Multi-criteria group decision-making (MCGDM) problems are widespread in real life. However, most existing methods, such as hesitant fuzzy set (HFS), hesitant fuzzy linguistic term set (HFLTS) and inter-valued hesitant fuzzy set (IVHFS) only consider the original evaluation data provided by experts but fail to dig the concealed valuable information. The normal wiggly hesitant fuzzy set (NWHFS) is a useful technique to depict experts' complex evaluation information toward MCGDM issues. In this paper, on the basis of the score function of NWHFS, we propose the linear best-worst method (BWM)-based weight-determining models with normal wiggly hesitant fuzzy (NWHF) information to compute the optimal weights of experts and criteria. In addition, we present some novel distance measures between NWHFSs and discuss their properties. After fusing the individual evaluation matrices, the NWHF-ranking position method is put forward to develop the group MULTIMOORA method, which can be determined by the final decision results. Moreover, we investigate the Spring Festival travel rush phenomenon deeply and apply our methodology to solve the train selection problem during the Spring Festival period. Finally, the applicability and superiority of the proposed approach is demonstrated by comparing with traditional methods based on two aggregation operators of NWHFSs.
As a useful mathematical tool to solve the multi-attribute decision-making (MADM) problems, Pythagorean hesitant fuzzy set (PHFS) permits decision makers (DMs) to give several evaluation values in membership and non-membership degrees. Given that much cognitive preferences of DMs may be hidden in the original evaluation information and cannot be fully expressed, we propose the normal wiggly Pythagorean hesitant fuzzy set (NWPHFS) to comprehensively mine the uncertain preferences from original Pythagorean hesitant fuzzy information. NWPHFS can help DMs more accurately express their potential valuable preferences for objects while giving the original evaluation information. We put forward some operational laws and comparison rules of NWPHFS, then present the formulas of projection and bidirectional projection measures between normal wiggly Pythagorean hesitant fuzzy elements (NWPHFEs). Furthermore, we propose the normal wiggly Pythagorean hesitant fuzzy bidirectional projection (NWPHFBP) method and its specific application steps to solve MADM problems. The proposed approach can accurately reflect the projection relationship between the alternatives evaluated and ideal solutions by the NWPHF information. Through constructing a reasonable criteria system, we apply the NWPHFBP method to the issue of electric vehicle (EV) power battery recycling mode selection. Finally, we conduct the sensitivity analysis and verify the effectiveness of the proposed method by comparisons with other approaches. INDEX TERMS Normal wiggly Pythagorean hesitant fuzzy set (NWPHFS), multi-attribute decision-making (MADM), bidirectional projection, EV power battery recycling mode.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.