Defuzzification of the Discretised Generalised Type-2 Fuzzy Set: Experimental Evaluation

CCI - Centre for Computational Intelligence NOTICE: this is the author’s version of a work that was accepted for publication in Information Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version can be found by following the DOIThe work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised generalised type-2 fuzzy sets as created by the inference stage of a Mamdani Fuzzy Inferencing System. The exhaustive method of defuzzification for type-2 fuzzy sets is extremely slow, owing to its enormous computational complexity. Several approximate methods have been devised in response to this defuzzification bottleneck. In this paper we begin by surveying the main alternative strategies for defuzzifying a generalised type-2 fuzzy set: (1) Vertical Slice Centroid Type-Reduction; (2) the sampling method; (3) the elite sampling method; and (4) the $\alpha$-planes method. We then evaluate the different methods experimentally for accuracy and efficiency. For accuracy the exhaustive method is used as the standard. The test results are analysed statistically by means of the Wilcoxon Nonparametric Test and the elite sampling method shown to be the most accurate. In regards to efficiency, Vertical Slice Centroid Type-Reduction is demonstrated to be the fastest technique

Partitioning Relational Matrices of Similarities or Dissimilarities using the Value of Information

In this paper, we provide an approach to clustering relational matrices whose entries correspond to either similarities or dissimilarities between objects. Our approach is based on the value of information, a parameterized, information-theoretic criterion that measures the change in costs associated with changes in information. Optimizing the value of information yields a deterministic annealing style of clustering with many benefits. For instance, investigators avoid needing to a priori specify the number of clusters, as the partitions naturally undergo phase changes, during the annealing process, whereby the number of clusters changes in a data-driven fashion. The global-best partition can also often be identified.Comment: Submitted to the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP

Type-2 Fuzzy Logic: Circumventing the Defuzzification Bottleneck

Type-2 fuzzy inferencing for generalised, discretised type-2 fuzzy sets has been impeded by the computational complexity of the defuzzification stage of the fuzzy inferencing system. Indeed this stage is so complex computationally that it has come to be known as the defuzzification bottleneck. The computational complexity derives from the enormous number of embedded sets that have to be individually processed in order to effect defuzzification. Two new approaches to type-2 defuzzification are presented, the sampling method and the Greenfield-Chiclana Collapsing Defuzzifier. The sampling method and its variant, elite sampling, are techniques for the defuzzification of generalised type-2 fuzzy sets. In these methods a relatively small sample of the totality of embedded sets is randomly selected and processed. The small sample size drastically reduces the computational complexity of the defuzzification process, so that it may be speedily accomplished. The Greenfield-Chiclana Collapsing Defuzzifier relies upon the concept of the representative embedded set, which is an embedded set having the same defuzzified value as the type-2 fuzzy set that is to be defuzzified. By a process termed collapsing the type-2 fuzzy set is converted into a type-1 fuzzy set which, as an approximation to the representative embedded set, is known as the representative embedded set approximation. This type-1 fuzzy set is easily defuzzified to give the defuzzified value of the original type-2 fuzzy set. By this method the computational complexity of type-2 defuzzification is reduced enormously, since the representative embedded set approximation replaces the entire collection of embedded sets. The strategy was conceived as a generalised method, but so far only the interval version has been derived mathematically. The grid method of discretisation for type-2 fuzzy sets is also introduced in this thesis. Work on the defuzzification of type-2 fuzzy sets began around the turn of the millennium. Since that time a number of investigators have contributed methods in this area. These different approaches are surveyed, and the major methods implemented in code prior to their experimental evaluation. In these comparative experiments the grid method of defuzzification is employed. The experimental results show beyond doubt that the collapsing method performs the best of the interval alternatives. However, though the sampling method performs well experimentally, the results do not demonstrate it to be the best performing generalised technique

Attitudes expressed in online comments about environmental factors in the tourism sector: an exploratory study

The object of this exploratory study is to identify the positive, neutral and negative environment factors that affect users who visit Spanish hotels in order to help the hotel managers decide how to improve the quality of the services provided. To carry out the research a Sentiment Analysis was initially performed, grouping the sample of tweets (n = 14459) according to the feelings shown and then a textual analysis was used to identify the key environment factors in these feelings using the qualitative analysis software Nvivo (QSR International, Melbourne, Australia). The results of the exploratory study present the key environment factors that affect the users experience when visiting hotels in Spain, such as actions that support local traditions and products, the maintenance of rural areas respecting the local environment and nature, or respecting air quality in the areas where hotels have facilities and offer services. The conclusions of the research can help hotels improve their services and the impact on the environment, as well as improving the visitors experience based on the positive, neutral and negative environment factors which the visitors themselves identified

Fuzzy in 3-D: Contrasting Complex Fuzzy Sets with Type-2 Fuzzy Sets

CCIComplex 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. 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 line, and type-2 fuzzy sets by a surface, but a surface is simply a generalisation of a line. This similarity is particularly evident between pure complex fuzzy sets and type-2 fuzzy sets, which are both mappings from the domain onto the unit square. Type-2 fuzzy sets were found not to be isomorphic to pure complex fuzzy sets

Weighted‐selective aggregated majority‐OWA operator and its application in linguistic group decision making

This paper focuses on the aggregation operations in the group decision-making model based on the concept of majority opinion. The weighted-selective aggregated majority-OWA (WSAM-OWA) operator is proposed as an extension of the SAM-OWA operator, where the reliability of information sources is considered in the formulation. The WSAM-OWA operator is generalized to the quanti- fied WSAM-OWA operator by including the concept of linguistic quantifier, mainly for the group fusion strategy. The QWSAM-IOWA operator, with an ordering step, is introduced to the individual fusion strategy. The proposed aggregation operators are then implemented for the case of alternative scheme of heterogeneous group decision analysis. The heterogeneous group includes the consensus of experts with respect to each specific criterion. The exhaustive multicriteria group decision-making model under the linguistic domain, which consists of two-stage aggregation processes, is developed in order to fuse the experts' judgments and to aggregate the criteria. The model provides greater flexibility when analyzing the decision alternatives with a tolerance that considers the majority of experts and the attitudinal character of experts. A selection of investment problem is given to demonstrate the applicability of the developed model

Hierarchical fuzzy logic based approach for object tracking

In this paper a novel tracking approach based on fuzzy concepts is introduced. A methodology for both single and multiple object tracking is presented. The aim of this methodology is to use these concepts as a tool to, while maintaining the needed accuracy, reduce the complexity usually involved in object tracking problems. Several dynamic fuzzy sets are constructed according to both kinematic and non-kinematic properties that distinguish the object to be tracked. Meanwhile kinematic related fuzzy sets model the object's motion pattern, the non-kinematic fuzzy sets model the object's appearance. The tracking task is performed through the fusion of these fuzzy models by means of an inference engine. This way, object detection and matching steps are performed exclusively using inference rules on fuzzy sets. In the multiple object methodology, each object is associated with a confidence degree and a hierarchical implementation is performed based on that confidence degree.info:eu-repo/semantics/publishedVersio