Algorithm for simultaneous defuzzification under constraints: shifted mean-max

Verstraete, Jörg

doi:10.2991/ifsa-eusflat-15.2015.48

Cited by 3 publications

(5 citation statements)

References 10 publications

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“…In [13], an attempt at algorithmically performing a constraint defuzzification of multiple fuzzy sets under a shared constraint was made. The algorithm was limited to convex fuzzy sets and shifted the values of the Mean Of Max defuzzifers, maximizing the lowest membership grade.…”

Section: B Constrained Defuzzificationmentioning

confidence: 99%

“…The key difference between the constraints on defuzzification in literature and the presented method is that the presented method relates to a constraint that affects the defuzzification of multiple fuzzy sets at once. The methods in [4] and [13] share this problem but the proposed methods are not generally applicable and not suitable for a comparison that involves more general fuzzy sets.…”

Section: B Constrained Defuzzificationmentioning

confidence: 99%

“…The goal function G.1 is the only one that creates a maximization problem (easily rewritten as a minimization problem of complements), whereas the others constitute minimization problems. The goal function G.1 provides for finding a solution that maximizes the lowest membership (as in [13]), reflecting the notion that values with higher membership are better values. The underlying defuzzifier D may however not share this notion: the defuzzified value using COG for example, is not guaranteed to have the highest membership value.…”

Section: B Goal Functionsmentioning

confidence: 99%

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Combined Defuzzification Under Shared Constraint

Verstraete,

Radziszewska,

Kaczmarek-Majer

et al. 2024

IEEE Trans. Fuzzy Syst.

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Defuzzification of fuzzy sets is an important aspect of fuzzy processing, as it determines how the fuzziness is dealt with when performing the final step to obtain crisp solutions. In this contribution, we consider the possibility of defuzzifying multiple general type-1 fuzzy sets, given that their defuzzified values are bound by a single, known constraint. This stems from an application in spatial data processing, where we obtained a number of fuzzy sets whose defuzzified values should sum up to a crisp and known value. It is possible to defuzzify each fuzzy set individually and rescale the outcomes to meet the constraint. However, considering that the fuzzy set contains information on what constitutes good values, accounting for the constraint in the defuzzification process has the potential to yield better results. We considered this as an optimization problem and investigated appropriate goal functions. The approach and goal functions are discussed with respect to typical properties of defuzzifiers.

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Section: B Constrained Defuzzificationmentioning

confidence: 99%

Section: B Constrained Defuzzificationmentioning

confidence: 99%

Section: B Goal Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Combined Defuzzification Under Shared Constraint

Verstraete,

Radziszewska,

Kaczmarek-Majer

et al. 2024

IEEE Trans. Fuzzy Syst.

Self Cite

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show abstract

“…The rule-based approach calculates weights implicitly (as explained in Section 2.2) to perform the remapping. The result of these calculations are then corrected for the constraint imposed by the (b) (a) value of the input cell, either due to simple rescaling or by using combined defuzzification (Verstraete 2015a). In case of the segment grid, the same procedure is applied for each segment: the fuzzy rule-based approach will determine values and ranges for parameters used in the rules.…”

Section: Usage and Special Combination With Fuzzy Rule-based Approachmentioning

confidence: 99%

“…These are aggregated and a single value is extracted for each output cell. This last phase is achieved using the algorithm presented in Verstraete (2015a), to ensure satisfaction of the constraint that the partitions of an input cell should add up to that input cell.…”

Section: Spatial Disaggregation Using the Fuzzy Rule-based Approachmentioning

confidence: 99%

Solving the general map overlay problem using a fuzzy inference system designed for spatial disaggregation

Verstraete

2018

Mitig Adapt Strateg Glob Change

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Identification of mitigation and adaptation strategies in any situation has to be a well informed decision. This decision not only has to be based on quantifiable data (e.g. amounts or concentrations of emissions), but it also needs to consider spatial aspects such as the source of emissions, the impact of policies on the population or the identification of responsible parties. As such, it is important that the decisions are based on accurate reports made by experts in the field. Many data are available to the experts, and combining this data tends to increase the inherently contained uncertainty. Novel operations that exhibit a lower increase of uncertainty can yield outcomes that contain less uncertainty, which subsequently improves the accuracy of the resulting reports. At the same time, the decisionmakers are confronted with different reports, and the comparison of the contained spatial aspects requires combining the data, which exhibits similar issues relating to uncertainty. With data usually represented in gridded structures, comparing them often requires a process called regridding: this is the process of mapping one grid onto a second grid, a process which increases spatial uncertainty. In this contribution, a novel regridding algorithm is presented. While mainly intended as a preprocessing tool for the experts, it is also applicable for supporting the comparison of gridded datasets as used by decision-makers. In the context of this article, a grid can be irregular, allowing the presented algorithm to also be used for remapping a grid onto, e.g. administrative borders or vice versa. The presented algorithm for regridding is a modification that is generally applicable on spatial disaggregation algorithms. It was developed in parallel with a novel method that uses artificial intelligence (in the form of fuzzy rule-based systems) to involve proxy data to obtain better results, and it will be demonstrated using this approach for spatial disaggregation. Mitig Adapt Strateg Glob Change to perform regridding using an algorithm designed for spatial disaggregation is detailed in this article and the performance of the combination with the artificial intelligent system for disaggregation is illustrated by means of an example.

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Rulebase construction using variables with data-dependent domains

Verstraete

Radziszewska

2021

Information Sciences

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Algorithm for simultaneous defuzzification under constraints: shifted mean-max

Cited by 3 publications

References 10 publications

Combined Defuzzification Under Shared Constraint

Combined Defuzzification Under Shared Constraint

Solving the general map overlay problem using a fuzzy inference system designed for spatial disaggregation

Rulebase construction using variables with data-dependent domains

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