Dorota Kuchta

In this paper it is shown how to assess the degree of influence of various factors on the value of the project (NPV). The assessment is based on grouping and ranking of cash flows linked to various factors. The formulas are generated both for crisp and fuzzy net present value analysis. The projects are then evaluated on the basis of at least two criteria: the NPV and the risk (positive or negative) linked to the factors which have most influence on the project's NPV whose change may change the NPV considerably. In applications, fuzzy present values of different factors are calculated and compared for two different cases.

Fuzzy equivalents of all the classical capital budgeting (investment choice) methods are generalised or proposed. These equivalents can be used to evaluate and compare projects in which the cash flows, duration time and required rate of return (cost of capital) are given imprecisely, in ...

We put forward a fuzzy way of measuring the criticality of project activities and of the whole project. In the proposed approach both the decision maker attitude and the project network structure are taken into account. The criticality measure obtained may serve as a measure of risk or of the supervision effort needed and can help in making the decision whether to accept or to reject the project. Its numerical implementation is as difficult as that of the classical CPM method.

One machine scheduling problem with fuzzy processing times and a penalty for e ach job being late (the penalty is ind e - pendent of the magnitude of the lateness) i s considered. The optimal sequence is de- fined as one minimizing the e xpected v alue of the total penalty (the e xpected weighted number of jobs being late).

The least squares method is used to determine the fuzzy regression. The data for the regression equation are observations for the output and input variables. Analogous assumptions for those used in case of the classical regression are adopted - concerning the fuzzy random component of the model. It is shown how to determine the possibilistic distributions of the output variable and the model coefficients if the random component of the model is an L-R fuzzy variable and its generative probabilistic distribution is known.

The paper proposes three fuzzy regression models - concerning temperature and electricity load - based on real data. In the first two models the monthly temperature in a period of four years in a Polish city is analyzed. We assume the temperature to be fuzzy and its dependence on time and on the temperature in the previous month is determined. In the construction of the fuzzy regression models the least square methods was used. In the third model we analyze the dependence of the daily electricity load (assumed to be a fuzzy number) on the (crisp) temperature. Outliers, i.e. non-typical instances in the observations are identified, using a modification of an identification method known from the literature. The proposed method turns out to identify the outliers consistently with the real meaning of the experimental data.

The chapter presents selected problems and algorithms of fuzzy discrete optimization. The problems discussed constitute fuzzy equivalents of the following crisp ones: the maximal and cheapest flow and the shortest route problem in a network, the transportation and assignment problems, the CPM and PERT method, a selection of scheduling problems, the set covering problem, the knapsack problem as well as the general 0–1 programming problem.

We generalize known concepts (those introduced by Ishihuchi and Tanaka [1] and Rommerlfanger et al. [2]) of the solution of the linear programming problem with interval coefficients in the objective function based on preference relations between intervals. We unify all the discussed concepts as well as the corresponding solution methods into one general framework.

The paper presents an algorithm for determining non-dominated basic solutions of thelinear programming problem with two objectives in which the coefficients depend in a linearway on a parameter, and a modified version of an algorithm for the non-parametric case.