Dealing with Interaction Between Bipolar Multiple Criteria Preferences in PROMETHEE Methods

In this paper, we consider the bipolar approach to Multiple Criteria Decision Analysis (MCDA). In particular we aggregate positive and negative preferences by means of the bipolar PROMETHEE method. To elicit preferences we consider Robust Ordinal Regression (ROR) that has been recently proposed to derive robust conclusions through the use of the concepts of possible and necessary preferences. It permits to take into account the whole set of preference parameters compatible with the preference information provided by the Decision Maker (DM)

A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.Choquet integral, Sugeno integral, capacity, bipolarity, preferences

Interior Point Decoding for Linear Vector Channels

In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector channels include many practically important channels such as inter symbol interference channels and partial response channels. It is shown that the maximum likelihood decoding (MLD) rule for a linear vector channel can be relaxed to a convex optimization problem, which is called a relaxed MLD problem. The proposed decoding algorithm is based on a numerical optimization technique so called interior point method with barrier function. Approximate variations of the gradient descent and the Newton methods are used to solve the convex optimization problem. In a decoding process of the proposed algorithm, a search point always lies in the fundamental polytope defined based on a low-density parity-check matrix. Compared with a convectional joint message passing decoder, the proposed decoding algorithm achieves better BER performance with less complexity in the case of partial response channels in many cases.Comment: 18 pages, 17 figures, The paper has been submitted to IEEE Transaction on Information Theor

Power Optimizations in MTJ-based Neural Networks through Stochastic Computing

Artificial Neural Networks (ANNs) have found widespread applications in tasks such as pattern recognition and image classification. However, hardware implementations of ANNs using conventional binary arithmetic units are computationally expensive, energy-intensive and have large area overheads. Stochastic Computing (SC) is an emerging paradigm which replaces these conventional units with simple logic circuits and is particularly suitable for fault-tolerant applications. Spintronic devices, such as Magnetic Tunnel Junctions (MTJs), are capable of replacing CMOS in memory and logic circuits. In this work, we propose an energy-efficient use of MTJs, which exhibit probabilistic switching behavior, as Stochastic Number Generators (SNGs), which forms the basis of our NN implementation in the SC domain. Further, error resilient target applications of NNs allow us to introduce Approximate Computing, a framework wherein accuracy of computations is traded-off for substantial reductions in power consumption. We propose approximating the synaptic weights in our MTJ-based NN implementation, in ways brought about by properties of our MTJ-SNG, to achieve energy-efficiency. We design an algorithm that can perform such approximations within a given error tolerance in a single-layer NN in an optimal way owing to the convexity of the problem formulation. We then use this algorithm and develop a heuristic approach for approximating multi-layer NNs. To give a perspective of the effectiveness of our approach, a 43% reduction in power consumption was obtained with less than 1% accuracy loss on a standard classification problem, with 26% being brought about by the proposed algorithm.Comment: Accepted in the 2017 IEEE/ACM International Conference on Low Power Electronics and Desig

Graph-Based Decoding in the Presence of ISI

We propose an approximation of maximum-likelihood detection in ISI channels based on linear programming or message passing. We convert the detection problem into a binary decoding problem, which can be easily combined with LDPC decoding. We show that, for a certain class of channels and in the absence of coding, the proposed technique provides the exact ML solution without an exponential complexity in the size of channel memory, while for some other channels, this method has a non-diminishing probability of failure as SNR increases. Some analysis is provided for the error events of the proposed technique under linear programming.Comment: 25 pages, 8 figures, Submitted to IEEE Transactions on Information Theor

Crisp-linear-and Models in Fuzzy Multiple Objective Linear Fractional Programming

The aim of this paper is to introduce two crisp linear models to solve fuzzy multiple objective linear fractional programming problems. In a novel manner we construct two piece-wise linear membership functions to describe the fuzzy goal linked to a linear fractional objective. They are related to the numerator and denominator of the fractional objective function; and we show that using the fuzzy-and operator to aggregate them a convenient description of the original fractional fuzzy goal is obtained. Further on, with the help of the fuzzy-and operator we aggregate all fuzzy goals and constraints, formulate a crisp linear model, and use it to provide a solution to the initial fuzzy multiple objective linear fractional programming problem. The second model embeds in distinct ways the positive and negative information, the desires and restrictions respectively; and aggregates in a bipolar manner the goals and constraints. The main advantage of using the new models lies in the fact that they are linear, and can generate distinct solutions to the multiple objective problem by varying the thresholds and tolerance limits imposed on the fuzzy goals