Dr Sarah Greenfield

Job: Research Fellow

Faculty: Technology

School/department: School of Computer Science and Informatics

Research group(s): The De Montfort University Interdisciplinary Group in Intelligent Transport Systems (DIGITS), Centre for Computational Intelligence (CCI)

Address: De Montfort University, The Gateway, Leicester, LE1 9BH

T: +44 (0)116 250 6171

E: s.greenfield@dmu.ac.uk

W: www.dmu.ac.uk/digits

 

Personal profile

Sarah Greenfield received the BA in Mathematics and Philosophy from London University in 1978. In 2005 she was awarded a distinction in the MSc IT degree from De Montfort University, Leicester, UK, and in 2012 she was awarded a PhD at De Montfort's Centre for Computational Intelligence, working under the supervision of Prof Chiclana. Her enduring interest in logic and the philosophy of mathematics was reflected in her original choice of degree subject. Her MSc project was in the field of type-2 fuzzy logic, and her PhD studies continued this theme in her exploration of mathematical and philosophical aspects of type-2 fuzzy logic in relation to such topics as uncertainty modelling and defuzzification.   Since completing her studies she has widened her research interests to include complex fuzzy inferencing and computational intelligence in transport.

Publications and outputs 

  • Geometric Defuzzification Revisited
    Geometric Defuzzification Revisited Greenfield, Sarah In this paper the Geometric Defuzzification strategy for type-2 fuzzy sets is reappraised. For both discretised and geometric fuzzy sets the techniques for type-1, interval type-2, and generalised type-2 defuzzification are presented in turn. In the type-2 case the accuracy of Geometric Defuzzification is assessed through a series of test runs on interval type-2 fuzzy sets, using Exhaustive Defuzzification as the benchmark method. These experiments demonstrate the Geometric Defuzzifier to be wildly inaccurate. The test sets take many shapes; they are not confined to those type-2 sets with rotational symmetry that have previously been acknowledged by the technique’s developers to be problematic as regards accuracy. Type-2 Geometric Defuzzification is then examined theoretically. The defuzzification strategy is demonstrated to be built upon a fallacious application of the concept of centroid. This explains the markedly inaccurate experimental results. Thus the accuracy issues of type-2 Geometric Defuzzification are revealed to be inevitable, fundamental and significant. The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.
  • The Collapsing Defuzzifier for discretised generalised type-2 fuzzy sets
    The Collapsing Defuzzifier for discretised generalised type-2 fuzzy sets Greenfield, Sarah; Chiclana, Francisco The Greenfield–Chiclana Collapsing Defuzzifier is an established efficient accurate technique for the defuzzification of the interval type-2 fuzzy set. This paper reports on the extension of the Collapsing Defuzzifier to the generalised type-2 fuzzy set. Existing techniques for the defuzzification of generalised type-2 fuzzy sets are presented after which the interval Collapsing Defuzzifier is summarised. The collapsing technique is then extended to generalised type-2 fuzzy sets, giving the Generalised Greenfield–Chiclana Collapsing Defuzzifier. This is contrasted experimentally with both the benchmark Exhaustive Defuzzifier and the α-Planes/Karnik–Mendel Iterative Procedure approach in relation to efficiency and accuracy. The GGCCD is demonstrated to be many times faster than the Exhaustive Defuzzifier and its accuracy is shown to be excellent. In relation to the α-Planes/Karnik–Mendel Iterative Procedure approach it is shown to be comparable in accuracy, but faster. The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.
  • Type-Reduced Set Structure and the Truncated Type-2 Fuzzy Set
    Type-Reduced Set Structure and the Truncated Type-2 Fuzzy Set Greenfield, Sarah; Chiclana, Francisco In this paper, the Type-Reduced Set (TRS) of the continuous type-2 fuzzy set is considered as an object in its own right. The structures of the TRSs of both the interval and generalised forms of the type-2 fuzzy set are investigated. In each case the respective TRS structure is approached by first examining the TRS of the discretised set. The TRS of a continuous interval type-2 fuzzy set is demonstrated to be a continuous horizontal straight line, and that of a generalised type-2 fuzzy set, a continuous, convex curve. This analysis leads on to the concept of truncation, and the definition of the truncation grade. The truncated type-2 fuzzy set is then defined, whose TRS (and hence defuzzified value) is identical to that of the non-truncated type-2 fuzzy set. This result is termed the Type-2 Truncation Theorem, an immediate corollary of which is the Type-2 Equivalence Theorem which states that the defuzzified values of type-2 fuzzy sets that are equivalent under truncation are equal. Experimental corroboration of the equivalence of the non-truncated and truncated generalised type-2 fuzzy set is provided. The implications of these theorems for uncertainty quantification are explored. The theorem’s repercussions for type-2 defuzzification employing the α-Planes Representation are examined; it is shown that the known inaccuracies of the α-Planes Method are deeply entrenched. The file attached to this record is the author's final peer reviewed version.
