Petr Ekel

Fuzzy Multicriteria Decision-Making: Models, Methods and Applications

Fuzzy Multicriteria Decision-Making: Models, Algorithms and Applications addresses theoretical and practical gaps in considering uncertainty and multicriteria factors encountered in the design, planning, and control of complex systems. Including all prerequisite knowledge and augmenting some parts with a step-by-step explanation of more advanced concepts, the authors provide a systematic and comprehensive presentation of the concepts, design methodology, and detailed algorithms. These are supported by many numeric illustrations and a number of application scenarios to motivate the reader and make some abstract concepts more tangible.

A dynamic consensus scheme based on a nonreciprocal fuzzy preference relation modeling

In this paper, we propose a dynamical consensus scheme which makes use of an index of comparability and of an index of concordance to regulate the information flow in the discussion among the experts. In addition to the traditional use of a concordance index to identify the discordant expert, who can be invited to review his opinion or to explain his judgment to the other experts, here an index of comparability is utilized to identify the experts that have faced difficulties in expressing their preferences. With this information at hand, a moderator can invite the experts that are confident on their opinions to support the experts that are hesitating in the construction of the fuzzy preference relations.

Fuzzy Preference Relations: Methods and Power Engineering Applications

Two classes of problems are considered within the framework of a general approach to solve optimisation problems with fuzzy coefficients, referred to as and models in the literature. This paper is concerned with the latter and proposes an approach which replaces the initial problem by a set of associated mutually interrelated models. To reduce the decision uncertainty region, the problem is converted to a multicriteria decision problem in a fuzzy environment using two methods. The first method reduces the region sequentially through a step-by-step comparison of alternatives. The second method analyses membership functions of a subset of non-dominated alternatives, considering all criteria simultaneously. The results have general applicability and are being used in power engineering planning in Brazil.

An interval space reducing method for constrained problems with particle swarm optimization

In this paper, we propose a method for solving constrained optimization problems using Interval Analysis combined with Particle Swarm Optimization. A Set Inverter Via Interval Analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a Space Cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified Particle Swarm Optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100,000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.

Construction of nonreciprocal fuzzy preference relations with the use of preference functions

In order to model the preferences of a decision-maker (DM) by means of fuzzy preferencerelations, a DM can utilize different preference formats (such as ordering of the alternatives, utility values, multiplicative preference relations, fuzzy estimates, and reciprocal as well as nonreciprocal fuzzy preference relations) to express his/her judgments. Afterward, the obtained information is utilized to constructfuzzy preference relations. Here we introduce a procedure that allows the use of so-called preference functions (which is a preference format utilized in the methods of PROMETHEE family) to construct nonreciprocal fuzzy preference relations. With diverse preference formats being offered, a DM can select the onethat is the most convenient to articulate his/her preferences. In order to demonstrate the applicability of theproposed procedure a multicriteria decision-making problem related to the site selection for constructing anew hospital is considered here.

Fuzzy logic based control of voltage and reactive power in subtransmission system

This paper presents results of research related to the second stage of the project dedicated to developing and employing the xOMNI system (software of the SCADA type). This stage is associated with the elaboration of the Energy Management System (EMS) for the subtransmission system of the Minas Gerais State Energy Company. One of the most important EMS functions is voltage and reactive power control. Its implementation is based on the use of fuzzy logic technology. Taking this into account, the paper covers the consideration of questions of building diverse types of sensitivity indices and forming production rules providing comprehensive and flexible solutions in conditions of regulated and deregulated environments. Some aspects of rational carrying out fuzzy logic procedures are considered as well.

Fuzzy Coefficients and Fuzzy Preference Relations in Models of Decision Making

Analysis of models is considered as part of a general approach to solving a wide class of optimization problems with fuzzy coefficients. This approach consists in formulating and solving one and the same problem within the framework of interrelated models to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty region is based on reduction of the problem to multiobjective decision making in a fuzzy environment with applying techniques based on fuzzy preference relations. The results of the paper are of a universal character and are already being used to solve power engineering problems.

Fuzzy Preference Based Organizational Performance Measurement

This paper introduces a methodology for constructing a multidimesional indicator designed for organizational performance measurement. The methodology involves the application of fuzzy models and methods of their analysis. Its use requires the construction of fuzzy preference relations by means of the comparison of performance measures with respect to a reference standard defined as a predetermined scale consisting of linguistic terms. The exploitation of the fuzzy preference relations is carried out by means of the Orlovsky choice procedure. An application example related to the organizational performance evaluation with the use of the proposed methodology is considered, in order to demonstrate its applicability.

Artificial neural network engine: parallel and parameterized architecture implemented in FPGA

In this paper we present and analyze an artificial neural network hardware engine, its architecture and implementation. The engine was designed to solve performance problems of the serial software implementations. It is based on a hierarchical parallel and parameterized architecture. Taking into account verification results, we conclude that this engine improves the computational performance, producing speedups from 52.3 to 204.5 and its architectural parameterization provides more flexibility.

Fuzzy Preference Relations and Multiobjective Decision Making

Analysis of models is considered as part of a general approach to solving optimization problems with fuzzy coefficients. This approach consists in formulating and solving one and the same problem within the framework of mutually interrelated models with constructing equivalent analogs with fuzzy coefficients in objective functions alone. The use of the approach allows one to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty regions is based on reduction of the problem to models of multiobjective decision-making in a fuzzy environment with the use of fuzzy preference relation techniques for analyzing these models. Three techniques are considered in the paper. The first technique is of a lexicographic character and consists in step-by-step introducing criteria (fuzzy preference relations). The second technique is based on building of a membership function of a subset of nondominated alternatives with simultaneous considering all preference relations. The third technique is related to aggregating membership functions of subsets of nondominated alternatives corresponding to each preference relation. The results of the paper are of a universal character and are already being used to solve problems of power engineering and management.