The sampling method of defuzzification for type-2 fuzzy sets: Experimental evaluation

Greenfield, Sarah; Chiclana, Francisco; John, Robert; Coupland, Simon

doi:10.1016/j.ins.2011.11.042

Cited by 70 publications

(48 citation statements)

References 28 publications

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“…This structure was observed during investigations into the sampling method of type-2 defuzzification [21,8]. The membership function of the TRS of a discretised type-2 fuzzy set may be thought of as a set of tuples (Section 3).…”

Section: Stratification In the Discretised Trsmentioning

confidence: 93%

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The Structure of the Type-Reduced Set of a Continuous Type-2 Fuzzy Set

Greenfield¹,

Chiclana²

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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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.

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Section: Stratification In the Discretised Trsmentioning

confidence: 93%

“…Strategies have been developed that reduce the computational complexity of all stages of the generalised type-2 FIS [7,8,9,10]. We believe that the research presented in this paper will lead to further complexity reducing techniques.…”

Section: Introductionmentioning

confidence: 99%

The Structure of the Type-Reduced Set of a Continuous Type-2 Fuzzy Set

Greenfield¹,

Chiclana²

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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“…An explanation for this might reside in the complexity of type-2 computation. In any case, a possible approach to develop in this case would necessarily involve the decomposition of each type-2 fuzzy sets in its associated set of type-1 embedded sets to which type-1 fuzzy approaches are possible to be applied in conduction to the application of Zadeh's extension principle to obtain the type-2 fuzzy set output [21,[31][32][33][34].…”

Section: Development Of Management Procedures Of Incomplete Preferencmentioning

confidence: 99%

Managing incomplete preference relations in decision making: A review and future trends

Ureña

Chiclana

Morente-Molinera

et al. 2015

Information Sciences

246

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“…Formally, this is a discrete type-2 fuzzy sets [50,51]. However, in [6] these type-2 fuzzy set were transformed into discrete type-1 fuzzy sets by associating to each element (linguistic label), l h , of the BLTS set its subindex, h, in order to carry out the next step of the unification based consensus model, i.e.…”

Section: Dr2 If Cve Lkmentioning

confidence: 99%

Type-1 OWA methodology to consensus reaching processes in multi-granular linguistic contexts

Mata

Pérez

Zhou

et al. 2014

Knowledge-Based Systems

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A crucial step in group decision making (GDM) processes is the aggregation of individual opinions with the aim of achieving a "fair" representation of each individual within the group. In multi-granular linguistic contexts where linguistic term sets with common domain but different granularity and/or semantic are used, the methodology widely applied until now requires, prior to the aggregation step, the application of a unification process. The reason for this unification process is the lack of appropriate aggregation operators for directly aggregating uncertain information represented by means of fuzzy sets. With the recent development of the Type-1 Ordered Weighted Averaging (T1OWA) operator, which is able to aggregate fuzzy sets, alternative approaches to multi-granular linguistic GDM problems are possible. Unlike consensus models based on unification processes, this paper presents a new T1OWA based consensus methodology that can directly manage linguistic term sets with different cardinality and/or semantic without the need to perform any transformation to unify the information. Furthermore, the linguistic information could be assumed to be balanced or unbalanced in its mathematical representation, and therefore the new T1OWA approach to consensus is more general in its application than previous consensus reaching processes with muti-granular linguistic information. To test the goodness of the new consensus reaching approach, a comparative study between the T1OWA based consensus model and the unification based consensus model is carried out using six randomly generated GDM problems with balanced multi-granular information. When distance between fuzzy sets used in the T1OWA based approach is defined as the corresponding distance between their centroids, a higher final level of consensus is achieved in four out of the six cases although no significant differences were found between both consensus approaches.

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The sampling method of defuzzification for type-2 fuzzy sets: Experimental evaluation

Cited by 70 publications

References 28 publications

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

Managing incomplete preference relations in decision making: A review and future trends

Type-1 OWA methodology to consensus reaching processes in multi-granular linguistic contexts

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