  • Join and Meet Operations for Interval-Valued Complex Fuzzy Logic
    Join and Meet Operations for Interval-Valued Complex Fuzzy Logic Greenfield, Sarah; Chiclana, Francisco; Dick, Scott Interval-valued complex fuzzy logic is able to handle scenarios where both seasonality and uncertainty feature. The interval-valued complex fuzzy set is defined, and the interval valued complex fuzzy inferencing system outlined. Highly pertinent to complex fuzzy logic operations is the concept of rotational invariance, which is an intuitive and desirable characteristic. Interval-valued complex fuzzy logic is driven by interval-valued join and meet operations. Four pairs of alternative algorithms for these operations are specified; three pairs possesses the attribute of rotational invariance, whereas the other pair lacks this characteristic. DMU Interdisciplinary Group in Intelligent Transport Systems
  • Slicing Strategies for the Generalised Type-2 Mamdani Fuzzy Inferencing System
    Slicing Strategies for the Generalised Type-2 Mamdani Fuzzy Inferencing System Greenfield, Sarah; Chiclana, Francisco As a three-dimensional object, there are a number of ways of slicing a generalised type-2 fuzzy set. In the context of the Mamdani Fuzzy Inferencing System, this paper concerns three accepted slicing strategies, the vertical slice, the wavy slice, and the horizontal slice or alpha -plane. Two ways of de ning the generalised type-2 fuzzy set, vertical slices and wavy slices, are presented. Fuzzi cation and inferencing is presented in terms of vertical slices. After that, the application of all three slicing strategies to defuzzi cation is described, and their strengths and weaknesses assessed. The final publication is available at Springer via http://dx.doi.org/[insert DOI]".
  • Interval-Valued Complex Fuzzy Logic
    Interval-Valued Complex Fuzzy Logic Greenfield, Sarah; Chiclana, Francisco; Dick, Scott Data is frequently characterised by both uncertainty and seasonality. Type-2 fuzzy sets are an extension of type-1 fuzzy sets offering a conceptual scheme within which the effects of uncertainties in fuzzy inferencing may be modelled and minimised. Complex fuzzy sets are type-1 fuzzy sets extended by an additional phase term which permits them to intuitively represent the seasonal aspect of fuzziness in time-series applications. Type-2 fuzzy sets take two forms, generalised, and the simpler interval. Interval-valued fuzzy sets are type-1 fuzzy sets whose behaviour and properties are equivalent to interval type-2 fuzzy sets. This paper is concerned with the combination of interval-valued fuzzy sets and complex fuzzy sets to develop interval-valued complex fuzzy sets, an adaption of complex fuzzy sets such that the membership function assigns each point on the domain to an interval. From the definition of the interval-valued complex fuzzy set, the principles of interval-valued complex fuzzy logic are developed. DMU Interdisciplinary Group in Intelligent Transport Systems (DIGITS)
  • Uncertainty Measurement for the Interval Type-2 Fuzzy Set
    Uncertainty Measurement for the Interval Type-2 Fuzzy Set Greenfield, Sarah In this paper, two measures of uncertainty for interval type-2 fuzzy sets are presented, evaluated, compared and contrasted. Wu and Mendel regard the length of the type-reduced set as a measure of the uncertainty in an interval set. Green eld and John argue that the volume under the surface of the type-2 fuzzy set is a measure of the uncertainty relating to the set. For an interval type-2 fuzzy set, the volume measure is equivalent to the area of the footprint of uncertainty of the set. Experiments show that though the two measures give di erent results, there is considerable commonality between them. The concept of invariance under vertical translation is introduced; the uncertainty measure of a fuzzy set has the property of invariance under vertical translation if the value it generates remains constant under any vertical translation of the fuzzy set. It is left unresolved whether invariance under vertical translation is an essential property of a type-2 uncertainty measure.
  • Fuzzy in 3-D: Two Contrasting Paradigms
