Search results for "fuzzy classification"
showing 10 items of 34 documents
On central algorithms of approximation under fuzzy information
2005
We consider the problem of approximation of an operator by information described by n real characteristics in the case when this information is fuzzy. We develop the well-known idea of an optimal error method of approximation for this case. It is a method whose error is the infimum of the errors of all methods for a given problem characterized by fuzzy numbers in this case. We generalize the concept of central algorithms, which are always optimal error algorithms and in the crisp case are useful both in practice and in theory. In order to do this we define the centre of an L-fuzzy subset of a normed space. The introduced concepts allow us to describe optimal methods of approximation for lin…
Fuzzy expected utility
1984
Decision making under uncertainty requires not only measures of the uncertainty of situations that we try to recognize , but also an estimate of the imprecision from which they are determined. This imprecision can be the result either of a lack of exactness in the measure of the elements which are necessary to the determination of the states of nature or the purely subjective interpretation of these states. Through a subjective measure of the non-measurable imprecision, the purpose of the fuzzy expected utility, which is investigated, is to translate with a great accuracy the imprecise behaviour of the decision-maker in an uncertain world. Consequently we propose to introduce first the prob…
The fuzzy p-median problem
2004
In many location models, the strong crisp assumptions, like known demands and distances, are not realistic in most cases. The fuzzy p-median problem relaxes this hypothesis giving to the decision maker a necessary degree of freedom to solve real-world problems. It allows a decision maker to improve an optimal covering of a location problem by considering partially feasible solutions in which some demand is left uncovered. Here we revise the main facts and results about this problem emphasising different specific algorithms of resolution. Finally we show that this fuzzy version can be used to analyse the global structure of a given instance of the crisp problem.
Soft-computing based heuristics for location on networks: The p-median problem
2011
We propose a genetic algorithm for the fuzzy p-median problem in which the optimal transport cost of the associated crisp problem is unknown. Our algorithm works with two populations: in one, the solutions with a better crisp transport cost are favored by the selection criterion, whereas in the second one, solutions with a better fuzzy satisfaction level are preferred. These populations are not independent. On the contrary, the first one periodically invades the second one, thus providing new starting points for finding fuzzy improvements. Our computational results also reveal the importance of choosing adequate functions for selecting the parents. Our best results are obtained with functio…
Involving fuzzy orders for multi-objective linear programming
2012
This paper presents a solution approach for multi-objective linear programming problem. We propose to involve fuzzy order relations to describe the objective functions where in ”classical” fuzzy approach the membership functions which illustrate how far the concrete point is from the solution of individual problem are studied. Further the global fuzzy order relation is constructed by aggregating the individual fuzzy order relations. Thus the global fuzzy relation contains the information about all objective functions and in the last step we find a maximum in the set of constrains with respect to the global fuzzy order relation. We illustrate this approach by an example.
Controller Design Under Fuzzy Pole-Placement Specifications: An Interval Arithmetic Approach
2006
This paper discusses fuzzy specifications for robust controller design, as a way to define different specification levels for different plants in a family and allow the control of performance degradation. Controller synthesis will be understood as mapping a fuzzy plant onto a desired fuzzy set of closed-loop specifications. In this context, a fuzzy plant is considered as a possibility distribution on a given plant space. In particular, pole placement in linear plants with fuzzy parametric uncertainty is discussed, although the basic idea is general and could be applied to other settings. In the case under consideration, the controller coefficients are the solution of a fuzzy linear system o…
Mathematical Morphology Based on Fuzzy Operators
1993
A vision procedure may be considered as the repeated application of image operators until the vision goal is reached. The type of these operators and the spaces on which they are defined and act depends on the specific problem and on what we are searching on the image. Morphological operations, as filtering, edge detection, skeletonizing, and so on, are mainly required at low and medium levels of the vision procedure, where local and global knowledge is used to enhance the image information content, before a final decision about the image is taken.
An exact algorithm for the fuzzy p-median problem
1999
In this paper we propose a fuzzy version of the classical p-median problem. We consider a fuzzy set of constraints so that the decision-maker will be able to take into account solutions which provide significantly lower costs by leaving a part of the demand uncovered. We propose an algorithm for solving the problem which is based on Hakimi's works and we compare the crisp and the fuzzy approach by means of an example.
On the equivalence of two optimization methods for fuzzy linear programming problems
2000
Abstract The paper analyses the linear programming problem with fuzzy coefficients in the objective function. The set of nondominated (ND) solutions with respect to an assumed fuzzy preference relation, according to Orlovsky's concept, is supposed to be the solution of the problem. Special attention is paid to unfuzzy nondominated (UND) solutions (the solutions which are nondominated to the degree one). The main results of the paper are sufficient conditions on a fuzzy preference relation allowing to reduce the problem of determining UND solutions to that of determining the optimal solutions of a classical linear programming problem. These solutions can thus be determined by means of classi…
Viability of infeasible portfolio selection problems: A fuzzy approach
2002
Abstract This paper deals with fuzzy optimization schemes for managing a portfolio in the framework of risk–return trade-off. Different models coexist to select the best portfolio according to their respective objective functions and many of them are linearly constrained. We are concerned with the infeasible instances of such models. This infeasibility, usually provoked by the conflict between the desired return and the diversification requirements proposed by the investor, can be satisfactorily avoided by using fuzzy linear programming techniques. We propose an algorithm to repair infeasibility and we illustrate its performance on a numerical example.