A note on fuzzy neighbourhood base spaces

Elsalamony, G.

doi:10.1016/j.fss.2006.04.006

Fuzzy Sets and Systems

2006

DOI: 10.1016/j.fss.2006.04.006

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A note on fuzzy neighbourhood base spaces

G. Elsalamony

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Cited by 10 publications

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References 16 publications

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“…Fuzzy mathematics is a powerful tool for dealing with uncertainty problems (Elsalamony 2006). After the fuzzy set theory was established by Zadeh (1965Zadeh ( , 1978, many scholars started to perform risk analysis by applying fuzzy set methods (Riečan 2005;Wu 2007).…”

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The application of fuzzy risk in researching flood disasters

Hong

Wan

2009

Nat Hazards

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To perform a fuzzy risk assessment the simplest way is to calculate the fuzzy expected value and convert fuzzy risk into non-fuzzy risk, i.e., a crisp value. In doing so, there is a transition from a fuzzy set to a crisp set. Therefore, the first step is to define an a level value, followed by selecting the elements x with a subordinate degree A(x) C a. The fuzzy expected values, E a ðxÞ and E a ðxÞ, of a possibility-probability distribution represent the fuzzy risk values being calculated. Therefore, we can obtain a conservative risk value, a venture risk value and a maximum probability risk value. Under such an a level, three risk values can be calculated. As a adopts all values between the set [0, 1], it is possible to obtain a series of risk values. Therefore, the fuzzy risk may either be a multi-valued risk or a set-valued risk. Calculation of the fuzzy expected value of a flood risk in the Jinhua River basin has been performed based on the interior-outer-set model. The selection of an a value is dependent on the confidence in different groups of people, while the selection of a conservative risk value or a venture risk value is dependent on the risk preference of these people.

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confidence: 99%

The application of fuzzy risk in researching flood disasters

Hong

Wan

2009

Nat Hazards

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“…Fuzzy mathematics is a powerful tool for dealing with uncertainty problems [5]. After the fuzzy set theory was established by Zadeh [23,24], many scholars started to perform risk analysis by applying fuzzy set methods [18,21].…”

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Practical Study on the Fuzzy Risk of Flood Disasters

Luo

2008

Acta Appl Math

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The simplest way to perform a fuzzy risk assessment is to calculate the fuzzy expected value and convert fuzzy risk into non-fuzzy risk, i.e., a crisp value. In doing so, there is a transition from the fuzzy set to the crisp set. Therefore, the first step is to define an α level value, and then select the elements x with a subordinate degree A(x) ≥ α. The higher the value of α, the lower the degree of uncertainty-the probability is closer to its true value. The lower the value of α, the higher the degree of uncertainty-this results in a lower probability serviceability. The possibility level α is dependant on technical conditions and knowledge. A fuzzy expected value of the possibility-probability distribution is a set with E α (x) and E α (x) as its boundaries. The fuzzy expected values E α (x) and E α (x) of a possibility-probability distribution represent the fuzzy risk values being calculated. Therefore, we can obtain a conservative risk value, a venture risk value and a maximum probability risk value. Under such an α level, three risk values can be calculated. As α adopts all values throughout the set [0, 1], it is possible to obtain a series of risk values. Therefore, the fuzzy risk may be a multi-valued risk or set-valued risk. Calculation of the fuzzy expected value of flood risk in the Jinhua River basin has been performed based on the interior-outer set model. Selection of an α value depends on the confidence in different groups of people, while selection of a conservative risk value or venture risk value depends on the risk preference of these people.

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Practical Research on Fuzzy Risk of Water Resources in Jinhua City, China

Luo

2010

Math Geosci

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A note on fuzzy neighbourhood base spaces

Cited by 10 publications

References 16 publications

The application of fuzzy risk in researching flood disasters

The application of fuzzy risk in researching flood disasters

Practical Study on the Fuzzy Risk of Flood Disasters

Practical Research on Fuzzy Risk of Water Resources in Jinhua City, China

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