Fuzzy Inference System (FIS) Extensions Based on the Lattice Theory

Kaburlasos, Vassilis G.; Kehagias, Athanasios

doi:10.1109/tfuzz.2013.2263807

Cited by 59 publications

(45 citation statements)

References 68 publications

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“…Hence, -FAMs can be viewed as approaches towards lattice computing, "an evolving collection of tools and mathematical modeling methodologies with the capacity to process lattice ordered data per se including logic values, numbers, sets, symbols, graphs, etc." [69][70][71][72][73].…”

Section: Resultsmentioning

confidence: 99%

Tunable equivalence fuzzy associative memories

Esmi

Sussner

Sandri

2016

Fuzzy Sets and Systems

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Section: Resultsmentioning

confidence: 99%

Tunable equivalence fuzzy associative memories

Esmi

Sussner

Sandri

2016

Fuzzy Sets and Systems

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“…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.

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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.

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“…The mapping 1 → 1 and 2 → 2 , where the INs 1 , 2 , 1 and 2 are shown in Fig.3 (a) and (b), can be reproduced by the piecewise linear weight function 1 : [0, 6]∪ [11,14] → [0, 4] ∪ [10,13] in Fig.5(a). Apparently, it is both 1 ( 1 ) = 1 and 1 ( 2 ) = 2 .…”

Section: An Interesting Extension Is To Use a Non-decreasing Real Funmentioning

confidence: 99%

Intervals' Numbers (INs) interpolation/extrapolation

Kaburlasos

Papakostas

Pachidis

et al. 2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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An Intervals' Number (IN) is a mathematical object known to represent either a probability distribution or a possibility distribution. The space of INs has been studied during the last years. After summarizing some instrumental mathematical results, this work demonstrates comparatively novel schemes for tunable fuzzy rule interpolation and extrapolation. Extensions to Type-2 fuzzy sets are straightforward. Finally, this work demonstrates a preliminary application, regarding the reconstruction of partially occluded human facial expressions, based on a neural network that may predict a data distribution from other ones. Far reaching extensions of the proposed techniques are discussed.

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Fuzzy Inference System (FIS) Extensions Based on the Lattice Theory

Cited by 59 publications

References 68 publications

Tunable equivalence fuzzy associative memories

Tunable equivalence fuzzy associative memories

Multiple Instance Mamdani Fuzzy Inference

Intervals' Numbers (INs) interpolation/extrapolation

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