Stefan Chanas

The use of parametric programming in fuzzy linear programming

In this paper the possibility of the identification of a complete fuzzy decision (not only the maximizing alternative) in fuzzy linear programming by use of the parametric programming technique is presented. Also, it is shown that this fact can be useful in the Zimmermann approach to multiple objective linear programming. The presented remarks are illustrated by some numerical examples.

The use of fuzzy variables in pert

Abstract In this paper we present a method—called Fpert —for estimating a project completion time in the situation when activity duration times in the project network model are given in the form of fuzzy variables—fuzzy sets on time space. Theoretical foundations of the method as well as results of calculations derived from a simple example are included.

A concept of the optimal solution of the transportation problem with fuzzy cost coefficients

Abstract In the paper a definition of the optimal solution of the transportation problem with fuzzy cost coefficients as well as an algorithm determining this solution are proposed.

Multiobjective programming in optimization of interval objective functions -- A generalized approach

Abstract 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.

Critical path analysis in the network with fuzzy activity times

A natural generalization of the criticality notion in a network with fuzzy activity times is given. It consists in direct application of the extension principle of Zadeh to the notion of criticality of a path (an activity, an event) treated as a function of the activities duration times in the network. There are shown some relations between the notion of fuzzy criticality, introduced in the paper, and the notion of interval criticality (criticality in the network with interval activity times) proposed by the authors in another paper. Two methods of calculation of the path degree of criticality (according to the proposed concept of fuzzy criticality) are presented.

A fuzzy approach to the transportation problem

Abstract The transportation problem with fuzzy supply values of the deliverers and with fuzzy demand values of the receivers is analysed. For the solution of the problem the technique of parametric programming is used. This makes it possible to obtain not only the maximizing solution (according to the Bellman-Zadeh criterion) but also other alternatives close to the optimal solution.

Single value simulation of fuzzy variables

Abstract The basic ideas of the present paper arise from relations between random sets and fuzzy ones. The suggested approach, which may be called Fuzzy-Numerical Simulation, allows for ascribing a precise numerical value to a fuzzy variable by generating a value of a random variable related in some way to the fuzzy variable. The so-called generative characteristics of a fuzzy variable being the expected value and variance of the generating random variable are introduced. The problem of simultaneous generating values of two fuzzy variables is also discussed. Finally, methods of generating when a fuzzy variable is described with a complex body of evidence are presented.

On the interval approximation of a fuzzy number

The notion of an approximation interval of a fuzzy number is introduced. It is the interval which fulfills two conditions. In the first, its width is equal to the width of a fuzzy number being approximated. In the second, the Hamming distance between this interval and the approximated number is minimal. The introduced notion is compared with the notion of expected interval of a fuzzy number known in literature.

Fuzzy integer transportation problem

An algorithm has been proposed which solves the transportation problem with fuzzy supply and demand values and the integrality condition imposed on the solution. This algorithm is exact and computationally effective, although the problem is formulated in the general way, i.e. its fuzzy supply and demand values can differ from each other and be fuzzy numbers of any type.

The computational complexity of the criticality problems in a network with interval activity times

Abstract The paper analyzes the criticality in a network with interval activities duration times. A natural generalization of the criticality notion (for a path, an activity and an event) for the case of network with interval activity duration times is given. The computation complexity of five problems linked to the introduced criticality notion is presented.