Parameterized bilinear programming methodology for solving triangular intuitionistic fuzzy number bimatrix games

A measure of probabilistic hesitant I‐fuzzy sets and decision makings for strategy choice

“…P 1 and P 2 can get the approximate ranges of real numbers based on analyzing and reading the mass data. Take à = ( (19,20,21), (18,20,22) , 0.8);…”

“…where (19,20,21), (18,20,22) in à 11 is a triangular IFN, the membership and nonmembership functions of it are given as follows: respectively, depicted as in Figure 5A; f f (15.5, 17, 18, 19)…”

“…1 Nowadays, there exist lots of studies on fuzzy optimization modeling and decision making [14][15][16] and matrix games. [17][18][19][20] Obviously, these research can be classified as the types of IFSs, interval-valued IFNs, 4 triangular IFNs, 14,15,17,19 and trapezoidal IFNs. 16 But they are just only special forms of I-fuzzy numbers, and do not involve nonlinear phenomena.…”

“…( (16,18,19), (16,18,20) , 0.2) ( (15.5, 17, 18, 19), , ; (15.5, 16.5, 18, 20), , , 0.8); ( (14,15,16,17), , , (13.5, 15, 16, 17.5), , , 0.2) ( (15,17,18), , ; (14, 16, 17, 18.5), , , 0.9); ( (14,15,16), ,…”

“…( (12,13,14,15), (11,12,13,14) , 0.2) = ( (22,25,27), (22,26,28) , 0.7); ( (20,21,22), (19,21,23) . Therefore, we have proven that à Ã″ ≥ .…”