    Fuzzy in 3-D: Two Contrasting Paradigms Greenfield, Sarah; Chiclana, Francisco Type-2 fuzzy sets and complex fuzzy sets are both three dimensional extensions of type-1 fuzzy sets. Complex fuzzy sets come in two forms, the standard form, postulated in 2002 by Ramot et al., and the 2011 innovation of pure complex fuzzy sets, proposed by Tamir et al.. In this paper we compare and contrast both forms of complex fuzzy set with type-2 fuzzy sets, as regards their rationales, applications, definitions, and structures. In addition, pure complex fuzzy sets are compared with type-2 fuzzy sets in relation to their inferencing operations. Complex fuzzy sets and type-2 fuzzy sets differ in their roles and applications; complex fuzzy sets are pertinent to inferencing where there is seasonality, and type-2 fuzzy sets are applicable to reasoning under uncertainty. Their definitions differ also, though there is equivalence between those of a pure complex fuzzy set and a type-2 fuzzy set. Structural similarity is evident between these three- dimensional sets. Complex fuzzy sets are represented by a 3–D line, and type- 2 fuzzy sets by a 3–D surface, but a surface is simply a generalisation of a line. This similarity is particularly apparent between pure complex fuzzy sets and type- 2 fuzzy sets, which are both mappings from the domain onto the unit square. However type-2 fuzzy sets were found not to be isomorphic to pure complex fuzzy sets. The mechanisms by which complex fuzzy sets model and quantify periodicity, and type-2 fuzzy sets model and quantify uncertainty are discussed. A type-2 fuzzy set can be represented as the union of its type-2 embedded set. An embedded type-2 fuzzy set is a type-2 fuzzy set in itself, whose geomet- rical representation is a 3-D line. Thus, geometrically an embedded type-2 fuzzy set can be seen as equivalent to a pure complex fuzzy set and therefore a type-2 fuzzy set can be represented as the union of a collection pure complex fuzzy sets, which in turn can be regarded as embedded complex fuzzy sets of a type-2 fuzzy set. This relationship is exploited to provide a complex definition of a type-2 fuzzy set. DIGITS The full text of this article can be read via open access on the publisher's page.
  • Travels with My App: Computational Intelligence for Individualised Dynamic Rail Journey Planning
    Travels with My App: Computational Intelligence for Individualised Dynamic Rail Journey Planning Greenfield, Sarah This presentation describes ongoing research for the Transport iNet funded project Evolutionary Computation for Optimised Rail Travel (EsCORT), which is running from 11th November 2013 to 13th December 2014. The recently completed first phase of the project was a literature review which considered what computational intelligence might offer to dynamic, individualised, passenger rail journey planning. Of particular interest was whether it is feasible to create an app to dynamically assist in selecting and updating rail journey itineraries, and if so what improvements this would bring relative to a dynamically updated timetable. The study was concerned specifically with station to station railway journeys within the British Railway System. There was found to be nothing in the published literature referring to an app that plans passenger rail journeys, then responds to unforeseen disruptions by alerting the passenger and offering an adjusted itinerary. The literature review concluded that the development of such an app would therefore be timely, filling a gap in the market. The project is now at its mid-point according to the calendar. However only one sixth of the days funded have been worked; the remaining five sixths will be devoted to investigating the journey planning algorithms that would drive the app. To begin with, the extent to which solutions may be arrived at deductively through mathematical modelling is being explored. The relevant field of mathematics here is graph theory. Complexity theory is also highly pertinent; it is anticipated that any mathematical model produced will be far too computationally complex to be incorporated into usable software. This negative result would justify a computational intelligence approach. The three main forms of computational intelligence, each in its own way inspired by nature, are artificial neural networks, evolutionary computation, and fuzzy logic; each paradigm’s potential for contributing to passenger journey planning will be evaluated. Presentation for the 2014 London Hopper Research Spotlight Competition
  • The Structure of the Type-Reduced Set of a Continuous Type-2 Fuzzy Set
    The Structure of the Type-Reduced Set of a Continuous Type-2 Fuzzy Set Greenfield, Sarah; Chiclana, Francisco This paper is concerned with the structure of the type-reduced set (TRS) of the continuous type-2 fuzzy set, in both its interval and generalised forms. In each case the TRS structure is approached by first investigating the discretised set. The TRS of a continuous interval type-2 fuzzy set is shown to be a continuous straight line, and that of a generalised type-2 fuzzy set, a continuous, convex curve. CCI

