Correlation coefficients of Pythagorean hesitant fuzzy sets and their application to radar LPI performance evaluation

Authors: CHENG XIU YANG, Qianzhe WANG, Weidong PENG, Shaoting PEI

Abstract: Evaluating low probability of intercept (LPI) performance is the first step to design parameters and arrange radar resources. In the evaluation process it is hard to rely on the intercept receiver?s working scenarios and operating parameters. On the other hand, indicators that affect the LPI performance of radiating side are difficult to consider comprehensively. Thus, building an effective evaluation system is crucial. This research considers the natural parameters of radar extracted from a radiating scenario. Subsequently, a number of criteria are selected, including spatial, time, frequency domain, polarization status, energy status, and waveform features. A multidomain radar LPI performance evaluation method is established, which is based on Pythagorean hesitant fuzzy sets (PHFSs). The paper is motivated by other scholars? research on fuzzy set theories and derives correlation coefficients as well as their properties for PHFSs. Concretely speaking, this study takes account of membership degree, nonmembership degree, and the hesitation of decision makers, so it integrates the benefits of correlation coefficients of hesitant fuzzy sets with Pythagorean fuzzy sets. Meanwhile, weighted correlation coefficients of PHFSs and their properties are proposed in detail. This provides a feasible approach for evaluation problems. For the sake of application, this article gives the specific LPI performance evaluation process. Finally, a novel method is presented to evaluate four fire control radars? LPI performances and is proved to be viable.

Keywords: Correlation coefficients, Pythagorean hesitant fuzzy sets, low probability of interception, multidomain evaluation

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