Development of Linear Programming Technique for Multidimensional Analysis of Preference in Fuzzy Environment

Due to the nature of real world problems, the collected data usually involve some kind of uncertainty. As a matter of fact, many parts of information cannot be quantified due to their nature. Incomplete information or partial ignorance is also another cause for resorting to fuzziness. In many decision making problems, fuzzy values are approximated by crisp data. This defuzzification leads to loss of main portion of information. In this paper we develop “crisp LINMAP method” into fuzzy environment. A nonlinear programming decision model is developed based on the distance of each alternative to an unknown fuzzy positive ideal solution. Then the fuzzy positive ideal solution and the weights of attributes are estimated and ranking order of alternatives is obtained using these values. The significant features of developed model are decision maker's ideal solution considered as fuzzy variable with triangular possibility distribution and pair-wise comparisons between alternatives have degree of truth in the interval [0,1]. To illustrate the algorithm developed here, two numerical examples are presented. © 2009 World Academic Press, UK. All rights reserved.