On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision (Q881854)

The paper offers a concise and focused view at intuitionistic fuzzy sets cast in the framework of various formalisms used to model uncertainty. In a nutshell, intuitionistic sets are useful in capturing concepts where a degree of membership of a certain point, \(A(x)\), taken along with a degree of non-membership, \(A^\sim(x)\), satisfy the relationship \(A(x)+A^\sim(x)\leq 1\). This concept is compared vis-à-vis some other commonly encountered models of uncertainty, in particular interval-valued fuzzy sets, \(L\)-fuzzy sets, soft sets and a number of interesting linkages between them and intuitionistic fuzzy sets are revealed. The study offers an interesting diagram summarizing the main dependencies between all these constructions.