Similarity is a basic concept in in many research areas such as biology, chemistry, image retrieval, information retrieval, machine learning, psychology, cluster analysis, data mining, statistics etc. To make a general purpose definition of similarity measure as a mathematical concept is still a challenging task. Reflexivity and Symmetry are accepted as fundamental properties of similarity measures whreas there is a lack of consensus on the axioms of Monotonicity or Transitivity. In this monograph we focus on the study of relationship between concept of monotonicity of the fuzzy similarity relations with the concept of strong and weak fuzzy transitivity.

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