From Interval-Valued Data to General Type-2 Fuzzy Sets

Abstract

Abstract-In this paper a new approach is presented to model interval-based data using Fuzzy Sets (FSs). Specifically, we show how both crisp and uncertain intervals (where there is uncertainty about the endpoints of intervals) collected from individual or multiple survey participants over single or repeated surveys can be modelled using type-1, interval type-2, or general type-2 FSs based on zSlices. The proposed approach is designed to minimise any loss of information when transferring the intervalbased data into FS models, and to avoid, as much as possible assumptions about the distribution of the data. Furthermore, our approach does not rely on data pre-processing or outlier removal which can lead to the elimination of important information. Different types of uncertainty contained within the data, namely intra-and inter-source uncertainty, are identified and modelled using the different degrees of freedom of type-2 FSs, thus providing a clear representation and separation of these individual types of uncertainty present in the data. We provide full details of the proposed approach, as well as a series of detailed examples based on both real-world and synthetic data. We perform comparisons with analogue techniques to derive fuzzy sets from intervals, namely the Interval Approach (IA) and the Enhanced Interval Approach (EIA) and highlight the practical applicability of the proposed approach.

Exploring differences in interpretation of words essential in medical expert-patient communication

“…The IAA is designed to avoid assumptions about the data or FS shape [6], instead, it models the agreement/disagreement (in y) and the uncertainty associated (in x) from multiple intervals capturing a linguistic term. In this paper, we have used it to create FSs of the standardised vocabulary used in the TESS by three key stakeholder groups.…”

“…In [6], the Interval Agreement Approach (IAA) is introduced as a method for generating FSs from interval-valued data representing uncertainty in people's opinions/perceptions. It is built on top of the work presented in [12], where an agreementbased method [19] of capturing interval-valued survey data is demonstrated.…”

“…As part of this recent interest, modelling the subjective meaning of words and perceptions of people has been investigated and a number of techniques have been proposed, such as the Interval Approach (IA) [3], the Enhanced Interval Approach (EIA) [4], [5], and the Interval Agreement Approach (IAA) [6]. Such techniques allow the creation of FS models (from data) for words and/or concepts in order to subsequently perform computation and reasoning.…”

“…On the other hand, we explore the practical application of the IAA [6], [12], [13] to capture interval-valued data and generate FS models associated with such words.…”

Novel similarity measure for interval-valued data based on overlapping ratio

“…Thus, intervals have been used in many applications, including the modeling of survey data [3], the clustering of symbolic data [4], and the capturing of natural language expressions [2].…”