Department of Computer Science & Engineering

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IIT Jodhpur

School of Artificial Intelligence and Data Science (AIDE)

In this article we want to demonstrate that under mild conditions the barrier method is an effective solution approach for convex optimization problems whose objective is nonsmooth and whose feasible set is described by smooth inequality constraints in which all the constraint functions need not be convex. © 2014, Springer-Verlag Berlin Heidelberg.

Optimization Letters

Barrier method in nonsmooth convex optimization without convex representation

A class of compensative weighted averaging (CWA) aggregation operators, having a dedicated parameter to model compensation, is presented. The variants of CWA operator with ordered weighted averaging (OWA) operator are developed. The proposed operators are compared, both theoretically and empirically, with other operators in terms of their compensation abilities. Two approaches are proposed to learn the compensation parameter and the weight vector from the given data. The proposed learning approaches are applied in four case-studies, involving real experimental data. The usefulness of CWA operators in strategic multi-criteria decision making and supplier selection is also highlighted. © 2014 Elsevier B.V. All rights reserved.

Applied Soft Computing Journal

Compensative weighted averaging aggregation operators

Directionality analysis of time-series, recorded from task-activated regions-of-interest (ROIs) during functional Magnetic Resonance Imaging (fMRI), has helped in gaining insights of complex human behavior and human brain functioning. The most widely used standard method of Granger Causality for evaluating directionality employ linear regression modeling of temporal processes. Such a parameter-driven approach rests on various underlying assumptions about the data. The short-comings can arise when misleading conclusions are reached after exploration of data for which the assumptions are getting violated. In this study, we assess assumptions of Multivariate Autoregressive (MAR) framework which is employed for evaluating directionality among fMRI time-series recorded during a Sensory-Motor (SM) task. The fMRI time-series here is an averaged time-series from a user-defined ROI of multiple voxels. The 'aim' is to establish a step-by-step procedure using statistical methods in conjunction with graphical methods to seek the validity of MAR models, specifically in the context of directionality analysis of fMRI data which has not been done previously to the best of our knowledge. Here, in our case of SM task (block design paradigm) there is violation of assumptions, indicating the inadequacy of MAR models to find directional interactions among different task-activated regions of brain. © 2015 IEEE.

World University root node

Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS

Assessing assumptions of multivariate linear regression framework implemented for directionality analysis of fMRI

A new family of induced ordered weighted averaging (OWA) operators is proposed by invoking the order-inducing variables at the aggregation step. The objective is to consider the variations in the magnitudes of the order-inducing variables. The new family of operators include weighted induced OWA, weighted generalized induced OWA, and weighted induced ordered weighted geometric operators. These are further extended to the intuitionistic fuzzy domain. The usefulness of these operators is shown in a supplier selection problem. © 2014 Wiley Periodicals, Inc.

International Journal of Intelligent Systems

A new family of induced OWA operators

Evolutionarymulti- andmany-objective optimization (EMO) methods attempt to find a set of Pareto-optimal solutions, instead of a single optimal solution. To evaluate these algorithms, performancemetrics either require the knowledge of the true Pareto-optimal solutions or, are ad-hoc and heuristic based. In this paper, we suggest a KKT proximity measure (KKTPM) that can provide an estimate of the proximity of a set of trade-off solutions from the true Pareto-optimal solutions. Besides theoretical results, the proposed KKT proximity measure is computed for iteration-wise trade-off solutions obtained from specific EMO algorithms on two, three, five and 10-objective optimization problems. Results amply indicate the usefulness of the proposed KKTPM as a termination criterion for an EMO algorithm. © Springer International Publishing Switzerland 2015.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

An optimality theory based proximity measure for evolutionary multi-objective and many-objective optimization

The compensative weighted averaging (CWA) operator is generalized to develop a class of powerful generalized compensative weighted averaging (GCWA) operators with a very fine range of compensatory effects. The conventional means are shown to be the special cases of the proposed GCWA operator. A few extensions are investigated by combining GCWA operator with ordered weighted averaging (OWA) and induced OWA (IOWA) operators. An exponential class of aggregation operators such as exponential CWA, exponential OWA and exponential IOWA operators are developed. The usefulness of GCWA operators is shown through several examples and a case-study. © 2015 Elsevier Ltd. All rights reserved.

Computers and Industrial Engineering

Generalized compensative weighted averaging aggregation operators

Abstract We present a method to learn the criteria weights in multi-criteria decision making (MCDM) by applying emerging learning-to-rank machine learning techniques. Given the pairwise preferences by a decision maker (DM), we learn the weights that the DM attaches to the multiple criteria, characterizing each alternative. As the training information, our method requires the pairwise preferences of alternatives, as revealed by the DM. Once, the DM's decision model is learnt in terms of the criteria weights, it can be applied to predict his choices for any new set of alternatives. The empirical validation of the proposed approach is done on a collection of 12 standard datasets. The accuracy values are compared with those obtained for the state-of-the-art methods such as ranking-SVM and TOPSIS. © 2015 Elsevier Inc.

Information Sciences

On learning of weights through preferences

In this article, we intend to study several scalar-valued gap functions for Stampacchia and Minty-type vector variational inequalities. We first introduce gap functions based on a scalarization technique and then develop a gap function without any scalarizing parameter. We then develop its regularized version and under mild conditions develop an error bound for vector variational inequalities with strongly monotone data. Further, we introduce the notion of a partial gap function which satisfies all, but one of the properties of the usual gap function. However, the partial gap function is convex and we provide upper and lower estimates of its directional derivative. © 2014, © 2014 Taylor & Francis.

Optimization

Gap functions for vector variational inequalities

We extend the fuzzy rough set as probabilistic fuzzy rough set (PFRS) on a fuzzy probabilistic approximation space. The proposed PFRS models both vague and uncertain information at the same time. The viability of PFRS in decision making is illustrated through a case study. PFRS is shown to be useful for both probabilistic as well as deterministic problems. © 2015 - IOS Press and the authors. All rights reserved.

Journal of Intelligent and Fuzzy Systems

Probabilistic fuzzy rough sets

Combining established modelling techniques from multiple-criteria decision aiding with recent algorithmic advances in the emerging field of preference learning, we propose a new method that can be seen as an adaptive version of TOPSIS, the technique for order preference by similarity to ideal solution decision model (or at least a simplified variant of this model). On the basis of exemplary preference information in the form of pairwise comparisons between alternatives, our method seeks to induce an 'ideal solution' that, in conjunction with a weight factor for each criterion, represents the preferences of the decision maker. To this end, we resort to probabilistic models of discrete choice and make use of maximum likelihood inference. First experimental results on suitable preference data suggest that our approach is not only intuitively appealing and interesting from an interpretation point of view but also competitive to state-of-the-art preference learning methods in terms of prediction accuracy. © 2014 John Wiley & Sons, Ltd.