44,989 research outputs found

    MULTI CRITERIA DECISION MAKING MODELS: AN OVERVIEW ON ELECTRE METHODS

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    In portfolio analysis, there are a few models that can be used. Therefore, the aim of this paper is to make an overview on multi criteria decision making models, in particular, on ELECTRE methods. We discuss the different versions of ELECTRE, which exist and why they exist. So, when speaking about ELECTRE methods structure, we have to consider two main procedures: construction of one or several outranking relation(s) procedure, and exploitation procedure. In the exploitation procedure, recommendations are elaborated from the results obtained in the first phase. The nature of the recommendation depends on the problematic: choosing, ranking or sorting. Each method is characterized by its construction and exploitation procedure. For choice problem, we can apply ELECTRE I, ELECTRE Iv, and ELECTRE IS; for ranking problem, we can apply ELECTRE II, ELECTRE III, ELECTRE IV and ELECTRE-SS; and for sorting problem we can apply ELECTRE TRI. Finally, some failings on ELECTRE methods assumptions are discussed, for instance, rank reversals. So, when analyzing portfolio management decision problem, the literature suggests AHP method and PROMETHEE family.CAPM; decision problem; multi criteria decision making models; ELECTRE family; ELECTRE rank reversals

    Dual-lattice ordering and partial lattice reduction for SIC-based MIMO detection

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    This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, we propose low-complexity lattice detection algorithms for successive interference cancelation (SIC) in multi-input multi-output (MIMO) communications. First, we present a dual-lattice view of the vertical Bell Labs Layered Space-Time (V-BLAST) detection. We show that V-BLAST ordering is equivalent to applying sorted QR decomposition to the dual basis, or equivalently, applying sorted Cholesky decomposition to the associated Gram matrix. This new view results in lower detection complexity and allows simultaneous ordering and detection. Second, we propose a partial reduction algorithm that only performs lattice reduction for the last several, weak substreams, whose implementation is also facilitated by the dual-lattice view. By tuning the block size of the partial reduction (hence the complexity), it can achieve a variable diversity order, hence offering a graceful tradeoff between performance and complexity for SIC-based MIMO detection. Numerical results are presented to compare the computational costs and to verify the achieved diversity order

    Ordering Metro Lines by Block Crossings

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    A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually equivalent. We suggest merging crossings into block crossings, that is, crossings of two neighboring groups of consecutive lines. Unfortunately, minimizing the total number of block crossings is NP-hard even for very simple graphs. We give approximation algorithms for special classes of graphs and an asymptotically worst-case optimal algorithm for block crossings on general graphs. That is, we bound the number of block crossings that our algorithm needs and construct worst-case instances on which the number of block crossings that is necessary in any solution is asymptotically the same as our bound

    Multi-criteria analysis applied to multi-objective optimal pump scheduling in water systems

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    This work presents a multi-criteria-based approach to automatically select specific non-dominated solutions from a Pareto front previously obtained using multi-objective optimization to find optimal solutions for pump control in a water supply system. Optimal operation of pumps in these utilities is paramount to enable water companies to achieve energy efficiency in their systems. The Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) is used to rank the Pareto solutions found by the Non-Dominated Sorting Genetic Algorithm (NSGA-II) employed to solve the multi-objective problem. Various scenarios are evaluated under leakage uncertainty conditions, resulting in fuzzy solutions for the Pareto front. This paper shows the suitability of the approach for quasi real-world problems. In our case-study, the obtained solutions for scenarios including leakage represent the best trade-off among the optimal solutions, under some considered criteria, namely, operational cost, operational lack of service, pressure uniformity and network resilience. Potential future developments could include the use of clustering alternatives to evaluate the goodness of each solution under the considered evaluation criteria

    Securing level 2 in mathematics (National Strategies: primary)

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    "The guidance identifies key areas of learning that children need to secure to attain level 2 in mathematics. While you will integrate the ideas from these materials into your ongoing planning, you could also use them to plan targeted support for particular groups of children. There is a double-page spread for each of the six areas of mathematics: ‱ Counting, comparing and ordering numbers ‱ Understanding addition and subtraction and their relationship ‱ Using mental calculation strategies to solve problems involving addition and subtraction ‱ Recognising and describing shapes ‱ Understanding and using standard units and equipment to measure ‱ Organising and interpreting data to answer questions" - Page 1

    System optimization by multiobjective genetic algorithms and analysis of the coupling between variables, constraints and objectives

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    This paper presents a methodology based on Multiobjective Genetic Algorithms (MOGA’s) for the design of electrical engineering systems. MOGA’s allow to optimize multiple heterogeneous criteria in complex systems, but also simplify couplings and sensitivity analysis by determining the evolution of design variables along the Pareto-optimal front. A rather simplified case study dealing with the optimal dimensioning of an inverter – permanent magnet motor – reducer – load association is carried out to demonstrate the interest of the approach

    Fuzzy Weighted Average: Analytical Solution

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    An algorithm is presented for the computation of analytical expressions for the extremal values of the α-cuts of the fuzzy weighted average, for triangular or trapeizoidal weights and attributes. Also, an algorithm for the computation of the inverses of these expressions is given, providing exact membership functions of the fuzzy weighted average. Up to now, only algorithms exist for the computation of the extremal values of the α-cuts for a fixed value of α. To illustrate the power of our algorithms, they are applied to several examples from the literature, providing exact membership functions in each case
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