Manish Aggarwal

Representing Uncertainty With Information Sets

We develop new methods for the representation of uncertainty in the granularized information source values by making use of the entropy framework in the possibilistic domain. An information-theoretic entropy function is used to map the information source values to information (entropy) values. We term a collection of such information values as an information set. The information values are then used in an adaptive form of this entropy function to formulate Shannon transforms. A few uncertainty measures are derived from these transforms for the quantification of uncertainty. Information set is also extended to other domains, such as probabilistic, intuitionistic, and probabilistic-intuitionistic domains. A biometric application is included to demonstrate the usefulness of the study.

Probabilistic Variable Precision Fuzzy Rough Sets

In the real world, we often encounter varying membership grades due to varying information source values. The fuzzy rough set model is refurbished to develop probabilistic variable precision fuzzy rough set (P-VP-FRS) to deal with this imprecision. The main inspiration behind the proposed P-VP-FRS is our inability to precisely represent the imprecision, which necessitates generalization in the approximations. The adjustable parameters in P-VP-FRS control the tradeoff between the generalization and accuracy. A few measures for quality of approximation and generalization are proposed. The usefulness of P-VP-FRS is shown through a case study.

Rough Information Set and Its Applications in Decision Making

The decision making in the real world is inevitably characterized with vagueness, and imprecision due to incomplete knowledge. To this end, we combine the information set with the rough set theory to represent both the vagueness and imprecision at the same time. We term the proposed structure as rough information set that has information sets based on fuzzy equivalence relations as its building blocks. The usefulness of the proposed structure is demonstrated through a case study in credit scoring analysis, and a biometrics application on knuckle-based recognition.

Linguistic Discriminative Aggregation in Multicriteria Decision Making

Several new aggregation operators are proposed in the context of multicriteria decision making (MCDM) in the linguistic domain. The proposed operators first infer the discrimination index, based on the extent of variability in the various linguistic evaluations against a criterion. This value is then utilized in the actual aggregation step to discriminate among the alternatives. Besides, the proposed operators also take into account the a priori weights associated with the criteria. The proposed concepts are illustrated through an example in group MCDM.

Representation of Uncertainty with Information and Probabilistic Information Granules

Linguistic representations by human brain are often characterized with an intertwined combination of imprecision (due to incomplete knowledge), vagueness, or uncertainty. A powerful framework of information and probabilistic information granules is proposed to model this combination of different facets of uncertainty in natural representations without distortion of the underlying meaning. The proposed notions are deployed in formulation of a comprehensive approach to model complex uncertain situations involving imprecise/inexact probabilities of fuzzy events. The concepts are based upon the principle of information granulation that can be viewed as a human way of achieving data compression. The proposed approach closely resembles the implementation of the strategy of divide-and-conquer which brings it close to human problem-solving thought process. The study also makes an attempt to minimize distortion of information in its representation by fuzzy logic.

Adaptive linguistic weighted aggregation operators for multi-criteria decision making

Abstract In this paper, we propose new aggregation operators for multi-criteria decision making under linguistic settings. The proposed operators are based on two sets of criteria weights. Besides the primary conventional criteria weights, we introduce a method to deduce secondary criteria weights from the criteria evaluations, which reflect the role of the different criteria in discriminating among the alternatives. The properties of the proposed operators are investigated. An approach for the application of the said operators in a group multi-criteria decision making problem is presented. Following the same, the proposed operators are applied in a case study on supplier selection. The empirical validation of the proposed operators is performed on a set of 12 real datasets. Note: All usages of he, him, his in the paper, also refer to she, and her.

Discriminative aggregation operators for multi criteria decision making

A general formalism for aggregation operators.New operators based on the general formalism.Some new aggregation operators for decision making problems.Proposed aggregation operators extended to Int-fuzzy domain.Illustration through real case study A general aggregation formalism for multi criteria decision making (MCDM) applications is presented. Using this formalism, we derive the existing aggregation operators, and also develop some new ones. The proposed general formalism is further extended to develop discriminative class of aggregation operators for aiding MCDM. The proposed discriminative aggregation operators are based on the consideration of the variability in the various evaluations of a criterion. Four families of discriminative aggregation operators are developed using the extended formalism. These operators and applied in a managerial real world case-study.

Attitudinal Choquet integrals and applications in decision making

The compensation capabilities of Choquet integral are augmented to consider the complex attitudinal character of a decision maker. The resulting operator is termed as attitudinal Choquet integral (ACI). The proposed ACI is further extended as induced ACI. The special cases of ACI are investigated. The usefulness of ACI is shown through a case study.

Learning of aggregation models in multi criteria decision making

Generalized attitudinal Choquet integral (GACI) is a recent aggregation operator that subsumes a multitude of aggregation operators, including both linear as well as non-linear and exponential integrals. In this study, against the background of preference learning, we use the GACI operator to represent the utility function of a decision-maker (DM), and learn its parameters. The exemplary preference information in the form of pair-wise comparisons of alternatives constitutes the training information. More specifically, given the exemplary pairwise choices of a DM, we present an approach to infer the unique preference model of the DM, in terms of the parameter values of GACI operator. We test our approach on standard datasets, and the prediction performance is compared with state-of-the-art methods.

On Learning of Choice Models with Interactive Attributes

Introducing recent advances in the machine learning techniques to state-of-the-art discrete choice models, we develop an approach to infer the unique and complex decision making process of a decision-maker (DM), which is characterized by the DMs priorities and attitudinal character, along with the attributes interaction, to name a few. On the basis of exemplary preference information in the form of pairwise comparisons of alternatives, our method seeks to induce a DMs preference model in terms of the parameters of recent discrete choice models. To this end, we reduce our learning function to a constrained non-linear optimization problem. Our learning approach is a simple one that takes into consideration the interaction among the attributes along with the priorities and the unique attitudinal character of a DM. The experimental results on standard benchmark datasets suggest that our approach is not only intuitively appealing and easily interpretable but also competitive to state-of-the-art methods.