Method for solving fully fuzzy linear programming problems using deviation degree measure

A new fully fuzzy linear programming （FFLP） problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming （LP） problem. Giving the value of deviation degree in each constraint, the 6-fuzzy optimal solution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict： to improve the values of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to illustrate the proposed method.

A KIND OF FUZZY LINEAR PROGRAMMING PROBLEMS BASED ON INTERVAL-VALUED FUZZY SETS

The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval\|valued fuzzy sets (IVFLP) through the medium of procedure that turns IVFLP into parametric linear programming via the mathematical programming.Some useful results for the benefit of solving IVFLP are expounded and proved,developed and discussed.Furthermore,that the proposed techniques in this paper allow the decision\|maker to assign a different degree of importance can provide a useful way to efficiently help the decision\|maker make their decisions.

Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

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.

Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method

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.

Improved Group Fuzzy Preference Programming Method Based on Fuzzy Random Theory

A new prioritization method in the analytic hierarchy process （AHP）, which improves the group fuzzy preference programming （GFPP） method, is proposed. The fuzzy random theory is applied in the new prioritization method. By modifying the principle of decision making implied in the GFPP method, the improved group fuzzy preference programming （IGFPP） method is formulated as a fuzzy linear programming problem to maximize the average degree of the group satisfaction with all possible group priority vectors. The IGFPP method inherits the advantages of the GFPP method, and solves the weighting trouble existed in the GFPP method. Numerical tests indicate that the IGFPP method performs more effectively than the GFPP method in the case of very contradictive comparison judgments from decision makers.

Fuzzy linear model for production optimization of mining systems with multiple entities

Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.

Optimal Irrigation Planning and Operation of Multi Objective Reservoir Using Fuzzy Logic

In the present study the MOFLP models have been developed for the optimal cropping pattern planning which maximizes the four objectives such as Net Benefits (NB), Crop Production (CP), Employment Generation (EG) and Manure Utilization (MU) under conflicting situation and also, for maximization of Releases for Irrigation (RI) and Releases for Power (RP) simultaneously under uncertainty by considering the fuzziness in the objective functions. The developed models have been applied using the LINGO 13 (Language for Interactive General Optimization) optimization software to the case study of the Jayakwadi Project Stage-II across Sindhphana River, in the State of Maharashtra India. The various constraints have been taken into consideration like sowing area, affinity to crop, labour availability, manure availability, water availability for optimal cropping pattern planning. Similarly constraints to find the optimal reservoir operating policy are releases for power and turbine capacity, irrigation demand, reservoir storage capacity, reservoir storage continuity. The level of satisfaction for a compromised solution of optimal cropping pattern planning for four conflicting objectives under fuzzy environment is worked out to be λ = 0.68. The MOFLP compromised solution provides NB = 1088.46 (Million Rupees), CP = 241003 (Tons), EG = 23.13 (Million Man days) and MU = 111454.70 (Tons) respectively. The compromised solution for optimal operation of multi objective reservoir yields the level of satisfaction (λ) = 0.533 for maximizing the releases for irrigation and power simultaneously by satisfying the constraint of the system under consideration. The compromised solution provides the optimal releases, i.e. RI = 348.670 Mm3 and RP = 234.285 Mm3 respectively.