Complex fuzzy sets

Ramot, D.; Milo, Ron; Friedman, Menahem; Kandel, Abraham

doi:10.1109/91.995119

Cited by 763 publications

(506 citation statements)

References 12 publications

Supporting

Mentioning

494

Contrasting

Unclassified

Order By: Relevance

“…These approaches can be classified under the first category. Work that can be classified under the second category, include complex fuzzy logic [40] and complex fuzzy reasoning [41]. Under the third category, we can cite the contribution of Kaburlasos and Kehagias [42] that consisted of an extension of fuzzy inference systems based on lattice theory.…”

Section: Related Workmentioning

confidence: 99%

Multiple Instance Mamdani Fuzzy Inference

Khalifa

Frigui

2015

Int. J. Fuzzy Log. Intell. Syst.

View full text Add to dashboard Cite

A novel fuzzy learning framework that employs fuzzy inference to solve the problem of Multiple Instance Learning (MIL) is presented. The framework introduces a new class of fuzzy inference systems called Multiple Instance Mamdani Fuzzy Inference Systems (MIMamdani). In multiple instance problems, the training data is ambiguously labeled. Instances are grouped into bags, labels of bags are known but not those of individual instances. MIL deals with learning a classifier at the bag level. Over the years, many solutions to this problem have been proposed. However, no MIL formulation employing fuzzy inference exists in the literature. Fuzzy logic is powerful at modeling knowledge uncertainty and measurements imprecision. It is one of the best frameworks to model vagueness. However, in addition to uncertainty and imprecision, there is a third vagueness concept that fuzzy logic does not address quiet well, yet. This vagueness concept is due to the ambiguity that arises when the data have multiple forms of expression, this is the case for multiple instance problems. In this paper, we introduce multiple instance fuzzy logic that enables fuzzy reasoning with bags of instances. Accordingly, a MI-Mamdani that extends the standard Mamdani inference system to compute with multiple instances is introduced. The proposed framework is tested and validated using a synthetic dataset suitable for MIL problems. Additionally, we apply the proposed multiple instance inference to fuse the output of multiple discrimination algorithms for the purpose of landmine detection using Ground Penetrating Radar.

show abstract

Section: Related Workmentioning

confidence: 99%

Multiple Instance Mamdani Fuzzy Inference

Khalifa

Frigui

2015

Int. J. Fuzzy Log. Intell. Syst.

View full text Add to dashboard Cite

show abstract

“…Ramot et al [30] introduced complex fuzzy sets as type-1 fuzzy sets extended by an additional phase term which permits them to represent fuzziness in time-series applications. A significant portion of this paper ".…”

Section: Introductionmentioning

confidence: 99%

“…They include the analysis of solar activity as measured by the recorded number of sunspots [30], signal processing [30], stock trading on the New York Stock Exchange [29], prediction of voter turnout in elections [29], multi periodic factor prediction [24] and multi-variate time-series forecasting [37].…”

Section: Introductionmentioning

confidence: 99%

Interval-valued complex fuzzy logic

Greenfield

Chiclana

Dick

2016

2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

View full text Add to dashboard Cite

Abstract-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.

show abstract

“…Then these two operations, called necessity operation, denoted by , A, A and possibility operation, denoted by , A are introduced in the case of CAIFS. The advantage from generalising these two operations is to demonstrate/illustrate an attached relation between the concepts CAIFS [1] and CFS [3].…”

Section: Power ( )mentioning

confidence: 99%

Some operations on complex Atanassov's intuitionistic fuzzy sets

Alkouri

Salleh

2013

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. Several innovative uncertainty sets were introduced recently. Complex Atanassov's intuitionistic fuzzy set (CAIFS) is one of these uncertainty sets, where Atanassov's intuitionistic fuzzy membership and non-membership functions take values in the unit circle in the complex plane. In this paper, some operations are generalised to the case of CAIFS. Two main operations and are introduced and various properties are investigated. Also, we conclude the advantage from generalising these two operations to the realm of complex numbers, by finding out a relationship between the concepts of CAIFS and complex fuzzy sets (CFS).

show abstract

Complex fuzzy sets

Cited by 763 publications

References 12 publications

Multiple Instance Mamdani Fuzzy Inference

Multiple Instance Mamdani Fuzzy Inference

Interval-valued complex fuzzy logic

Some operations on complex Atanassov's intuitionistic fuzzy sets

Contact Info

Product

Resources

About