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An Efficient Centroid Type Reduction Strategy for General Type2 Fuzzy Logic System
"... To date, the computation complexity of general type2 fuzzy logic systems (T2 FLSs) is very high, which makes them very difficult to be deployed into practical applications; hence, only an interval T2 FLS (a special case of general type2 FLS) is today the most widely used T2 FLS. General T2 fuzzy s ..."
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Cited by 19 (2 self)
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To date, the computation complexity of general type2 fuzzy logic systems (T2 FLSs) is very high, which makes them very difficult to be deployed into practical applications; hence, only an interval T2 FLS (a special case of general type2 FLS) is today the most widely used T2 FLS. General T2 fuzzy sets are characterized by their footprints of uncertainty (FOU) [1, 2].
Type1 OWA operators for aggregating uncertain information with uncertain weights induced by type2 linguistic quantifiers
, 2008
"... ..."
NonStationary Fuzzy Sets
 In prep. for IEEE Transactions on Fuzzy Systems
, 2006
"... Abstract—In this paper, the notion termed a “nonstationary fuzzy set ” is introduced, and the concept of a perturbation function that is used for generating nonstationary fuzzy sets is presented. Definitions of the basic set operators (the union, the intersection, and the complement) for nonstationa ..."
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Cited by 8 (5 self)
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Abstract—In this paper, the notion termed a “nonstationary fuzzy set ” is introduced, and the concept of a perturbation function that is used for generating nonstationary fuzzy sets is presented. Definitions of the basic set operators (the union, the intersection, and the complement) for nonstationary fuzzy sets are given, together with proofs of selected properties of these operators. Two case studies were carried out in order to illustrate the use of nonstationary fuzzy sets in a nonstationary fuzzy inference, and to provide an initial insight into the relationships between nonstationary and interval type2 fuzzy sets. Index Terms—Nonstationary fuzzy sets, perturbation functions, type2 fuzzy sets. I.
Perceptual reasoning for perceptual computing
 IEEE Trans. on Fuzzy Systems
, 2008
"... Abstract—In 1996, Zadeh proposed the paradigm of computing with words (CWW). A specific architecture for making subjective judgments using CWW was proposed by Mendel in 2001. It is called a Perceptual Computer (PerC), and because words can mean different things to different people, it uses interval ..."
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Abstract—In 1996, Zadeh proposed the paradigm of computing with words (CWW). A specific architecture for making subjective judgments using CWW was proposed by Mendel in 2001. It is called a Perceptual Computer (PerC), and because words can mean different things to different people, it uses interval type2 fuzzy set (IT2 FS) models for all words. The PerC has three elements: the encoder, which transforms linguistic perceptions into IT2 FSs that activate a CWW engine; the decoder, which maps the output of a CWW engine back into a word; and the CWW engine. Although different kinds of CWW engines are possible, this paper only focuses on CWW engines that are rulebased and the computations that map its input IT2 FSs into its output IT2 FS. Five assumptions are made for a rulebased CWW engine, the most important of which is: The result of combining fired rules must lead to a footprint of uncertainty (FOU) that resembles the three kinds of FOU that have previously been shown to model words (interior, leftshoulder, and rightshoulder FOUs). Requiring this means that the output FOU from a rulebased CWW engine will look similar in shape to an FOU in a codebook (i.e., a vocabulary of words and their respective FOUs) for an application, so that the decoder can therefore sensibly establish the word most similar to the CWW engine output FOU. Because existing approximate reasoning methods do not satisfy this assumption, a new kind of rulebased CWW engine is proposed, one that is called Perceptual Reasoning, and is proved to always satisfy this assumption. Additionally, because all IT2 FSs in the rules as well as those that excite the rules are either an interior, leftshoulder, or rightshoulder FOU, it is possible to carry out the supmin calculations that are required by the inference engine, and those calculations are also in this paper. The results in this paper let us implement a rulebased CWW engine for the PerC. Index Terms—Computing with words, footprint of uncertainty, interval type2 fuzzy sets, perceptual computer, perceptual reasoning (PR), rulebased systems.