Click here to view a full listing of Sarah Greenfield's publications and outputs.

Key research outputs

[1] Sarah Greenfield, Francisco Chiclana, Simon Coupland and Robert I. John, “The collapsing method of defuzzification for discretised interval type-2 fuzzy sets”, Information Sciences Special Issue, “High Order Fuzzy Sets: Theory and Applications”, volume 179, issue 13, pages 2055–2069, June 2009. DOI: http://dx.doi.org/10.1016/j.ins.2008.07.011; ISSN: 0020–0255.

[2] Sarah Greenfield and Francisco Chiclana, “Type-Reduction of the Discretised Interval Type-2 Fuzzy Set: Approaching the Continuous Case through Progressively Finer Discretisation”, Journal of Artificial Intelligence and Soft Computing Research, volume 1, issue 3, pages 183–193, 2011. ISSN: 2083–2567.

[3] Sarah Greenfield, Francisco Chiclana, Robert I. John and Simon Coupland, “The sampling method of defuzzification for type-2 fuzzy sets: Experimental evaluation”, Information Sciences, volume 189, pages 77–92, April 2012. DOI: http://dx.doi.org/10.1016/j.ins.2011.11.042; ISSN: 0020–0255.

[4] Sarah Greenfield and Francisco Chiclana, “Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set”, The International Journal of Approximate Reasoning, volume 54, issue 8, pages 1013–1033, October 2013. DOI: http://dx.doi.org/10.1016/j.ijar.2013.04.013; ISSN: 0888–613X.

[5] Sarah Greenfield and Francisco Chiclana, “Defuzzification of the discretised generalised type-2 fuzzy set: Experimental evaluation”, Information Sciences, volume 244, pages 1–25, September 2013. DOI: http://dx.doi.org/10.1016/j.ins.2013.04.032; ISSN: 0020–0255.

Research interests/expertise

  • Logic
  • Fuzzy logic, including type-2 fuzzy logic and complex fuzzy logic
  • Defuzzification of type-2 fuzzy sets
  • Uncertainty modelling using type-2 fuzzy sets
  • Computational Intelligence in transport

Areas of teaching

  • IMAT 1205: Mathematics for Scientific Computing (Year 1 BSc CGP and AIR)
  • IMAT 3451: Final Year Computing Project supervision

Qualifications

  • PhD in Computational Intelligence, De Montfort University, Leicester, 2012;
  • MSc in Information Technology (Distinction), De Montfort University, Leicester, 2005;
  • HNC (BTEC) Software Engineering Design, Brighton College of Technology, 1989;
  • BA Mathematics & Philosophy (2 II Hons.), Kings College, University of London 1978;
  • A-levels in Mathematics (B), Physics (A) and Chemistry (B), Withington Girls’ School, Manchester 1975.

