On intuitionistic fuzzy compactness

General IF-sets with triangular norms and their applications to group decision making

“…One can easily give counterexamples showing that the resulting R = [r ij ] is not generally reciprocal. On the other hand, a reasonable relationship we like to have between r ij and m(r ji ) seems to be analogous to (3.1 1] with J i (s j ) = r ij for s j 2 S i . We see that J i , the ith row of R, excluding the diagonal element, is a fuzzy set of options such that s i is preferred over them by the group.…”

“…The name ''IF-set'' thus seems to be a reasonable compromise between terminological correctness on the one hand and some terminological tradition established by Atanassov and researchers dealing with his theory on the other hand (see e.g. [1,8]). Nevertheless, one should emphasize that there is still a dispute in the academic community and other forms of a terminological compromise for Atanassov's objects are also proposed, e.g.…”

On inclusion measures of intuitionistic and interval-valued intuitionistic fuzzy values and their applications to group decision making

“…. ; x n g be a discrete set of alternatives, and let D ¼ fd 1 Step 2 Utilize the IFAA operator: Step 3 Utilize the IFWA operator: Step 4 Utilize the HM inclusion measure on IFVs to compare any two b i and b j ,…”

“…Intuitionistic fuzzy set (IFS for short), proposed by Atanassov [3], is a generalization of fuzzy set theory which is defined by a membership degree, a non-membership degree and a hesitancy degree. Over the last decades, the IFS theory has been used to a wide range of applications, such as decision making [6,37,38,46], logic programming [7], topology [1,2,14,17,29,32], medical diagnosis [15], pattern recognition [26,28,31,39], machine learning and market prediction [28], and so on. Atanassov [4] further introduced the interval-valued intuitionistic fuzzy sets (IVIFSs), as a generalization of IFSs that are more actual.…”

Multiattribute decision making method based on generalized OWA operators with intuitionistic fuzzy sets

“…The IF set theory gives us the possibility to model hesitation and uncertainty by using an additional degree, i.e., the intuitionistic index. Over the last decades, the IF set theory has been applied to many different fields such as decision making (Atanassov, Pasi, and Yager, 2002;Herrera, Martinez, and Sanchez, 2005;Li, 2004Li, , 2005Kacprzyk, 2002, 2004), logic programming (Atanassov and Georgiev, 1993), topology (Abbas, 2005;Davvaz, Dudek, and Jun, 2006;Dudek, Davvaz, and Jun, 2005), medical diagnosis (De, Biswas, and Roy, 2001), pattern recognition (Li and Cheng, 2002;Wang and Xin, 2005) and machine learning as well as market prediction (Liang and Shi, 2003). In comparison with the fuzzy set, the IF set seems to be better suited for expressing a very important factor, i.e., the hesitation of the decision maker, which should be taken into account when we try to construct really adequate models and solutions of decision making problems.…”