On fractional continuous weighted OWA (FCWOWA) operator with applications

In order statistics, CWOWA operator in real line based on Choquet integral was recently introduced by Narukawa et al. (Ann Oper Res 244(2):571-581, 2016). Recently, the relation of Choquet integral with fractional integral on a continuous support was recently discussed by Sugeno (IEEE Trans Fuzzy Syst 23:1439-1457, 2015). As an open problem, Sugeno emphasized that "it is necessary to consider fractional Choquet integral with respect to any monotone measures". This reason permit us to consider this problem and introduce the fractional Choquet integral with respect to any monotone measures. We also introduce the fractional CWOWA operator (FCWOWA) which includes CWOWA and WOWA operators as special cases. As an application, we also present some important inequalities for FCWOWA operator.