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Assignment problems were widely applied in the field of production planning, telecommunication VLSI design, economic etc. Generally Fuzzy Numbers plays a vital role in many decision making problems. Here an optimal solution of the assignment problem had been derived from Hungarian method. The parameters were being given by using pentagonal fuzzy numbers which are further decomposed into triangular fuzzy numbers. The fuzzy numbers were defuzzfied into real numbers by using pascal's graded mean technique. Numerical example had been given to illustrate the solution procedure. [ABSTRACT FROM AUTHOR]

This paper presents a new multiple criteria optimization model of an assignment problem with imprecise coefficients. Besides, minimizing the total cost, total time of finishing jobs, and maximization of the overall achieved quality, we introduce a new criterion that minimizes the number of workers employed to finish all jobs. It contributes significantly in multi-job assignment to adjust the number of workers assigned to at least one job for balancing work allocation among the workers. Furthermore, we employ new diversification constraints to obtain a reasonable tradeoff between the number of workers employed and number of jobs assigned. A new interactive possibilistic programming approach is developed for trapezoidal possibility distributions, which uses $\alpha$ -level sets to incorporate confidence levels of the decision maker in his fuzzy judgments leading to $\alpha$ -efficient solutions. Numerical experiments are conducted using data coming from a manpower planning problem to demonstrate working of the proposed multiple criteria assignment model and effectiveness of the fuzzy interactive approach. [ABSTRACT FROM AUTHOR]

We consider the problem of multi-robot task-allocation when robots have to deal with uncertain utility estimates. Typically an allocation is performed to maximize expected utility; we consider a means for measuring the robustness of a given optimal allocation when robots have some measure of the uncertainty (e.g. a probability distribution, or moments of such distributions). We introduce the interval Hungarian algorithm, a new algorithm that extends the classic Kuhn—Munkres Hungarian algorithm to compute the maximum interval of deviation, for each entry in the assignment matrix, which will retain the same optimal assignment. The algorithm has a worst-case time complexity of O(n4); we also introduce a parallel variant with O(n3) running time, which is able to exploit the concurrent computing capabilities of distributed multi-robot systems. This provides an efficient measurement of the tolerance of the allocation to the uncertainties and dynamics, for both a specific interval and a set of interrelated intervals. We conduct experiments both in simulation and with physical robots to validate the approach and to gain insight into the effect of location uncertainty on allocations for multi-robot multi-target navigation tasks. [ABSTRACT FROM AUTHOR]