Fuzzy weighted averages and implementation of the extension principle
Fuzzy Sets and Systems
Fuzzy weighted average: an improved algorithm
Fuzzy Sets and Systems
Fuzzy sets, fuzzy logic, and fuzzy systems
Centroid of a type-2 fuzzy set
Information Sciences: an International Journal
Conceptual Spaces: The Geometry of Thought
Conceptual Spaces: The Geometry of Thought
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
Type 2 representation and reasoning for CWW
Fuzzy Sets and Systems - Special issue: Approximate Reasoning in Words
Computing with words and its relationships with fuzzistics
Information Sciences: an International Journal
Reformulation of the theory of conceptual spaces
Information Sciences: an International Journal
An Algorithm for Detecting Unimodal Fuzzy Sets and Its Application as a Clustering Technique
IEEE Transactions on Computers
The collapsing method of defuzzification for discretised interval type-2 fuzzy sets
Information Sciences: an International Journal
Fuzzy subsethood for fuzzy sets of type-2 and generalized type-n
IEEE Transactions on Fuzzy Systems
Uncertain Fuzzy Clustering: Insights and Recommendations
IEEE Computational Intelligence Magazine
Type-2 fuzzy sets and systems: an overview
IEEE Computational Intelligence Magazine
IEEE Transactions on Fuzzy Systems
Wireless Sensor Network Lifetime Analysis Using Interval Type-2 Fuzzy Logic Systems
IEEE Transactions on Fuzzy Systems
On type-2 fuzzy relations and interval-valued type-2 fuzzy sets
Fuzzy Sets and Systems
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This paper explores the link between type-2 fuzzy sets and multivariate modeling. Elements of a space X are treated as observations fuzzily associated with values in a multivariate feature space. A category or class is likewise treated as a fuzzy allocation of feature values (possibly dependent on values in X). We observe that a type-2 fuzzy set on X generated by these two fuzzy allocations captures imprecision in the class definition and imprecision in the observations. In practice many type-2 fuzzy sets are in fact generated in this way and can therefore be interpreted as the output of a classification task. We then show that an arbitrary type-2 fuzzy set can be so constructed, by taking as a feature space a set of membership functions on X. This construction presents a new perspective on the Representation Theorem of Mendel and John. The multivariate modeling underpinning the type-2 fuzzy sets can also constrain realizable forms of membership functions. Because averaging operators such as centroid and subsethood on type-2 fuzzy sets involve a search for optima over membership functions, constraining this search can make computation easier and tighten the results. We demonstrate how the construction can be used to combine representations of concepts and how it therefore provides an additional tool, alongside standard operations such as intersection and subsethood, for concept fusion and computing with words.