This chapter deals with the construction of distance and similarity measures by utilizing the theoretical advantages of the fuzzy implications. To this end the basic definitions of fuzzy implications are initially discussed and the conditions of typical
distance and similarity measures that need to be satisfied are defined next. On the basis of this theory a straightforward methodology for building fuzzy implications based measures is analysed. The main advantage of the proposed methodology is its generality that makes it easy to be adopted in several types of fuzzy sets.
A.G. Hatzimichailidis, G.A. Papakostas, V.G. Kaburlasos, On Constructing Distance and Similarity Measures based on Fuzzy Implications. In: Handbook of Fuzzy Sets Comparison – Theory, Algorithms and Applications, George A. Papakostas, Anestis G. Hatzimichailidis, Vassilis G. Kaburlasos (eds.), GCSR vol. 6, pp. 1-21, 2016.