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Paper in focus: Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders
Authors: H. Bustince, C. Marco-Detchart, J. Fernandez, C. Wagner, J.M. Garibaldi, Z. Takác
Abstract:
In this work we study a new class of similarity measures between interval-valued fuzzy sets. The novelty of our approach lays, firstly, on the fact that we develop all the notions with respect to total orders of intervals; and secondly, on that we consider the width of intervals so that the uncertainty of the output is strongly related to the uncertainty of the input. For constructing the new interval-valued similarity, interval valued aggregation functions and interval-valued restricted equivalence functions which take into account the width of the intervals are needed, so we firstly study these functions, both in line with the two above stated features. Finally, we provide an illustrative example which makes use of an interval-valued similarity measure in stereo image matching and we show that the results obtained with the proposed interval-valued similarity measures improve numerically (according to the most widely used measures in the literature) the results obtained with interval valued similarity measures which do not consider the width of the intervals.
Highlight:
We discuss similarity measures specifically for epistemic intervals, i.e. intervals which capture the bounds around an (unknown) crisp actual/true value. (Commonly used confidence intervals are an example of epistemic intervals.) Here, even if two epistemic intervals share the same endpoints, we cannot assume that they are the same, as the crisp, unknown, true value each of them captures may be different. In other words, we cannot assume their similarity is 1. In this paper, we put forward a new class of similarity measures which captures this additional complexity as part of the similarity output.
Full Paper available here: https://doi.org/10.1016/j.fss.2019.04.002
Abstract:
In this work we study a new class of similarity measures between interval-valued fuzzy sets. The novelty of our approach lays, firstly, on the fact that we develop all the notions with respect to total orders of intervals; and secondly, on that we consider the width of intervals so that the uncertainty of the output is strongly related to the uncertainty of the input. For constructing the new interval-valued similarity, interval valued aggregation functions and interval-valued restricted equivalence functions which take into account the width of the intervals are needed, so we firstly study these functions, both in line with the two above stated features. Finally, we provide an illustrative example which makes use of an interval-valued similarity measure in stereo image matching and we show that the results obtained with the proposed interval-valued similarity measures improve numerically (according to the most widely used measures in the literature) the results obtained with interval valued similarity measures which do not consider the width of the intervals.
Highlight:
We discuss similarity measures specifically for epistemic intervals, i.e. intervals which capture the bounds around an (unknown) crisp actual/true value. (Commonly used confidence intervals are an example of epistemic intervals.) Here, even if two epistemic intervals share the same endpoints, we cannot assume that they are the same, as the crisp, unknown, true value each of them captures may be different. In other words, we cannot assume their similarity is 1. In this paper, we put forward a new class of similarity measures which captures this additional complexity as part of the similarity output.
Full Paper available here: https://doi.org/10.1016/j.fss.2019.04.002
Short Bio
After growing up in Luxembourg, I moved to the UK for my university education in 2001. Today, I am a Professor of Computer Science at the University of Nottingham, UK and Director of the Lab for Uncertainty in Data and Decision Making (LUCID). Our research focuses on modelling & handling of uncertain data arising both from qualitative (people) and quantitative sources (eg sensors, processes), decision support systems and data-driven policy design.
A substantial share of our work combines interdisciplinary insights, for example in the context of interpretable and interactive AI, and the development of novel approaches for capturing and analysing data captured from people, working with Social Science, Psychology and Mathematics.
Applications of our work feed into cyber security, environmental management and smart product design.
For details of ongoing projects and publications, please see the links above.
I am an Associate Editor of the IEEE Transactions on Artificial Intelligence and Mathematics journals.
I have co/developed multiple open source software frameworks, making research outputs accessible both to peer researchers within and beyond computer science. For examples, have a look at JuzzyOnline and Juzzy on the LUCID software page.
A substantial share of our work combines interdisciplinary insights, for example in the context of interpretable and interactive AI, and the development of novel approaches for capturing and analysing data captured from people, working with Social Science, Psychology and Mathematics.
Applications of our work feed into cyber security, environmental management and smart product design.
For details of ongoing projects and publications, please see the links above.
I am an Associate Editor of the IEEE Transactions on Artificial Intelligence and Mathematics journals.
I have co/developed multiple open source software frameworks, making research outputs accessible both to peer researchers within and beyond computer science. For examples, have a look at JuzzyOnline and Juzzy on the LUCID software page.
Research Interests
My research focuses on the development, adaptation, deployment and evaluation of computational intelligence techniques in inter-disciplinary projects bringing together frequently uncertain data from heterogeneous sources to generate informed and transparent decision support. I am both interested in interdisciplinary research as well as the advancement of theoretical research within computer Science. In terms of real-world problems and applications, together with my team we are and have been working on a diverse set of projects in cyber security, environmental management and smart, continuous manufacturing.
A cross-cutting aspect of my research is an end-to-end approach to systematically handling uncertainty, from capturing in, for example through novel questionnaire approaches, to analysing uncertain data and generating/communicating appropriate decision support outputs.
Within the broad set of AI research, I am particularly interested in interpretable and interactive AI, including 'meaningful rules', from how we can generate them while appropriately handling causality to how we deliver potentially complex reasoning based on a concise set of rules.
A cross-cutting aspect of my research is an end-to-end approach to systematically handling uncertainty, from capturing in, for example through novel questionnaire approaches, to analysing uncertain data and generating/communicating appropriate decision support outputs.
Within the broad set of AI research, I am particularly interested in interpretable and interactive AI, including 'meaningful rules', from how we can generate them while appropriately handling causality to how we deliver potentially complex reasoning based on a concise set of rules.
Contact
Feel free to contact me about research. I am always looking for interesting real-world problems as well as students with a variety of backgrounds.
Email: christian.wagnerATnottingham.ac.uk
Or see my university profile page here.
Email: christian.wagnerATnottingham.ac.uk
Or see my university profile page here.
