No abstract

In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen's method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen's method.

In this paper, statistical averaging method (arithmetic mean, geometric mean) and new statistical averaging method (new arithmetic mean, new geometric mean) have been proposed for extreme point multi-objective linear programming problem (EPMOLPP). Extreme point can be taken from graphical representation of linear programming problem (LPP). Graphical solution of LPP has been discussed in this research The objective of this method is for making single objective from multi-objective extreme point linear programming problem. Chandra Sen's method is for making single objective from multi-objective linear programming problem (MOLPP). Here Chandra Sen's method has also been used to solve EPMOLPP. An algorithm and program solution have been given for our proposed method to solve such type of problems. A numerical example is given and the result in Table 2 indicates that the proposed technique gives better results.

A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen's method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen's method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

Generally fuzzy control system (FCS) is worked in washing machine. For the fuzzy set theory, membership functions are the building blocks. In a fuzzy set, fuzziness is determined by its membership functions. The shapes of membership functions are important, because it has an effect on fuzzy inference system. The shapes of membership functions can be triangular, trapezoidal and gaussian. The most widely used triangular membership function is used in this paper, because it can capture the short time period. In washing machine, open loop control system is found. This paper applies a fuzzy synthetic evaluation method (FSEM) for washing cloth in washing machine as FSEM can handle the multiple criteria with the help of evaluation matrix generated from membership function and weight matrix generated by Analytical Hierarchy Process (AHP). The purpose of this research is to minimize the wash time. By applying FSEM, we get a wash time which is less than that wash time got from applying the Mamdani approach in FCS. An example is given for illustration. For more reduction of wash time, statistical averaging method is also used. To reduce the wash time, statistical averaging method can be used in Mamdani approach also.