In this paper, we show a procedure for solving MULTILEVEL FRACTIONAL PROGRAMMING problems in a large hierarchical decentralized organization using fuzzy goal PROGRAMMING approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, fuzzy goal PROGRAMMING approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.

There are many cases that a nonlinear FRACTIONAL PROGRAMMING, generated as a result of studying FRACTIONAL stochastic PROGRAMMING, must be solved. Sometimes an approximate solution may be sufficient enough to start a new process of calculations. To this end, this author introduces a new linear approximation technique for solving a FRACTIONAL chance constrained PROGRAMMING (CCP) problem. After introducing the problem, the equivalent deterministic form of the FRACTIONAL nonlinear PROGRAMMING problem is developed. To solve the problem, a fuzzy goal PROGRAMMING model of the equivalent deterministic form of the FRACTIONAL chance constrained PROGRAMMING is provided and then the process of defuzzification and linearization of the problem is started. A sample test problem is solved for presentation purposes.