSs can outperform their type-1 FLSs counterparts in a variety of applications [1], [12]–[19].”
Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management (2021, background): “…FS was explored by Zadeh (1975), Torra (2010) elaborated the principle of hesitant FS (HFS), Karnik and Mendel (2001) utilized certain operational laws based on type-2 FS (T-2FS), Mendel and John (2002) developed T2FS made simple, and Mahmood (2020) developed the theory of bipolar soft sets.”
Encoding Words Into Interval Type-2 Fuzzy Sets Using an Interval Approach (2008, methodology): “Note that when the aggregation operation is the union, then this approach is based on the T2 FS representation theorem [18] for an IT2 FS, which states that the FOU of an IT2 FS equals the union of all of its embedded2 T1 FSs.”
An efficient centroid type-reduction strategy for general type-2 fuzzy logic system (2008, methodology): “Most of these definitions and concepts come from [1, 13].”
A Self-Evolving Interval Type-2 Fuzzy Neural Network With Online Structure and Parameter Learning (2008, background): “In recent years, studies on type-2 FLSs have drawn much attention [1], [2] and a complete theory of type-2 FLSs has been developed in [3].”
Advances in type-2 fuzzy sets and systems (2007, background): “Mendel and John [54] show how (7) and (9) can easily be derived without having to use the extension principle, when e A and e B are represented as in Theorem 1.”