Fuzzy techniques provide a theoretical explanation for the heuristic ℓ&lt;inf&gt;p&lt;/inf&gt;-regularization of signals and images

Cervantes, Fernando; Usevitch, Bryan; Valera, Leobardo; Kreinovich, Vladik; Kosheleva, Olga

doi:10.1109/fuzz-ieee.2016.7737842

Cited by 1 publication

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“…In [6], we used the same ideas of scale-invariance -that are used above to justify ℓ p -techniques -to show that the best choice is to use functions g 1 (z) = |z| p • ln(z) or g 1 (z) = |z| p 1 for some p 1 . The same approach also helps to decide which functions to use if we consider 3-and more-parametric families instead of 2-parametric ones [6].…”

Section: How To Improve the Existing Semi-heuristic Techniquementioning

confidence: 99%

Beyond Traditional Applications of Fuzzy Techniques: Main Idea and Case Studies

Kreinovich

Kosheleva

Dumrongpokaphan

2018

Recent Developments and the New Direction in Soft-Computing Foundations and Applications

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Fuzzy logic techniques were originally designed to translate expert knowledge-which is often formulated by using imprecise ("fuzzy") from natural language (like "small")-into precise computer-understandable models and control strategies. Such a translation is still the main use of fuzzy techniques. Lately, it turned out that fuzzy methods can help in another class of applied problems: namely, in situations when there are semi-heuristic techniques for solving the corresponding problems, i.e., techniques for which there is no convincing theoretical justification. Because of the lack of a theoretical justification, users are reluctant to use these techniques, since their previous empirical success does not guarantee that these techniques will work well on new problems. In this paper, we show that in many such situations, the desired theoretical justification can be obtained if, in addition to known (crisp) requirements on the desired solution, we also take into account requirements formulated by experts in natural-language terms. Naturally, we use fuzzy techniques to translate these imprecise requirements into precise terms.

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Section: How To Improve the Existing Semi-heuristic Techniquementioning

confidence: 99%