In this paper, two generalized hesitant fuzzy generalized Shapley-Choquet integral operators are defined, which globally consider the importance of elements in a set, and the correlations among them. Some important special cases are examined. An improvement order relationship between hesitant fuzzy elements (HFEs) is introduced, and a new distance measure of HFSs is defined. This distance measu...

Measuring uncertainty for fuzzy sets has been carried out by calculating fuzzy entropy. Fuzzy entropy of fuzzy set is derived with the help of distance measure. The distance proportional value between the fuzzy set and the corresponding crisp set is designed as the fuzzy entropy. The usefulness is verified by proving the proposed entropy. Generally, fuzzy entropy contains the complementary char...

This paper considers a flow shop problem with imprecise processing times with the objective to minimize the makespan. The processing times are described by triangular fuzzy numbers. The issue that arises is how to rank the constructed job sequences with respect to their obtained makespans, which are fuzzy numbers. A new distance measure between fuzzy makespans is introduced which includes an op...

Relational clustering is an extension of clustering for relational data. Fuzzy c-Medoids (FCMdd) based linear fuzzy clustering extracts intrinsic local linear substructures from relational data. However this linear clustering was affected by noise or outliers because of using Euclidean distance. Alternative Fuzzy c-Means (AFCM) is an extension of Fuzzy c-means, in which a modified distance meas...

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...

We present some similarity and distance measures between intuitionistic fuzzy sets (IFSs). Thus, we propose two semi-metric distance measures between IFSs. The measures are applied to classification of shapes and handwritten Arabic sentences described with intuitionistic fuzzy information. The experimental results permitted to do a comparative analysis between intuitionistic fuzzy similarity an...