A Cross-Entropy-Based Framework Using HyperSoft  Type-2 Neutrosophic Numbers for Innovation  Capability Evaluation in Central Cities of Emerging  Economies

Xiangke Zhang; Shoukui He; Xu Chen

Authors

Xiangke Zhang School of Economics and Management, Chongqing Jiaotong University, Chongqing, 400074, China
Shoukui He School of Economics and Management, Chongqing Jiaotong University, Chongqing, 400074, China
Xu Chen Division of Infrastructure and Logistics, Chongqing University of Arts and Sciences, Chongqing, 402160, China

Keywords:

Multiple-attributes decision-making (MADM); Type-2 neutrosophic number (T2NN); Cross-entropy approach; Comprehensive evaluation of innovation capability; HyperSoft (HS).

Abstract

The comprehensive evaluation of innovation capabilities in central cities of
emerging countries is essential for promoting regional economic growth. This evaluation
examines various factors, such as scientific activities, innovation infrastructure, talent
resources, and policy environments, offering insights into the current innovation
landscape and future potential. By guiding the allocation of resources and optimizing
innovation policies, it fosters the transformation of technological achievements and
accelerates urban economic transformation and sustainable development. Moreover, it
helps cities attract investment and skilled talent, enhancing their competitiveness and
influence. This evaluation is a multi-attribute decision-making (MADM) challenge, for
which the cross-entropy method has been recently adopted to handle complex criteria.
Type-2 neutrosophic numbers (T2NNs) are used to represent uncertainty in assessing
innovation capabilities. This study introduces the Type-2 neutrosophic number cross
entropy (T2NN-HS-CE) approach with HyperSoft to solve MADM problems involving
T2NNs. A numerical case study and sensitivity analysis validate the effectiveness of the
proposed method in assessing the innovation capacity of cities in developing nations.

DOI: 10.5281/zenodo.14232717