Bezhan Ghvaberidze

Using a minimal fuzzy covering in decision-making problems

A new criterion is introduced for minimal fuzzy covering problems, which is a minimal value of the average misbelief contained in the possible alternatives. A bicriteria problem is obtained using this new criterion and the criterion of covering price minimization. The proposed approach is illustrated by an example.

Fuzzy-probabilistic aggregations in the discrete covering problem

In this paper, a new criterion is introduced for the discrete covering problem. In this criterion, the a priori information represented by a fuzzy measure and a misbelief distribution on alternatives are condensed by aggregation instruments. Using the Dempster–Shafer belief structure and representations of fuzzy measures through associated probabilities, several variants of a new criterion for the discrete covering problem are constructed based on aggregations by two types of the most typical value, namely, monotone expectation and fuzzy expected value. A bicriterial problem is obtained using one of the variants of the new criterion and the criterion of average price minimisation. The example on the application of a new criterion is presented, where the possibility distribution on the optimal choice of the candidates (alternatives) is represented by expert valuations.

Multistage decision-making fuzzy methodology for optimal investments based on experts’ evaluations

A new methodology of making a decision on an optimal investment in several projects is proposed. The methodology is based on experts’ evaluations and consists of three stages. In the first stage, Kaufmann’s expertons method is used to reduce a possibly large number of applicants for credit. Using the combined expert data, the credit risk level is determined for each project. Only the projects with low risks are selected.

A comparison of probabilistic-based optimization approaches for vehicle routing problems

Estimation of distribution algorithms (EDAs) are evolutionary algorithms that use probabilistic modeling to lead a more efficient search for optimal solutions. While EDAs have been applied to several types of optimization problems, they exhibit some limitations to deal with constrained optimization problems. More study and understanding of how can EDAs deal with these problems is required. In this paper we investigate the application of EDAs to a version of the vehicle routing problem in which solutions should satisfy a number of constraints involving the customers, the fleet vehicle, and the items to be delivered. For this problem, we compare two different representations of the solutions, and apply EDAs that use three probabilistic models with different characteristics. Our results show that the combination of an integer representation with tree-based probabilistic model produces the best results and is able to solve vehicle routing problems that contain over thousands of promising paths.

On the new multistage Fuzzy Technology to Investment Decisions

This article proposes a novel Fuzzy Technology to support the Investment Decisions. While choosing among competitive investment projects, this technology provides the selection of projects with minimal crediting risks, makes ranking of chosen projects and then allows to optimally allocate investment amounts between several of them. The technology combines two fuzzy-statistical methods and solution of bicriteria discrete optimization problem, providing three stages of investment projects evaluation.

Possibilistic aggregation in the discrete covering problems based on the expert valuations

In this paper a new criterion is introduced for the discrete covering problem. Using the representation of a possibility measure through associated probabilities, a new criterion for discrete covering problem is constructed based on aggregation by the Monotone Expectation (ME) (or Choquet integral). In this criterion the a priori information represented by a possibility measure and a misbelief distribution on alternatives are condensed by aggregation instrument. A bicriterial problem is obtained using a new criterion and the criterion of average price minimization. The example on the application of a new criterion is presented, where the possibility distribution on the optimal choice of the alternatives (candidates) is represented by expert valuations.