Search

Triangular γ -graphyne has a special carbon–carbon bonding arrangement, which results in outstanding electrical characteristics. It is a potential material for semiconductors and conductors in nanoelectronic devices. The number of vertices at a distance of 2 from a vertex is known as the connection number (CN) of that vertex. In this paper, we computed Zagreb-type indices based on connection numbers. In order to give us a better knowledge of the structural properties of molecules or networks, these indices are calculated. Following the computation of these indices, we investigated their use in computing entropy, providing important new information about the thermodynamic characteristics and complexity of the understudied systems. We used Python language to find the Pearson correlation coefficient between indices and entropy and show its heat map. [ABSTRACT FROM AUTHOR]

Evaluating the water resources spatial equilibrium (WRSE) is the foundation for scientifically planning the construction of an optimized water resource allocation system and achieving the high-standard development of the China Water Network Project. To elucidate the characteristics of WRSE variation in Ulanqab City, this study explored a novel WRSE assessment model based on connection number and the subtraction set pair potential method. The results indicate that: (1) there exists a mismatch between the distribution of water resources in Ulanqab City and its socio-economic development. In 2020, the Gini coefficients of water resources total quantity concerning resident population, gross domestic product (GDP), industrial output value, and irrigated land area were 0.48, 0.48, 0.51, and 0.28, respectively. (2) From 2011 to 2020, the overall WRSE level in Ulanqab City showed an increasing trend year by year. Among them, the WRSE levels in six counties improved, while Jining District consistently remained at a low equilibrium state due to the prominent contradiction between water supply and demand. (3) In the future, Ulanqab City can further enhance the WRSE level by promoting the reuse of recycled water, intensifying groundwater pollution control, and implementing a quota management system for agricultural water use. HIGHLIGHTS The distribution of water resources in Ulanqab City is in a state of mismatch with social and economic development.; From 2011 to 2020, the water resources spatial equilibrium levels of six counties in Ulanqab City improved, while there was no significant change in five counties.; The vulnerability indicators of Ulanqab City are per capita water resources and ecological environment water demand load.;

Asthma is a widespread disease that has affected more than 300 million people worldwide. There is no efficient or preventive treatment for this disease yet. Drug scientists are striving hard to discover a variety of medicines that can treat asthma effectively. Quantitative structure‐property relationship (QSPR) analysis of drugs used in the treatment of a specific disease through topological descriptors is one of the best techniques adopted by drug scientists to cut down unnecessary laboratory expenses. In this article, we have done a QSPR analysis to identify the best predictor for the six properties namely, boiling point, enthalpy, flash point, log P, molar volume, and molar refractivity of 19 different anti‐asthmatic drugs using a set of 16 distance‐based topological indices. Also, we compare our results with QSPR analysis done by using certain degree‐based indices for the chosen drugs and obtain new directions. [ABSTRACT FROM AUTHOR]

In order to evaluate regional water resource carrying capacity, the subtraction set pair analysis is adopted to calculate the connection number, and an evaluation model of the regional water resource carrying capacity based on quadratic subtraction set pair potential is established. The model is applied to assess the water resource carrying capacity of 16 cities in Anhui province, China, 2015. The results show that the water resource carrying capacity was sever throughout the province in 2015. Specifically, the carrying capacity in southern part of Anhui province was better than that in the northern part. The main factor of water resource carrying status varied in different cities. [ABSTRACT FROM AUTHOR]

The adjoint function of connection number has unique advantages in solving uncertainty problems of water resource complex systems, and has become an important frontier and research hotspot in the uncertainty research of water resource complex problems. However, in the rapid evolution of the adjoint function, some problems greatly limit the application of the adjoint function in the research of water resources. Therefore, based on bibliometric analysis, development, practical application issues, and prospects of the hot directions are analyzed. It is found that the development of the connection number of water resource set pair analysis can be divided into three stages: (1) relatively sluggish development before 2005, (2) a period of rapid advancement in adjoint function research spanning from 2005 to 2017, and (3) a subsequent surge post-2018. The introduction of the adjoint function of connection number promotes the continuous development of set pair analysis of water resources. Set pair potential and partial connection number are the crucial research directions of the adjoint function. Subtractive set pair potential has rapidly developed into a relatively independent and important trajectory. The research on connection entropy is comparatively less, which needs to be further strengthened, while that on adjacent connection number is even less. The adjoint function of set pair potential can be divided into three major categories: division set pair potential, exponential set pair potential, and subtraction set pair potential. The subtraction set pair potential, which retains the original dimension and quantity variation range of the connection number, is widely used in water resources and other fields. Coupled with the partial connection number, a series of new connection number adjoint functions have been developed. The partial connection number can be mainly divided into two categories: total partial connection number, and semi-partial connection number. Among these, the calculation expression and connotation of total partial connection numbers have not yet reached a consensus, accompanied by the slow development of high-order partial connection numbers. Semi-partial connection number can describe the mutual migration movement between different components of the connection number, which develops rapidly. With the limitations and current situation described above, promoting the exploration and application of the adjoint function of connection number in the field of water resources and other fields of complex systems has become the focus of future research. [ABSTRACT FROM AUTHOR]

Connection number-based molecular descriptors are one type of quantitative measure that provides insight into the connectivity of atoms and bonds within a molecule. The investigation of skin cancer treatments based on connection number-based molecular descriptors requires quantifying the structural features of these pharmaceuticals based on their atom and bond connections. By employing connection number-based descriptors, it is possible to understand the chemical structure and connectivity patterns of these drugs. In this article, we calculated a few connection number-based molecular descriptors for skin cancer drugs, particularly Cobimetinib, Picato, Vismodegib, Odomzo, Imiquimod, Vemurafenib, Daurismo, Trametinib, Fluorouracil, Dacarbazine, Dabrafenib, Encorafenib, and Binimeinib. To summarise, the practical implementation of the research findings presented in the paper allows Dermathera Pharmaceuticals to effectively address obstacles in the process of discovering and developing drugs for skin cancer. The organization enhances its workflow by including molecular descriptors based on connection numbers. This allows for improved chemical selection, accurate prediction of therapy results, and the development of more efficient and safer treatments for patients with skin cancer. This application highlights the concrete advantages of the research in practical pharmaceutical engineering environments.

