Measuring inclusion, similarity and compatibility between Atanassov's intuitionistic fuzzy sets (Q2886938)

An axiomatic definition of inclusion (subsethood) measures of fuzzy sets was introduced by \textit{V. R. Young} [Fuzzy Sets Syst. 77, No. 3, 371--384 (1996; Zbl 0872.94062)]. Definitions and properties of similarity and compatibility measures of fuzzy sets were described, e.g., by \textit{V. V. Cross} and \textit{T. A. Sudkamp} in [Similarity and compatibility in fuzzy set theory. Assessment and applications. Heidelberg: Physica-Verlag (2002; Zbl 0992.03066)]. This paper concerns generalizations of the above notions from the case of fuzzy sets to the case of intuitionistic fuzzy sets. At first, the authors recall some recent generalizations of this kind. Then they give constructions of new examples of such generalizations. In particular, formulas (2)--(6) bring new inclusion measures with particular properties of measure (6) (Theorem 6). Examples of similarity measures are constructed on the basis of inclusion measures (Theorems 7, 8). New compatibility measures are constructed using triangular norms and conorms.NEWLINENEWLINENEWLINENEWLINEThe paper contains a rich list of references (45 items). However, the numbering of some references is not correct; e.g., on pp. 262, 266, the reference ``Young [34]'' rather concerns [35]; similarly, reference to [43] in Theorem 1 rather concerns [40].