Ivan Popchev

Properties of the aggregation operators related with fuzzy relations

Abstract The problem of information generalization in multicriteria decision making is considered in this paper. The information is unified by fuzzy relations and the generalization is realized with the help of aggregation operators. Some of the most oftenly used operators are presented and their properties depending on the properties of the fuzzy relations, which they aggregate, are proved. The sensitivity of the operators with respect to variations in their arguments is investigated. The numerical example deciding the problem of alternatives’ ranking is given as well.

Comparison of clusters from fuzzy numbers

Fuzzy numbers are used for representation of numerical quantities in a vague environment. Their comparison or ranking is important for application purposes. A new index for comparing of fuzzy numbers based on their geometrical properties is suggested in this paper. This geometrical index is tested on a group of selected examples and compared with the other well-known indexes. A method for comparison of m-tuples of fuzzy numbers and an algorithm for comparison of subsets (clusters) of similar, closed m-tuples of trapezoidal fuzzy numbers are presented.

Aggregation of fuzzy preference relations to multicriteria decision making

Weighted aggregation of fuzzy preference relations on the set of alternatives by several criteria in decision-making problems is considered. Pairwise comparisons with respect to importance of the criteria are given in fuzzy preference relation as well. The aggregation procedure uses the composition between each two relations of the alternatives. The membership function of the newly constructed fuzzy preference relation includes t-norms and t-conorms to take into account the relation between the criteria importance. Properties of the composition and new relation, giving a possibility to make a consistent choice or to rank the alternatives, are proved. An illustrative numerical study and comparative examples are presented.

An ontology based CBR architecture for knowledge management in BULCHINO catalogue

In this paper we present otology-based architecture for knowledge management in BULCHINO web-based catalogue for Bulgarian cultural heritage. Our approach for realizing content-based search and retrieval in the catalogue implies the application of the CBR technology for the representation of metadata characterizations of the cultural objects and the integration of ontology for semantic formalization of these characterizations. We provide an insight of the technical aspects of the architecture by enumerating the technological requirements, where we pay specific attention to the CBR framework jCOLIBRI and its features for implementing concept-based similarity assessment.

Enhancement of DeLC for the provision of intelligent mobile services

This paper presents new enhanced version of Distributed eLearning Center (DeLC), providing intelligent mobile services for users in a university campus. The main enhancements are related to the extension of DeLC network model to a 3-tier structure and introduction of new intelligent elements into it. A re-engineering approach for the realization of required changes in DeLC system architecture is proposed, which allows re-use of services already deployed in the existing version of DeLC and development of new mobile services based on intelligent agents used as personal helpers for DeLC users. A description of some of the mobile services along with supporting communication infrastructure is also provided.

FUZZY LOGIC OPERATORS IN DECISION-MAKING

The fuzzy logic operators are used to decide the following multicriteria decision-making problem. A finite set of alternatives is evaluated by a set of fuzzy criteria, i.e., fuzzy relations, which may be either fuzzy preference, or similarity, or likeness relations. The problem is to construct an evaluation procedure to compare the set of alternatives according to the whole set of criteria, i.e., to aggregate the private fuzzy relations in order to get the union relation as a fuzzy one, enhancing to solve the ranking, choice, or cluster problem. Some properties of these operators, required to decide the ranking, choice, or cluster problems and depending on the properties of the private relations, are proved. A numerical example is given as well.

New upper estimates for the solution of the continuous algebraic Lyapunov equation

A new result for bounding the summations for solution eigenvalues of the algebraic Lyapunov equation is presented. This makes possible to generate the best known upper scalar solution estimates.

A Multi-Step Procedure for Asset Allocation in Case of Limited Resources

Abstract Portfolio management is a process involving decision making in dynamic and unpredictable environment. Asset allocation plays a key role in this process, since the optimal use of the capital is a complex and resource-consuming problem. During our research in this field we have detected some problems that lead to biased results and one of them occurs in case of limited financial resources. In this paper a mathematical assessment of the dependence of the capital, used on asset prices is derived, and a multi-step procedure for asset allocation, aiming at optimization of the investor’s utility in case of limited resources is described. The procedure is implemented as a module in a decision support system based on fuzzy logic. The paper contains comparison of the obtained test results with results from the classical Markowitz portfolio model. The conducted tests are on real data from the Bulgarian stock exchange.

Cardinality Problem in Portfolio Selection

There is a variety of models for portfolio selection. However, in portfolio theory applications little or no attention is paid to the cardinality problem. In this paper, an algorithm for dealing with this problem is presented. The proposed allocation algorithm is implemented in a software system, which is based on the Fuzzy Logic Q-measure Model and manages financial investments in real time. Tests on real data from Bulgarian Stock Exchange are presented as illustration to the solution.

Perturbation Bounds for the Nonlinear Matrix Equation

In this paper we make a complete perturbation analysis of the nonlinear matrix equation, where A and B are square complex matrices, denotes the complex conjugate transpose of the matrix A and I is the identity matrix. We obtain local (first order) perturbation bounds and a non-local perturbation bound for the solution to the equation. The perturbation bounds allow to derive condition and accuracy estimates for the computed solution, when using a stable numerical algorithm to solve the equation.