Chapter
Lfuzzy Sets and Intuitionistic Fuzzy Sets
DOI: 10.1007/9783540726876_16 In book: Computational Intelligence Based on Lattice Theory, Publisher: Springer, pp.325339

Conference Paper: Some New Entropies on the IntervalValued Fuzzy Set.
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ABSTRACT: In this paper, we review some existing entropies of intervalvalued fuzzy set, and propose some new formulas to calculate the entropy of intervalvalued fuzzy set. Finally, we give one comparison with some existing entropies to illustrate our proposed entropies reasonable.Nonlinear Mathematics for Uncertainty and its Applications, NLMUA 2011, Beijing, China, September 79, 2011; 01/2011  Italian Journal of Pure and Applied Mathematics. 01/2012; 33.
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ABSTRACT: Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to grayscale morphology. Extensions of classical binary morphology to grayscale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of \mathbbL\mathbb{L}fuzzy set generalizes not only the concept of fuzzy set but also the concepts of intervalvalued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of \mathbbL\mathbb{L}fuzzy sets forms a complete lattice whenever the underlying set \mathbbL\mathbb{L} constitutes a complete lattice. Based on these observations, we develop a general approach towards \mathbbL\mathbb{L}fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for intervalvalued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of \mathbbL\mathbb{L}fuzzy MM. As an application of these ideas, we generate a combination of some wellknown medical image reconstruction techniques in terms of intervalvalued fuzzy image processing. KeywordsMathematical morphology–Complete lattice– \mathbbL\mathbb{L}fuzzy sets–Intervalvalued fuzzy sets–Atanassov’s intuitionistic fuzzy sets– \mathbbL\mathbb{L}fuzzy mathematical morphology– \mathbbL\mathbb{L}fuzzy connectives–Inclusion measure–Duality–Negation–AdjunctionJournal of Mathematical Imaging and Vision 01/2012; 43(1):5071. · 1.77 Impact Factor
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