The collapsing method of defuzzification for discretised interval type-2 fuzzy sets

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

doi:10.1016/j.ins.2008.07.011

Cited by 172 publications

(91 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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

View full text Add to dashboard Cite

“…The fuzzification process is based on the minimum t-norm while the center-of-area has been chosen for type-reduction. The collapsing method proposed in [18] has been used to calculate the centroids of the interval type-2 sets needed to compute the center-of-area. This is done by using the composite outward right-left variant of the collapsing method as it is described in [18] .…”

Section: The Initial Fuzzy Logic Systemsmentioning

confidence: 99%

“…The collapsing method proposed in [18] has been used to calculate the centroids of the interval type-2 sets needed to compute the center-of-area. This is done by using the composite outward right-left variant of the collapsing method as it is described in [18] . The training procedure aims to learn the parameters of the antecedent parts and the consequent parts of the fuzzy system rules.…”

Section: The Initial Fuzzy Logic Systemsmentioning

confidence: 99%

Learning of interval and general type-2 fuzzy logic systems using simulated annealing: Theory and practice

Almaraashi

John

Hopgood

et al. 2016

Information Sciences

View full text Add to dashboard Cite

a b s t r a c tThis paper reports the use of simulated annealing to design more efficient fuzzy logic systems to model problems with associated uncertainties. Simulated annealing is used within this work as a method for learning the best configurations of interval and general type-2 fuzzy logic systems to maximize their modeling ability. The combination of simulated annealing with these models is presented in the modeling of four benchmark problems including real-world problems. The type-2 fuzzy logic system models are compared in their ability to model uncertainties associated with these problems. Issues related to this combination between simulated annealing and fuzzy logic systems, including type-2 fuzzy logic systems, are discussed. The results demonstrate that learning the third dimension in type-2 fuzzy sets with a deterministic defuzzifier can add more capability to modeling than interval type-2 fuzzy logic systems. This finding can be seen as an important advance in type-2 fuzzy logic systems research and should increase the level of interest in the modeling applications of general type-2 fuzzy logic systems, despite their greater computational load.

show abstract

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

The collapsing method of defuzzification for discretised interval type-2 fuzzy sets

Cited by 172 publications

References 19 publications

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

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

Learning of interval and general type-2 fuzzy logic systems using simulated annealing: Theory and practice

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

Contact Info

Product

Resources

About