Navarro Barron, Francisco Javier
(2019)
Towards using Interval-Valued responses in questionnaires through Fuzzy Set based techniques.
PhD thesis, University of Nottingham.
Abstract
The measuring of individuals' perceptions, attitudes and opinions using rating scales is a core approach in many empirical research areas. This is due to their relative easiness to design and administer by using a set of (`crisp') anchor points from which the rater selects the most appropriate description. However, a serious limitation with this approach is that in general, characterising human perception involves dealing with more vague and imprecise information than the ordinal based information actually employed by standard rating scales. Moreover,capturing and modelling of uncertainty in participant responses has attracted only very limited attention, driven by a lack of appropriate tools and methodologies. Computational Intelligence (CI) techniques such as fuzzy set based modelling and flexible aggregation operators with the capacity for dealing with non-numeric data have unique potential in addressing this gap.
Fuzzy set theory was introduced by Zadeh and has been widely applied in various fields as an approach for modelling uncertain and imprecise concepts which can be associated with natural language (e.g., linguistic expressions). Recent studies have proposed the use of interval-valued (IV) questionnaires for better capturing of evidence of sometimes ambiguous or inexact concepts (e.g., human perceptions) on continuous scales and their subsequent modelling, including using Fuzzy Sets (FSs). While some of these methods have specifically been advocated for modelling participants' perceptions of words (i.e., FSs representing Linguistic Terms (LTs)), other CI methods such as the Interval Agreement Approach (IAA) and Fuzzy Integrals & data-driven Fuzzy Measures on Intervals have shown potential in modelling/aggregating intra respondent uncertainty (i.e., variation in the perception of a particular respondent) on human perception/opinions when such information is captured through an IV format. Although these CI tools have been applied in a number of applications from numerous fields, their application has not been explored in the context of representing high level concepts relating to human perception, such as Quality of Life, which is an important subject in the Social Science and Psychometric research.
In this context, there is clear potential in exploring how CI tools can be used in leveraging data captured from IV questionnaires in contrast to that from standard rating scales (e.g., Likert-scale based questionnaires) as those abstract concepts can be subjective or vague, thus the ability to map uncertainty in the atomic perceptions which together - at an aggregate level - give rise to the high level constructs is highly attractive. Here, CI aggregation approaches designed to integrate multi-source (uncertain) information are promising tools to link uncertainty in multiple responses from a respondent to the comprehensive and possible uncertain notion of the respective construct(s) associated with this respondent. Further, there is also a need to look at CI methods for describing phenomenons of interest from multiple (vague) observations (coming from different populations'/individuals') as performed in descriptive research.
The research reported in this thesis aims to comprehensively explore, for the first time, the potential of using CI methods in respect to capturing and modelling of human perception and modelling of both atomic human perceptions (i.e., potentially uncertain responses to distinct questions) as well as high level constructs (arising from combinations of atomic responses). More specifically, in order to achieve this research aim a combination of measures on FSs which show great promise on enabling rich descriptions of human perception models is presented.
Furthermore, a series of comparisons of several CI approaches for IV data aggregation in respect to interval valued construct measurement is systematically explored and analysed, i.e. the measurement of constructs where some or all component variables are themselves interval-valued. In particular, these comparisons consider analysing the potential of CI aggregation methods including the Choquet Fuzzy Integral (associated with data-driven Fuzzy Measures), as well as Interval Arithmetic in the context of construct measurement.
Based on the results from the analysis, a method for human perception measurement through Interval/FS based representations using IV responses its proposed. This method allows for a weighted aggregation of responses as commonly done when it is known a priori that the effect of each value contributes to a different extent on the model construct. The Interval/FS valued output of this method, i.e., the generated construct, allows relating a range/interval of values to an individual's perception which in turn can then provide a more detailed and qualitative understanding.
As a final study, this thesis considers two specific real world cases, namely, Quality of Life (QoL) assessment and academic abilities. Analysis results on the generated representations are presented using well-established metrics from Social Sciences, highlighting the potential value of using IV questionnaires and CI techniques as psychometric tools to provide reasonable and consistent ways to summarise and represent human perceptions and attitudes.
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