en و موضوعات مربوط Other Related Subject پژوهشي Research <span style="FONT-FAMILY: "Times New Roman","serif" FONT-SIZE: 11pt mso-ansi-language: EN-US mso-fareast-font-family: 'Times New Roman' mso-fareast-language: EN-US mso-bidi-language: FA mso-no-proof: yes"><em>Until now single values of IRR are traditionally used to estimate the time value of cash flows. Since uncertainty exists in estimating cost data, the resulting decision may not be reliable. The most commonly cited drawbacks to using the internal rate of return in evaluatton of deterministic cash flow streams is the possibility of multiple conflicting internal rates of return. In this paper we present a fuzzy methodology for solving problems of multiple IRR in any type of streams. Utilization of fuzzy cash flow allows modeling of uncertainty in estimating cost data. The approach of </em><span style="POSITION: relative TOP: 3pt mso-text-raise: -3.0pt"><shapetype id="_x0000_t75" stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"><stroke joinstyle="miter" ><formulas><f eqn="if lineDrawn pixelLineWidth 0" ><f eqn="sum @0 1 0" ><f eqn="sum 0 0 @1" ><f eqn="prod @2 1 2" ><f eqn="prod @3 21600 pixelWidth" ><f eqn="prod @3 21600 pixelHeight" ><f eqn="sum @0 0 1" ><f eqn="prod @6 1 2" ><f eqn="prod @7 21600 pixelWidth" ><f eqn="sum @8 21600 0" ><f eqn="prod @7 21600 pixelHeight" ><f eqn="sum @10 21600 0" ></formulas><p ath o:connecttype="rect" gradientshapeok="t" o:extrusionok="f" ><lock aspectratio="t" v:ext="edit" ></shapetype><shape style="WIDTH: 12pt HEIGHT: 11.25pt" id="_x0000_i1025" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1userLOCALS~1Tempmsohtmlclip11clip_image001.wmz"><em></em></imagedata></shape></span><em>-cut is to decrease the range of the final fuzzy set by increasing the degree of membership. For each fuzzy IRR in an optimum </em><span style="POSITION: relative TOP: 3pt mso-text-raise: -3.0pt"><shape style="WIDTH: 12pt HEIGHT: 11.25pt" id="_x0000_i1026" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1userLOCALS~1Tempmsohtmlclip11clip_image003.wmz"><em></em></imagedata></shape></span><em>-cut, and an obtained present value of each stream, it is possible to decide on acceptance or rejection of a project according to the type of each stream (borrowing or investing). The upper bound of </em><span style="POSITION: relative TOP: 3pt mso-text-raise: -3.0pt"><shape style="WIDTH: 12pt HEIGHT: 11.25pt" id="_x0000_i1027" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1userLOCALS~1Tempmsohtmlclip11clip_image004.wmz"><em></em></imagedata></shape></span><em>-cut is the worst case for borrowing and the lower bound of </em><span style="POSITION: relative TOP: 3pt mso-text-raise: -3.0pt"><shape style="WIDTH: 12pt HEIGHT: 11.25pt" id="_x0000_i1028" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1userLOCALS~1Tempmsohtmlclip11clip_image005.wmz"><em></em></imagedata></shape></span><em>-cut is the worst case for investing. It is shown that both the internal rate of return and the present value are important in decision making and by analyzing the sensitivity of these values relative to the </em><span style="POSITION: relative TOP: 3pt mso-text-raise: -3.0pt"><shape style="WIDTH: 12pt HEIGHT: 11.25pt" id="_x0000_i1029" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1userLOCALS~1Tempmsohtmlclip11clip_image006.wmz"><em></em></imagedata></shape></span><em>-cut variation, one can see the behavior of the project and choose a narrower fuzzy range.</em></span> Internal Rate of Return, Uncertainty, Fuzzy numbers, Borrowing or Investing in a project 45 52 http://ijiepr.iust.ac.ir/browse.php?a_code=A-10-330-2&slc_lang=en&sid=1 B. Moradi 180031947532846001548 180031947532846001548 No Alzahra University H. Shakeri 180031947532846001549 180031947532846001549 No Amirkabir University of Technology S. NamdarZangeneh szangeneh@alzahra.ac.ir 180031947532846001550 180031947532846001550 Yes Faculty member of Industrial Engineering Department, Alzahra University