Similarity measure is a very important problem in fuzzy soft set theory. In this paper, seven similarity measures of fuzzy soft sets are introduced, which are based on the normalized Hamming distance, the normalized Euclidean distance, the generalized normalized distance, the Type-2 generalized normalized distance, the Type-2 normalized Euclidean distance, the Hausdorff distance and the Chebysh...

One of the key ingredients of A. Connes’ noncommutative geometry is a generalized Dirac operator which induces a metric(Connes’ distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al , whose Connes’ distance recovers the linear distance on a 1D lattice, into 2D lattice. This Dirac operator being “naturally” defined has the “local eigenvalue property” and i...