Fuzzy Hypothesis Testing for Radar Detection: A Statistical Approach for Reducing False Alarm and Miss Probabilities
This paper addresses a fundamental challenge in statistical radar detection systems: optimizing the trade-off between the probability of a false alarm (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><m...
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2025-07-01
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| author | Ahmed K. Elsherif Hanan Haj Ahmad Mohamed Aboshady Basma Mostafa |
| author_facet | Ahmed K. Elsherif Hanan Haj Ahmad Mohamed Aboshady Basma Mostafa |
| author_sort | Ahmed K. Elsherif |
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| description | This paper addresses a fundamental challenge in statistical radar detection systems: optimizing the trade-off between the probability of a false alarm (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mrow><mi>F</mi><mi>A</mi></mrow></msub></semantics></math></inline-formula>) and the probability of a miss (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>M</mi></msub></semantics></math></inline-formula>). These two metrics are inversely related and critical for performance evaluation. Traditional detection approaches often enhance one aspect at the expense of the other, limiting their practical applicability. To overcome this limitation, a fuzzy hypothesis testing framework is introduced that improves decision making under uncertainty by incorporating both crisp and fuzzy data representations. The methodology is divided into three phases. In the first phase, we reduce the probability of false alarm <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mrow><mi>F</mi><mi>A</mi></mrow></msub></semantics></math></inline-formula> while maintaining a constant probability of miss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>M</mi></msub></semantics></math></inline-formula> using crisp data characterized by deterministic values and classical statistical thresholds. In the second phase, the inverse scenario is considered: minimizing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>M</mi></msub></semantics></math></inline-formula> while keeping <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mrow><mi>F</mi><mi>A</mi></mrow></msub></semantics></math></inline-formula> fixed. This is achieved through parameter tuning and refined threshold calibration. In the third phase, a strategy is developed to simultaneously enhance both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mrow><mi>F</mi><mi>A</mi></mrow></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>M</mi></msub></semantics></math></inline-formula>, despite their inverse correlation, by adopting adaptive decision rules. To further strengthen system adaptability, fuzzy data are introduced, which effectively model imprecision and ambiguity. This enhances robustness, particularly in scenarios where rapid and accurate classification is essential. The proposed methods are validated through both real and synthetic simulations of radar measurements, demonstrating their ability to enhance detection reliability across diverse conditions. The findings confirm the applicability of fuzzy hypothesis testing for modern radar systems in both civilian and military contexts, providing a statistically sound and operationally applicable approach for reducing detection errors and optimizing system performance. |
| format | Article |
| id | doaj-art-7d69e45fba8d42b1a14458bc7b8c5744 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-7d69e45fba8d42b1a14458bc7b8c57442025-08-20T03:08:06ZengMDPI AGMathematics2227-73902025-07-011314229910.3390/math13142299Fuzzy Hypothesis Testing for Radar Detection: A Statistical Approach for Reducing False Alarm and Miss ProbabilitiesAhmed K. Elsherif0Hanan Haj Ahmad1Mohamed Aboshady2Basma Mostafa3Department of Mathematics, Military Technical College, Cairo, EgyptDepartment of Basic Science, The General Administration of Preparatory Year, King Faisal University, Al Ahsa 31982, Saudi ArabiaDepartment of Basic Science, Faculty of Engineering, The British University in Egypt, El Sherook City, Cairo, EgyptOperations Research Department, Faculty of Computers & Artificial Intelligence, Cairo University, Cairo, EgyptThis paper addresses a fundamental challenge in statistical radar detection systems: optimizing the trade-off between the probability of a false alarm (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mrow><mi>F</mi><mi>A</mi></mrow></msub></semantics></math></inline-formula>) and the probability of a miss (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>M</mi></msub></semantics></math></inline-formula>). These two metrics are inversely related and critical for performance evaluation. Traditional detection approaches often enhance one aspect at the expense of the other, limiting their practical applicability. To overcome this limitation, a fuzzy hypothesis testing framework is introduced that improves decision making under uncertainty by incorporating both crisp and fuzzy data representations. The methodology is divided into three phases. In the first phase, we reduce the probability of false alarm <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mrow><mi>F</mi><mi>A</mi></mrow></msub></semantics></math></inline-formula> while maintaining a constant probability of miss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>M</mi></msub></semantics></math></inline-formula> using crisp data characterized by deterministic values and classical statistical thresholds. In the second phase, the inverse scenario is considered: minimizing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>M</mi></msub></semantics></math></inline-formula> while keeping <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mrow><mi>F</mi><mi>A</mi></mrow></msub></semantics></math></inline-formula> fixed. This is achieved through parameter tuning and refined threshold calibration. In the third phase, a strategy is developed to simultaneously enhance both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mrow><mi>F</mi><mi>A</mi></mrow></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>M</mi></msub></semantics></math></inline-formula>, despite their inverse correlation, by adopting adaptive decision rules. To further strengthen system adaptability, fuzzy data are introduced, which effectively model imprecision and ambiguity. This enhances robustness, particularly in scenarios where rapid and accurate classification is essential. The proposed methods are validated through both real and synthetic simulations of radar measurements, demonstrating their ability to enhance detection reliability across diverse conditions. The findings confirm the applicability of fuzzy hypothesis testing for modern radar systems in both civilian and military contexts, providing a statistically sound and operationally applicable approach for reducing detection errors and optimizing system performance.https://www.mdpi.com/2227-7390/13/14/2299fuzzy hypothesis testingradar detectionprobability of false alarmprobability of missstatistical decision theorycrisp and fuzzy data |
| spellingShingle | Ahmed K. Elsherif Hanan Haj Ahmad Mohamed Aboshady Basma Mostafa Fuzzy Hypothesis Testing for Radar Detection: A Statistical Approach for Reducing False Alarm and Miss Probabilities Mathematics fuzzy hypothesis testing radar detection probability of false alarm probability of miss statistical decision theory crisp and fuzzy data |
| title | Fuzzy Hypothesis Testing for Radar Detection: A Statistical Approach for Reducing False Alarm and Miss Probabilities |
| title_full | Fuzzy Hypothesis Testing for Radar Detection: A Statistical Approach for Reducing False Alarm and Miss Probabilities |
| title_fullStr | Fuzzy Hypothesis Testing for Radar Detection: A Statistical Approach for Reducing False Alarm and Miss Probabilities |
| title_full_unstemmed | Fuzzy Hypothesis Testing for Radar Detection: A Statistical Approach for Reducing False Alarm and Miss Probabilities |
| title_short | Fuzzy Hypothesis Testing for Radar Detection: A Statistical Approach for Reducing False Alarm and Miss Probabilities |
| title_sort | fuzzy hypothesis testing for radar detection a statistical approach for reducing false alarm and miss probabilities |
| topic | fuzzy hypothesis testing radar detection probability of false alarm probability of miss statistical decision theory crisp and fuzzy data |
| url | https://www.mdpi.com/2227-7390/13/14/2299 |
| work_keys_str_mv | AT ahmedkelsherif fuzzyhypothesistestingforradardetectionastatisticalapproachforreducingfalsealarmandmissprobabilities AT hananhajahmad fuzzyhypothesistestingforradardetectionastatisticalapproachforreducingfalsealarmandmissprobabilities AT mohamedaboshady fuzzyhypothesistestingforradardetectionastatisticalapproachforreducingfalsealarmandmissprobabilities AT basmamostafa fuzzyhypothesistestingforradardetectionastatisticalapproachforreducingfalsealarmandmissprobabilities |