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

Abstract

Evaluating low probability of intercept (LPI) performance is the first step to design parameters and arrangeradar resources. In the evaluation process it is hard to rely on the intercept receiver’s working scenarios and operatingparameters. On the other hand, indicators that affect the LPI performance of radiating side are difficult to considercomprehensively. Thus, building an effective evaluation system is crucial. This research considers the natural parametersof 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 performanceevaluation method is established, which is based on Pythagorean hesitant fuzzy sets (PHFSs). The paper is motivatedby 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 ofdecision makers, so it integrates the benefits of correlation coefficients of hesitant fuzzy sets with Pythagorean fuzzysets. Meanwhile, weighted correlation coefficients of PHFSs and their properties are proposed in detail. This providesa feasible approach for evaluation problems. For the sake of application, this article gives the specific LPI performanceevaluation process. Finally, a novel method is presented to evaluate four fire control radars’ LPI performances and isproved to be viable.