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A new family of attitudinal discrete choice models is proposed by considering the attitudinal character and the weight vector, both of which are specific to a decision maker (DM). Given the attribute values of different alternatives, the proposed models give varying choice probabilities, as per the DM's-specific attitudinal character and the weight vector. It is also shown that the conventional discrete choice models are the special cases of the proposed attitudinal models. The proposed choice models are also generalized through an additional parameter to add to their capabilities. An application on real data is included to demonstrate their usefulness in the real world. © 2019 Wiley Periodicals, Inc.

School of Artificial Intelligence and Data Science (AIDE)

International Journal of Intelligent Systems

Attitudinal choice models with applications in human decision making

Attitudinal Choquet integral (ACI) extends Choquet integral (CI) through a consideration of a decision-maker's (DM's) attitudinal character. In this paper, we generalize ACI, and the resulting operator is termed as generalized ACI (GACI). GACI adds to the efficacy of the ACI in the representation of a DM's unique and complex attitudinal character. It also generates a vast range of exponential ACI operators, such as harmonic ACI, ACI, quadratic ACI, to name a few. We further present induced GACI to consider additional information that may be associated with the arguments of aggregation. The special cases of the proposed operators are investigated. The usefulness of the proposed operators in modelling human decision behavior is shown through a case study. © 2018 Wiley Periodicals, Inc.

Generalized attitudinal Choquet integral

In this chapter, the information set theory is extended with a moderator’s information about the elements of the information set. The role of moderator is to provide a second opinion about the validity of the information values comprising the information set. The properties of the proposed moderator information sets (MIS) are also investigated. Many illustrative examples are included to show the usefulness of MIS in the real world decision-making. © 2019, Springer Nature Switzerland AG.

World University root node

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

Moderated Information Sets

We introduce a novel entropy framework for the computation of utility on the basis of an agent’s subjective evaluation of the granularised information source values. A concept of evaluating agent as an information gain function of this entropy framework is presented, which takes as its arguments both an information source value and the agent’s evaluation of the same. A method to model the agent’s perceived utility values is proposed. Based on these values, several new measures are designed for the evaluation of the information source values, perceived utilities, and the evaluating agent. A real application is included. © 2018, © 2018 Operational Research Society.

Journal of the Operational Research Society

Modelling subjective utility through entropy

Often, the real world variables are characterized with vagueness (represented by fuzzy set theory), associated hesitancy of the agent (represented by intuitionistic fuzzy set theory), and randomness (represented by probability) at the same time. Intuitionistic fuzzy set theory extends the fuzzy set theory to take account of hesitancy of the observer in addition to vagueness. We propose an integrated framework based on intuitionistic fuzzy set and probability theories to deal with the uncertainty posed by vagueness and randomness. The study is applied in an intelligent oil level controller. © 2018 IEEE.

ICNC-FSKD 2018 - 14th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery

Intelligent controllers for uncertain systems

Purpose: This paper aims to learn a decision-maker’s (DM’s) decision model that is characterized in terms of the attitudinal character and the attributes weight vector, both of which are specific to the DM. The authors take the learning information in the form of the exemplary preferences, given by a DM. The learning approach is formalized by bringing together the recent research in the choice models and machine learning. The study is validated on a set of 12 benchmark data sets. Design/methodology/approach: The study includes emerging preference learning algorithms. Findings: Learning of a DM’s attitudinal choice model. Originality/value: Preferences-based learning of a DM’s attitudinal decision model. © 2018, Emerald Publishing Limited.

Kybernetes

Learning attitudinal decision model through pair-wise preferences

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. © 2018 Wiley Periodicals, Inc.

Attitudinal Choquet integrals and applications in decision making

The concept of information sets is inspired by the way we perceive information source values. However, they lack a provision to represent the hesitancy inevitably associated with the perceived values. To this end, recently the concept of hesitant information set (HIS) is proposed in the literature. In contrast to an information set that maps an information source value to a single perceived information value, HIS gives a set of multiple perceived information values for a single information source value. This paper explores HIS further for its properties. © 2018 Copyright is held by the owner/author(s).

ACM International Conference Proceeding Series

Properties for hesitant information sets

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. © 2017 Elsevier B.V.

Applied Soft Computing Journal

Adaptive linguistic weighted aggregation operators for multi-criteria decision making

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. © 2016 Elsevier B.V.

Discriminative aggregation operators for multi criteria decision making

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. © 2016, Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg.

International Journal of Fuzzy Systems

Representation of Uncertainty with Information and Probabilistic Information Granules

Evolutionary multi-objective algorithms (EMOAs) of the type of NSGA-2 approximate the Pareto-front, after which a decisionmaker (DM) is confounded with the primary task of selecting the best solution amongst all the equally good solutions on the Pareto-front. In this paper, we complement the popular NSGA-2 EMOA by posteriori identifying a DM’s best solution among the candidate solutions on the Pareto-front, generated through NSGA-2. To this end, we employ a preference-based learning approach to learn an abstract ideal reference point of the DM on the multi-objective space, which reflects the compromises the DM makes against a set of conflicting objectives. The solution that is closest to this reference-point is then predicted as the DM’s best solution. The pairwise comparisons of the candidate solutions provides the training information for our learning model. The experimental results on ZDT1 dataset shows that the proposed approach is not only intuitive, but also easy to apply, and robust to inconsistencies in the DM’s preference statements. © Springer International Publishing AG 2017.

Preferences-based choice prediction in evolutionary multi-objective optimization

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. © 1993-2012 IEEE.

IEEE Transactions on Fuzzy Systems

Rough Information Set and Its Applications in 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. © 2016 Elsevier B.V.

Knowledge-Based Systems

Learning of aggregation models in multi criteria decision making

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. © 1993-2012 IEEE.

Probabilistic variable precision fuzzy rough sets

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 DM's 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 DM's 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. © 1989-2012 IEEE.

IEEE Transactions on Knowledge and Data Engineering

On learning of choice models with interactive attributes

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. © 2016 Wiley Periodicals, Inc.

Linguistic Discriminative Aggregation in Multicriteria Decision Making

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. © 1993-2012 IEEE.

Representing uncertainty with information sets

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.

Compensative weighted averaging aggregation operators

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.