Parallel Machine Scheduling Models with Fuzzy Parameters and Precedence Constraints: A Credibility Approach

A method for modeling the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure is provided. For the given n jobs to be processed on m machines, it is assumed that the processing times and the due dates are nonnegative fuzzy numbers and all the weights are positive, crisp numbers. Based on credibility measure, three parallel machine scheduling problems and a goal-programming model are formulated. Feasible schedules are evaluated not only by their objective values but also by the credibility degree of satisfaction with their precedence constraints. The genetic algorithm is utilized to find the best solutions in a short period of time. An illustrative numerical example is also given. Simulation results show that the proposed models are effective, which can deal with the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure.

Fuzzy-TOPSIS Method with Multi-goal

To develop the technique for order preference by similarity to an ideal solution, namely, TOPSIS method with multi-goal in fuzzy decision environment. Firstly, a new approach to constructing fuzzy decision matrix by Choquet integral was proposed in multi-goal decision system. Secondly, the concepts of fuzzy positive-ideal solution and fuzzy negative-ideal solution related to the fuzzy decision matrix were given. Finally, the credibility measure was adopted to calculate the distances to fuzzy positive-ideal solution and fuzzy negative-ideal solution. The presented fuzzy-TOPSIS method embodies well both the predetermined preferences and the weights of goals.

Fuzzy Global Stability Analysis of the Dynamics of Malaria with Fuzzy Transmission and Recovery Rates

In this paper, fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (), we reach the model disease-free equilibrium. Using Choquet integral, the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible, Exposed, Infected, Recovered, susceptible-Susceptible, Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium is globally asymptotically stable if or if the basic reproduction number is less than one (). When and , there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set . Finally, the numerical simulation has been done for showing the effectiveness of our analytical results.