Fuzzy regression analysis: Systematic review and bibliography

Chukhrova, Nataliya; Johannssen, Arne

doi:10.1016/j.asoc.2019.105708

Cited by 95 publications

(64 citation statements)

References 384 publications

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“…Pourahmad et al, 2011, Namdari et al, 2014 replace probabilities by fuzzy numbers; they usually do not combine them. Fuzzy probabilities (Zadeh, 1984) are considered within the so-called fuzzy random regression field, however no fuzzy random logistic regression seems to have been developed to date (see Chukhrova and Johannssen, 2019, for a review of the fuzzy regression field).…”

Section: Approximation Of a Fuzzy-random Logistic Regressionmentioning

confidence: 99%

Possibilistic response surfaces combining fuzzy targets and hydro-climatic uncertainty in flood vulnerability assessment

Lachaut

Tilmant

2020

Preprint

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Abstract. Several alternatives have been proposed to shift the paradigms of water management under uncertainty from predictive to decision-centric. An often mentioned tool is the stress-test response surface; mapping system performance to a large sample of future hydro-climatic conditions. Dividing this exposure space between success and failure requires clear performance targets. In practice, however, stakeholders and decision-makers may be confronted with ambiguous objectives for which there are no clearly-defined (crisp) performance thresholds. Furthermore, response surfaces can be non-deterministic, as they do not fully capture all possible sources of hydro-climatic uncertainty. The challenge is thus to combine two different types of uncertainty: the irreducible uncertainty of the response itself relative to the variables that describe change, and the fuzziness of the performance target. We propose possibilistic surfaces to assess flood vulnerability with fuzzy performance thresholds. Three approaches are tested and compared on a un-gridded sample of the exposure space: (i) an aggregation of logistic regressions based on α-cuts combines the uncertainty of the response itself and the ambiguity of the target within a single possibility measure; (ii) an alternative approximates the response with a fuzzy analytical surface; and (iii) a convex delineation expresses the largest range of failure specific to a given management rule without probabilistic assumptions. To illustrate the proposed approaches, we use the flood-prone reservoir system of the Upper Saint-François River Basin in Canada as a case study. This study shows that ambiguity can be effectively be considered when generating a response surface and suggests how further research could build a possibilistic framework for hydro-climatic uncertainty.

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Section: Approximation Of a Fuzzy-random Logistic Regressionmentioning

confidence: 99%

Possibilistic response surfaces combining fuzzy targets and hydro-climatic uncertainty in flood vulnerability assessment

Lachaut

Tilmant

2020

Preprint

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“…For these reasons, some authors have considered approaches of fuzzy statistics to deal appropriately with fuzziness in data and hypotheses formulation. In the literature of fuzzy hypothesis testing, there are a few publications considering the sign test in fuzzy environments (see Chukhrova and Johannssen, 3 for a systematic review): Fuzzy/interval‐valued data caused by the imprecision of observations (see Grzegorzewski, 4,5 Grzegorzewski and Spiewak, 6‐8 Hesamian and Chachi, 9 Hesamian and Taheri, 10 Kahraman et al, 11 Momeni and Sadeghpour‐Gildeh, 12 and Shams and Hesamian 13 ), that is, fuzzy data as perception of a crisp but unobservable random variable (so called epistemic perspective, see Couso and Dubois 14 ), or fuzzy set‐/interval‐valued random variables (so called ontic perspective) (see Grzegorzewski and Spiewak 6,7 ). Fuzzy/interval‐valued hypotheses caused by fuzzy quantiles like the fuzzy median (see Grzegorzewski and Spiewak 6,7 ) or imprecision of linguistic statements on quantiles (see Hesamian and Chachi, 9 Hesamian and Taheri, 10 Momeni and Sadeghpour‐Gildeh, 12 and Shams and Hesamian 13 ).…”

Section: Introductionmentioning

confidence: 99%

Nonparametric fuzzy hypothesis testing for quantiles applied to clinical characteristics of COVID‐19

Chukhrova

Johannssen

2021

Int J Intell Syst

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The sign test is one of the most popular nonparametric tests for location problems and allows testing for any quantile of a population. However, the common sign test has serious drawbacks such as loss of information by considering solely signs of observations but not their magnitudes, various problems related to handling of ties in the data, and the lack of embedding uncertainty regarding the fraction of underlying quantile. To address these issues, we present an extended sign test based on fuzzy categories and fuzzy formulated hypotheses that improves the generality, versatility, and practicability of the common sign test. This generalized test procedure is neat in theory and practice and avoids disadvantages that are often associated with fuzzy tests (e.g., a considerably higher complexity of the underlying model, a fuzzy test decision, and a possibilistic instead of a probabilistic interpretation of test results). In addition, we perform a comprehensive case study on COVID‐19 in HIV‐infected individuals with a focus on human body temperature and related measurement problems. The results of the study clearly indicate that fuzzy categories and fuzzy hypotheses improve the performance of the sign test.

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“…Recently, many techniques have been proposed by different authors to combine the conventional statistical regression models with the concept of fuzzy set theory. In this regard, Chukhrova and Johannssen [1] provided a comprehensive systematic review of thenavailable methodologies and applications focused on fuzzy regression analysis as of 2019. Such studies can be classified as (1) possibilistic approaches, where linear and non-linear programming methods are minimized by minimizing the total spread of their fuzzy parameters, subject to the support observations at some specific levels (see for example Refs.…”

Section: Introductionmentioning

confidence: 99%

“…. , U N are independent random variables uniformly distributed over the interval [1,93], and N ∈ N is a large number. Here, it was assumed that N = 100.…”

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confidence: 99%

A Fuzzy Linear Regression Model With Functional Predictors And Fuzzy Responses

Hesamian¹,

Mg²

2021

Preprint

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A novel functional regression model was introduced, where the predictor was a curve linked to a scalar fuzzy response variable. An absolute error-based penalized method with SCAD loss function was proposed to evaluate the unknown components of the model. For this purpose, a concept of fuzzy-valued function was developed and discussed. Then, a fuzzy large number notion was proposed to estimate the fuzzyvalued function. Some common goodness-of-fit criteria were also used to examine the performance of the proposed method. Efficiency of the proposed method was then evaluated through two numerical examples, including a simulation study and an applied example in the scope of watershed management. The proposed method was also compared with several common fuzzy regression models in cases where the functional data was converted to scalar ones.

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Fuzzy regression analysis: Systematic review and bibliography

Cited by 95 publications

References 384 publications

Possibilistic response surfaces combining fuzzy targets and hydro-climatic uncertainty in flood vulnerability assessment

Possibilistic response surfaces combining fuzzy targets and hydro-climatic uncertainty in flood vulnerability assessment

Nonparametric fuzzy hypothesis testing for quantiles applied to clinical characteristics of COVID‐19

A Fuzzy Linear Regression Model With Functional Predictors And Fuzzy Responses

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