Search results for " Fuzzy"
showing 10 items of 209 documents
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.
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…
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.
The fuzzy p-median problem: A global analysis of the solutions
2001
Abstract We apply fuzzy techniques to incorporate external data into p-median problems. So we can detect certain solutions that would be discarded by usual crisp and fuzzy algorithms but that contrasted with this additional information can be advantageous. This usually reveals a pathology of the model and hence our methods provide some fuzzy validation criteria for p-median models.
Marginal analysis for the fuzzy p-median problem
2008
The solutions to the fuzzy p-median problem make it possible to leave part of the demand uncovered in order to obtain significant reductions in costs. Moreover, the fuzzy formulation provides the decision-maker with many flexible solutions that he or she may prefer to the classical crisp solution. We introduce some marginal analysis techniques to study how solutions depend on membership functions. Taking into account the internal structure of the problem, we propose a practical criterion to fix the tolerances for the uncovered demand, which happens to be the most sensitive aspect of the fuzzy p-median.
Applying fuzzy Particle Swarm Optimization to Multi-unit Double Auctions
2010
Abstract In the context of Quadratic Programming Problems, we use a fuzzy Particle Swarm Optimization (PSO) algorithm to analyze a Multi-unit Double Auction (MDA) market. We give also a Linear Programming (LP) based upper bound to help the decision maker in dealing with constraints in the mathematical model. In the computational study, we evaluate our algorithm and show that it is a feasible approach for processing bids and calculating assignments.
Relaxed Stability and Performance LMI Conditions for Takagi-Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function Shapes
2008
Most linear matrix inequality (LMI) fuzzy control results in literature are valid for any membership function, i.e., independent of the actual membership shape. Hence, they are conservative (with respect to other nonlinear control approaches) when specific knowledge of the shapes is available. This paper presents relaxed LMI conditions for fuzzy control that incorporate such shape information in the form of polynomial constraints, generalizing previous works by the authors. Interesting particular cases are overlap (product) bounds and ellipsoidal regions. Numerical examples illustrate the achieved improvements, as well as the possibilities of solving some multiobjective problems. The result…
Fuzzy green vehicle routing problem for designing a three echelons supply chain
2020
Abstract In this study, a three-echelon fuzzy green vehicle routing problem (3E-FGVRP) is considered for designing a regional agri-food supply chain on a time horizon. To account for the variability associated with the quantities requested by customers, it is assumed that the demands are fuzzy numbers simulated by a time-dependent algorithm. Moreover, the vehicle fleet and distribution centres are considered with a defined capacity. The credibility theory of fuzzy sets is used to implement a multi-objective fuzzy chance-constrained programming model, where the total costs and carbon emissions are minimised. The resolution of the 3E-FGVRP is conducted by using a non-dominated sorting genetic…