αPlane Representation for Type2 Fuzzy Sets: Theory and Applications
"... Abstract—This paper 1) reviews theαplane representation of a type2 fuzzy set (T2 FS), which is a representation that is comparable to theαcut representation of a type1 FS (T1 FS) and is useful for both theoretical and computational studies of and for T2 FSs; 2) proves that set theoretic operati ..."
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Cited by 6 (0 self)
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Abstract—This paper 1) reviews theαplane representation of a type2 fuzzy set (T2 FS), which is a representation that is comparable to theαcut representation of a type1 FS (T1 FS) and is useful for both theoretical and computational studies of and for T2 FSs; 2) proves that set theoretic operations for T2 FSs can be computed using very simple αplane computations that are the set theoretic operations for interval T2 (IT2) FSs; 3) reviews how the centroid of a T2 FS can be computed usingαplane computations that are also very simple because they can be performed using existing Karnik Mendel algorithms that are applied to eachαplane; 4) shows how many theoretically based geometrical properties can be obtained about the centroid, even before the centroid is computed; 5) provides examples that show that the mean value (defuzzified value) of the centroid can often be approximated by using the centroids of only 0 and 1 αplanes of a T2 FS; 6) examines a triangle quasiT2 fuzzy logic system (QT2 FLS) whose secondary membership functions are triangles and for which all calculations use existing T1 or IT2 FS mathematics, and hence, they may be a good next step in the hierarchy of FLSs, from T1 to IT2 to T2; and 7) compares T1, IT2, and triangle QT2 FLSs to forecast noisecorrupted measurements of a chaotic Mackey–Glass time series. Index Terms—αPlane, centroid, Mackey–Glass time series, quasitype2 fuzzy logic systems (QT2 FLSs), set theoretic operations, type2 fuzzy sets (T2 FSs). I.
Constructing general type2 fuzzy sets from intervalvalued data
 in Proceedings of the 2012 IEEE International Conference on Fuzzy Systems
, 2012
"... Abstract—In this paper we describe a method of using interval valued survey responses from multiple experts on multiple occassions to produce General Type2 fuzzy sets. In the method we propose, both the intra and interperson variability are modelled, with no loss of information. The resulting se ..."
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Cited by 6 (4 self)
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Abstract—In this paper we describe a method of using interval valued survey responses from multiple experts on multiple occassions to produce General Type2 fuzzy sets. In the method we propose, both the intra and interperson variability are modelled, with no loss of information. The resulting sets are completely determined by the data, providing an accurate representation (in terms of being defined solely by the data) of the opinions being modelled. A description of the method is provided, along with synthetic and realworld numeric examples and a comparison to an alternative method proposed in [1]. Index Terms—Survey data, zSlices, computing with words, Type2 Fuzzy Logic Sets I.
Autonomic Resource Provisioning for Cloudbased Software,”
 in Proceedings of the 9th International Symposium on Software Engineering for Adaptive and SelfManaging Systems, ser. SEAMS ’14,
, 2014
"... ABSTRACT Cloud elasticity provides a software system with the ability to maintain optimal user experience by automatically acquiring and releasing resources, while paying only for what has been consumed. The mechanism for automatically adding or removing resources on the fly is referred to as auto ..."
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Cited by 5 (1 self)
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ABSTRACT Cloud elasticity provides a software system with the ability to maintain optimal user experience by automatically acquiring and releasing resources, while paying only for what has been consumed. The mechanism for automatically adding or removing resources on the fly is referred to as autoscaling. The stateofthepractice with respect to autoscaling involves specifying thresholdbased rules to implement elasticity policies for cloudbased applications. However, there are several shortcomings regarding this approach. Firstly, the elasticity rules must be specified precisely by quantitative values, which requires deep knowledge and expertise. Furthermore, existing approaches do not explicitly deal with uncertainty in cloudbased software, where noise and unexpected events are common. This paper exploits fuzzy logic to enable qualitative specification of elasticity rules for cloudbased software. In addition, this paper discusses a control theoretical approach using type2 fuzzy logic systems to reason about elasticity under uncertainties. We conduct several experiments to demonstrate that cloudbased software enhanced with such elasticity controller can robustly handle unexpected spikes in the workload and provide acceptable user experience. This translates into increased profit for the cloud application owner.
