Distances and Similarities in Intuitionistic Fuzzy Sets by Eulalia Szmidt

By Eulalia Szmidt

This e-book provides the state of the art in concept and perform concerning similarity and distance measures for intuitionistic fuzzy units. Quantifying similarity and distances is important for lots of functions, e.g. facts mining, computer studying, selection making, and keep watch over. The paintings offers readers with a accomplished set of theoretical strategies and functional instruments for either defining and opting for similarity among intuitionistic fuzzy units. It describes an automated set of rules for deriving intuitionistic fuzzy units from facts, which could reduction within the research of knowledge in huge databases. The e-book additionally discusses different vital functions, e.g. using similarity measures to guage the level of contract among specialists within the context of determination making.

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E. 1007/978-3-319-01640-5_3, c Springer International Publishing Switzerland 2014 39 40 3 Distances If a measure fulfills requirements 1, 3 and 4, it is called a pseudometric (separability does not hold). A semimetric is defined with requirements 1, 2 and 3 (triangle inequality does not need to be satisfied). A semi-pseudometric satisfies 1 and 3 only. If a set of elements is identified with a vector space, the most known distances correspond to norms. A norm of a vector corresponds in a sense to the absolute value (magnitude) of numbers.

We refer again an interested reader to (Szmidt and Kacprzyk [163, 164, 167, 173, 177, 178, 179, 182]) where we exploit this fact - using the intuitionistic fuzzy sets to group decision making. In short, the problem boils down to selecting an option or a set of options which are best accepted by most of the individuals. The options are considered in pairs. Employing the intuitionistic fuzzy sets forces each individual to look at each pair (i,j) of the options considering: advantages of the first option over the second one (membership value), disadvantages of the first option over the second one (non-membership value), and taking into account lack of knowledge (intuitionistic fuzzy index) as far as the two options are concerned.

We refer again an interested reader to (Szmidt and Kacprzyk [163, 164, 167, 173, 177, 178, 179, 182]) where we exploit this fact - using the intuitionistic fuzzy sets to group decision making. In short, the problem boils down to selecting an option or a set of options which are best accepted by most of the individuals. The options are considered in pairs. Employing the intuitionistic fuzzy sets forces each individual to look at each pair (i,j) of the options considering: advantages of the first option over the second one (membership value), disadvantages of the first option over the second one (non-membership value), and taking into account lack of knowledge (intuitionistic fuzzy index) as far as the two options are concerned.

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