Courses taught

  • IMAT 1205: Mathematics for Scientific Computing (Year 1 BSc CGP and AIR)
  • IMAT 3451: Final Year Computing Project supervision
  • IMAT 2800: Artificial Intelligence and Modelling for Games (2011 - 2013)

Honours and awards

Anita Borg Scholarship In 2010 I reached the final of the Google Anita Borg Memorial Scholarship: Europe, the Middle East and Africa (www.google.com/anitaborg/emea). The scholarship aims to encourage women to excel in computing and technology, and become active role models and leaders. Awards are based on the strength of candidates’ academic performance, leadership experience and demonstrated passion for computer science. My prize as a finalist was to attend a networking retreat at Google’s Engineering Centre in Zurich.

Creative Thinking Award In 2010 I received the third prize of £2,000 in De Montfort University’s Creative Thinking Awards for my Collapsing Defuzzifier. In my submission for this award I argued that mathematics is a creative enterprise.

Membership of professional associations and societies

  • Member of the European Society for Fuzzy Logic and Technology (EUSFLAT)
  • Member of the Institute of Electrical and Electronics Engineers (IEEE)

Conference attendance

UKCI, September 2005, London, “A Novel Sampling Method for Type-2 Defuzzification”, Sarah Greenfield, Robert I. John and Simon Coupland, presentation. 

FUZZ-IEEE, July 2007, London, “Optimised Generalised Type-2 Join and Meet Operations”, Sarah Greenfield and Robert I. John, presentation.

UKCI, July 2007, London, “The Collapsing Method of Defuzzification for Discretised Interval Type-2 Fuzzy Sets”, Sarah Greenfield, Francisco Chiclana, Robert I. John and Simon Coupland, presentation. 

IPMU 2008, June 2008, Malaga, “Stratification in the Type-Reduced Set and the Generalised Karnik-Mendel Iterative Procedure”, Sarah Greenfield and Robert I. John, presentation.

IFSA-EUSFLAT, July 2009, Lisbon, “The Collapsing Method: Does the Direction of Collapse Affect Accuracy?”, Sarah Greenfield, Francisco Chiclana and Robert I. John, presentation. 

IEEE Symposium on Advances in Type-2 Fuzzy Logic Systems, April 2011, Paris, “Type-Reduction of the Discretised Interval Type-2 Fuzzy Set: What Happens as Discretisation Becomes Finer?”, Sarah Greenfield and Francisco Chiclana, presentation.

EUSFLAT-LFA, July 2011, Aix-Les-Bains, France, “Combining the alpha-Plane Representation with an Interval Defuzzification Method”, Sarah Greenfield and Francisco Chiclana, presentation. 

UKCI 2012, September 2012, Edinburgh, “The Grid Method of Discretisation for Type-2 Fuzzy Sets”, Sarah Greenfield, poster.

EUSFLAT 2013, September 2013, Milan, Italy, “The Structure of the Type-Reduced Set of a Continuous Type-2 Fuzzy Set”, Sarah Greenfield and Francisco Chiclana, presentation.

Externally funded research grants information

Evolutionary Computation for Optimised Rail Travel (EsCORT),  funded by Transport iNet, a research and development project running from 11/11/13 to 31/12/14.  Collaborators are Go Travel Solutions, the Rail Safety and Standards Board, and Network Rail.

Professional esteem indicators

Reviewer for:

  • Applied Soft Computing,
  • IEEE Transactions on Fuzzy Systems,
  • Soft Computing,
  • Journal of Intelligent and Fuzzy Systems,
  • Fuzzy Sets and Systems,
  • Information Sciences, and
  • The International Journal of Approximate Reasoning.

On the programme committee for FCTA 2013 and FCTA 2014. (Fuzzy Computation Theory and Applications).

Co-organiser of a special session on type-2 fuzzy logic at IFSA-EUSFLAT 2009, Lisbon.

Search Who's Who

 
News target area image
News

DMU is a dynamic university, read about what we have been up to in our latest news section.

Events target area image
Events

At DMU there is always something to do or see, check out our events for yourself.

Mission and vision target area image
Mission and vision

Read about our mission and vision and how these create a supportive and exciting learning environment.