In the field of fuzzy sets, distance measures can effectively quantify the relevant uncertainty. Regarding hesitant fuzzy sets (HFSs), improved hesitant fuzzy distance measures have recently been proposed by fusing classical distance measures with hesitation degrees, and the corresponding information enrichment can be probabilistically advanced to pursue new distance measures of probabilistic hesitant fuzzy sets (PHFSs). Aiming at PHFSs, the improved distance measures of HFSs are simulated and extended in this paper, and thus improved distance measures of PHFSs are proposed; the new PHFSs distances are utilized to construct a new method of probabilistic hesitant fuzzy decision-making, called MEREC-TODIM. Firstly, the new probabilistic hesitant fuzzy Hamming distance and Euclidean distance are directly and parametrically established by incorporating hesitation degrees; accordingly, the improved distance measures exhibit a 2× 2 system on (non-parameter, parameter) and (Hamming, Euclidean), and their distance property, measure size, parameter monotonicity, and promotion degeneration are investigated and acquired. Furthermore, a modified score function is proposed for MEREC to determine attribute weights, and thus a corresponding decision method with TODIM (i.e., MEREC-TODIM) is established for PHFSs applications on evaluation sorting and optimization selection. Finally, MEREC-TODIM is validated through parameter analyses and decision comparisons, and it is effectively applied to two practical examples: Carbon Capture Utilization Storage and PhD Admission Interviews.
By applying the weighted inequality and the real variable methods of harmonic analysis,the boundedness of the fractional maximal operator with rough kernel is proved on the weighted Morrey space.Meanwhile,the weighted boundedness of its commuta-tor generated by BMO function is also obtained.
Two graphs are called singularly cospectral if they have the same nonzero singular value with the same multiplicity.Singularly cospectral is weaker than cospectral but stronger than equienergetic.A new construction of singularly cospectral graph is derived using the operation of t-join(shadow)corona of a graph and the technique of block matrix which has great significance for studying the structural and spectral properties of equienergetic graphs.
Natural habitats are damaged by human interference to varying degrees during the urbanization process, which can impede a region’s high-quality development. In this study, we examined the spatial–temporal evolution characteristics of habitat quality and urbanization in the Lower Yellow River from 2000 to 2020 using the integrated valuation of ecosystem services and tradeoffs (InVEST) model and the comprehensive indicator method. We also evaluated the coupling relationship between the habitat quality and urbanization using the coupling coordination degree model. The findings indicate the following aspects: (1) Between 2000 and 2020, the Lower Yellow River’s habitat quality was typically mediocre, with a steady declining trend. The majority of cities displayed a trend toward declining habitat quality. (2) Both the urbanization subsystem and the urbanization level in 34 cities have demonstrated a consistent growth tendency. The urbanization level is most affected by economic urbanization among the subsystems. (3) The coupling coordination degree have revealed an ongoing trend of growth. In most cities, the relationship between habitat quality and urbanization has been evolving toward coordination. The results of this study have some reference value for ameliorating the habitat quality of the Lower Yellow River and solving the coupling coordination relationship between habitat quality and urbanization.
The filled function method is an effective way to solve global optimization problems. However, its effectiveness is greatly affected by the selection of parameters, and the non-continuous or non-differentiable properties of the constructed filled function. To overcome the above-mentioned drawbacks, in this paper, a new parameterless filled function is proposed that is continuous and differentiable. Theoretical proofs have been made to show the properties of the proposed filled function. Based on the new filled function, a filled function algorithm is proposed to solve unconstrained global optimization problems. Experiments are carried out on widely used test problems and an application of supply chain problems with equality and inequality constraints. The numerical results show that the proposed filled function is effective.
