Reza Etesami - Department of Statistics, Faculty of Mathematics & Computer, Shahid Bahonar University of Kerman,Kerman, Iran

Triangular fuzzy numbers (TFNs) have basic applications in fuzzy logic. In decision makingmethods, expert evaluations often turn into triangular fuzzy numbers. In this type of problems,different researchers have made different proposals for determining the upper and lowerboundaries of a triangular fuzzy number. This leads to the use of TNF numerical scales, most ofwhich are symmetric, to show results that are usually moderate values. These values are often closeto explicit values. Therefore, the results may not be produced at their best. The choice of upperand lower bounds for TFNs has always been questioned. In this paper, we propose that theBootstrap confidence interval method (BCIM) be used to determine the upper and lowerboundaries of a TFN in cases where expert opinions are used. One of the applications of BCIM isin decision making methods

Fuzzy optimization, Fuzzy-boundary interval, decision making, bootstrap confidenceinterval.