On Constructing Parsimonious Type2 Fuzzy Logic Systems via Influential Rule Selection
"... Abstract—Type2 fuzzy systems are increasing in popularity and there are many examples of successful applications. While many techniques have been proposed for creating parsimonious type1 fuzzy systems, there is a lack of such techniques for type2 systems. The essential problem is to reduce the nu ..."
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Cited by 4 (2 self)
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Abstract—Type2 fuzzy systems are increasing in popularity and there are many examples of successful applications. While many techniques have been proposed for creating parsimonious type1 fuzzy systems, there is a lack of such techniques for type2 systems. The essential problem is to reduce the number of rules, whilst maintaining the system’s approximation performance. In this paper, four novel indices for ranking the relative contribution of type2 fuzzy rules are proposed, termed Rvalues, cvalues, ω1values and ω2values. The Rvalues of type2 fuzzy rules are obtained by applying a QR decomposition pivoting algorithm to the firing strength matrices of the trained fuzzy model. The cvalues rank rules based on the effects of rule consequents, whilst the ω1values and ω2values consider both the rule base structure (via firing strength matrices) and the output contribution of fuzzy rule consequents. Two procedures for utilising these indices in fuzzy rule selection (termed ‘forward selection ’ and ‘backward elimination’) are described. Experiments are presented which demonstrate that, by using the proposed methodology, the most influential type2 fuzzy rules can be effectively retained in order to construct parsimonious type2 fuzzy models. Index Terms—Type2 fuzzy sets, parsimony, rule ranking, rule selection, index, QR, SVDQR I.
A novel fuzzy inferencing methodology for simulated car racing
 In To be Published in the Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZIEEE
, 2008
"... Abstract—This paper describes and further extends the fuzzy inferencing system which won the simulated car racing competition that was arranged as part of FuzzIEEE 2007 conference. The details of the winning nonstationary fuzzy controller and its results are presented. A novel approach to further ..."
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Cited by 3 (3 self)
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Abstract—This paper describes and further extends the fuzzy inferencing system which won the simulated car racing competition that was arranged as part of FuzzIEEE 2007 conference. The details of the winning nonstationary fuzzy controller and its results are presented. A novel approach to further improve the performance of the winning controller is described and formalised. We term the new fuzzy inferencing method a ‘contextdependent fuzzy inference system’. The concept of a ‘contextdependent fuzzy set ’ that is utilised by the fuzzy system is introduced. Finally, a comparison between contextdependent fuzzy inference system and various existing techniques are carried out on the simulated car racing application. The results show a better performance for contextdependent fuzzy inference systems in stochastic circumstances.
An interval type2 fuzzy distribution network
 In Proceedings of 2009 IFSA World Congress/EUSFLAT Conference
, 2009
"... Abstract — Planning resources for a supply chain is a major factor determining its success or failure. In this paper we introduce an Interval Type2 Fuzzy Logic model of a distribution network. It is believed that the additional degree of uncertainty provided by Interval Type2 Fuzzy Logic will al ..."
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Abstract — Planning resources for a supply chain is a major factor determining its success or failure. In this paper we introduce an Interval Type2 Fuzzy Logic model of a distribution network. It is believed that the additional degree of uncertainty provided by Interval Type2 Fuzzy Logic will allow for better representation of the uncertainty and vagueness present in resource planning models. First, the subject of Supply Chain Management is introduced, then some background is given on related work using Type1 Fuzzy Logic. A description of the Interval Type2 Fuzzy model is given, and a test scenario detailed. A Genetic Algorithm uses the model to search for a nearoptimal plan for the scenario. A discussion of the results follows, along with conclusions and details of intended further work.