The equalizer and the lexicographical solutions for cooperative fuzzy games: characterization and properties

Max-consistency, complement-consistency and the core of fuzzy games

“…2 In the meantime, many solution concepts have been developed. Related results may be found in Branzei et al [4][5][6], Butnariu [7], Molina and Tejada [13], Nishizaki and Sakawa [15], Sakawa and Nishizaki [19], Tsurumi et al [26] and so on. rationality, max-consistency (w.r.t.…”

Hypercubes and compromise values for cooperative fuzzy games

“…Shapley values as one−point solution concept for this kind of games are studied in Aubin (1974Aubin ( , 1981, Butnariu (1978), Butnariu and Klement (1993), Tsurumi et al (2001). In Molina and Tejada (2002), and Sakawa and Nishizaki (1994) the equalizer and the lexicographical solutions are considered. We enlarge the existing literature concerning one−point solution concepts for cooperative fuzzy games with compromise values.…”

The core configuration for fuzzy games

“…For example, Aubin [2,3], Butnariu [10], Hwang [14], Hwang and Liao [15] and Tijs et al [37] investigated the core and related results of fuzzy games; Branzei et al [6], Butnariu and Klement [11], Butnariu and Kroupa [12], Hwang and Liao [16], Li and Zhang [20,21], Meng et al [23] and Tsurumi et al [38] investigated the Shapley value and related results of fuzzy games; Branzei et al [5,7], Muto et al [26] and Tijs et al [37] investigated the compromise value, the stable sets, the Weber set and related results of fuzzy games; and fuzzy and multiobjective games were also analyzed by Nishizaki and Sakawa [27]. Related results also can be found in Branzei et al [8], Lu et al [22], Molina and Tejada [24], Sakawa and Nishizaki [32] and so on. In addition, fuzzy games have proved to be suit-able for modeling cooperative behavior by players in economic situations (Billot [4]; Aplak and Türkbey [1]; Nishizaki and Sakawa [27]) and political situations (Butnariu [10]; Lebret and Ziad [19]) in which some players participate in a coalition only to a certain extent, not fully.…”