Type-2 fuzzy entropy sets

Abstract

The final goal of this study is to adapt the concept of fuzzy entropy of De Luca and Termini to deal with Type-2 Fuzzy Sets. We denote this concept Type-2 Fuzzy Entropy-Set. However, the construction of the notion of entropy measure on an infinite set, such us [0, 1], is not effortless. For this reason, we first introduce the concept of quasi-entropy of a Fuzzy Set on the universe [0, 1]. Furthermore, whenever the membership function of the considered Fuzzy Set in the universe [0, 1] is continuous, we prove that the quasi-entropy of that set is a fuzzy entropy in the sense of De Luca y Termini. Finally, we present an illustrative example where we use Type-2 Fuzzy Entropy-Sets instead of fuzzy entropies in a classical fuzzy algorithm.

Interval‐valued equivalence measures respecting uncertainty in image processing

“…The carried out experiments illustrate the usability of the proposed equivalence measures in image thresholding. We have put our method to the test using a collection of 10 images that have been previously used to test image thresholding algorithms in the literature 49,50 …”

Weak and directional monotonicity of functions on Riesz spaces to fuse uncertain data

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Extension of Restricted Equivalence Functions and Similarity Measures for Type-2 Fuzzy Sets

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