Burillo, P.; Bustince, H. Two operators on interval-valued intuitionistic fuzzy sets. II. (English) Zbl 0834.04008 C. R. Acad. Bulg. Sci. 48, No. 1, 17-20 (1995). [For Part I see ibid. 47, No. 12, 9–12 (1994; Zbl 0834.04007).]The interval-valued intuitionistic fuzzy sets (IVIFSs) [the reviewer and G. Gargov, Fuzzy Sets Syst. 31, No. 3, 343–349 (1989; Zbl 0674.03017)]are extensions of the intuitionistic fuzzy sets (IFSs) [the reviewer, ibid. 20, 87–96 (1986; Zbl 0631.03040)]and interval-valued fuzzy sets (IVFSs). Let \(X\neq \emptyset\) be a given universe. An IVIFS in \(X\) is defined by \(\{\langle x, M_A (x), N_A (x)\rangle \mid x\in X\}\) where \(M_A: X\to D[0,1 ]\), \(N_A: X\to D[0,1 ]\) with the condition \(0\leq \sup M_A (x)+ \sup N_A (x)\leq 1\), for every \(x\in X\), and where \(D[0,1 ]\) is the set of closed subintervals of \([0,1 ]\). The operator \(H_{p,r}: \text{IVIFS} \to \text{IFS}\) is defined by \[ H_{p,r} (A)= \{\langle x, g_p (M_A (x)), g_r (N_A (x)) \rangle\mid x\in X\}, \] where \(0\leq p, r\leq 1\) and \(g_p ([M_L, M_U ])= M_L+ p\cdot (M_U- M_L)\), and its basic properties are studied. Reviewer: Krassimir Atanassov (Sofia) Cited in 3 Documents MSC: 03E72 Theory of fuzzy sets, etc. Keywords:interval-valued intuitionistic fuzzy sets Citations:Zbl 0674.03017; Zbl 0631.03040; Zbl 0834.04007 PDFBibTeX XMLCite \textit{P. Burillo} and \textit{H. Bustince}, C. R. Acad. Bulg. Sci. 48, No. 1, 17--20 (1995; Zbl 0834.04008)