Tripolar fuzzy sets offer a robust framework that integrates the aspects of intuitionistic fuzzy sets and bipolar fuzzy sets. Complex decision-making problems often involve multiple attributes with specific properties that reflect both negative and positive aspects. In such cases, intuitionistic fuzzy sets (IFS) and bipolar fuzzy sets (BFS) may be insufficient to handle these complexities that makes tripolar fuzzy sets an essential tool for identifying optimal solutions. In our study, we introduce a Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method using connection number of set pair analysis under the tripolar fuzzy environment. Initially, we express tripolar fuzzy number as a connection number, which is a pivotal concept in set pair analysis. We then extend the TOPSIS method based on the connection number of set pair analysis within the realm of tripolar fuzzy sets. By applying the proposed methodology, we provide the computational framework for the problem related to multi-criteria decision making. Moreover, we observe that our proposed technique also satisfies the existing test criterions. In this context, we conduct the comparative study of the newly established technique with the other ones existing in intuitionistic fuzzy and bipolar fuzzy environments. Finally, we show that our proposed technique is superior than the others.

The use of optoelectronic technology in Optical Transposition Interconnection Systems (OTIS) offers an effective solution to the ongoing problem of storing and sending data with comprehensive information. This is due to the reduced power requirements and broad bandwidth capabilities of optoelectronic systems, which make them well-suited for this task. The integration of radio communication and electrical technology has transformed OTIS into a highly valued network, enhancing the efficiency of existing optoelectronic computers. OTIS is characterized by the swapped network that is formed with the help of path graph $\mathfrak {P}_{m}$ and denoted as $B(\mathfrak {P}_{m})$ . This research work focused on certain topological invariants (TIs) about the number of connections between nodes of the graph $B(\mathfrak {P}_{m})$ and its largest subgraph that preserves twin nodes ( $M(B(\mathfrak {P}_{m}))$ ). First Zagreb connection index, geometric-arithmetic connection index, Randić connection index, reduced reciprocal Randić connection index, sum-connectivity connection index, first, second and third redefined Zagreb connection indices are considered in this work two types of biswapped and OTIS networks.

The assessment of seawater quality is a complex process as it involves the influence of several factors and is characterized by dynamic changes in these factors. Herein, a novel model coupled with the semi-partial subtraction set pair potential method (SSSPP) and game theory was discussed for the dynamic assessment of seawater quality. In the proposed model, the identity–discrepancy–contrary degrees were calculated to construct the evaluation matrix, and then the classification and the dynamic risk trends of the seawater quality were determined. A case study and comparison with the single-factor approach and Nemerow index evaluation method were carried out to confirm the accuracy and dependability of the suggested model. The results indicate that the proposed method can be used to measure trends in seawater quality evolution and also to diagnose key indicators affecting seawater quality. It provides a new and effective way to accurately identify the quality of seawater and its trends. [ABSTRACT FROM AUTHOR]

The progression of the 2D novel, metal trihalides MX3 has been learned in Dirac half-metallicity topological spintronic possessions because of their interest that are inherited magnetic processes reflected by 2D metal trihalides. Additionally, the effects of the orbital pair create a big relative spin. Furthermore, because of spin-orbital coupling joined with force and high bend temperature, 2D materials like Bil3 discover significant applications in room temperature radiation indicators bringing about an unfamiliar band gap.

To further quantitatively assess the water resources carrying capacity (WRCC) system and analyze and identify the regional water resources carrying state and the physical mechanism of the state change, WRCC and obstacle factor diagnosis were carried out. In this paper, we proposed the mobility matrix to determine the connection number components, considered the dynamic attributes of the difference degree coefficient, and calculated it using the semi-partial subtraction set pair potential and triangular fuzzy number, so as to construct the quantitative diagnosis method of regional WRCC obstacle factors based on the connection number and TOPSIS. The results applied to six cities in the Huaibei Plain showed that the WRCC fluctuated around grade 2 and was in a poor state, which was mainly due to the insufficient support force; the water resources carrying state of the six cities gradually improved from 2011 to 2018, but the state became worse in 2019, which was related to the low precipitation in that year, the reduction in water resources, and the high degree of water resource utilization. The WRCC of Fuyang and Huainan was worse than that of the other four cities; over the 9 years, the average grades of Fuyang and Huainan were 2.26 and 2.43, while those of Huainan, Bozhou, Suzhou, and Bengbu were 2.19, 2.12, 2.05, and 2.05, respectively. The key obstacles limiting the improvement in the WRCC of the Huaibei Plain were per capita water resources, annual water production modulus, per capita water supply, vegetation coverage ratio, utilization ratio of water resources, water consumption per 104 yuan value-added by industry, and population density. In time, the key obstacle factors in neighboring years generally tended to have similarity, and conversely appeared as a difference; in space, neighboring regions showed similarity and conversely presented as a difference. The results of this study can offer technical support and a decision-making basis for water resources management in the Huaibei Plain. The method constructed in this paper is extremely interpretive, easy to calculate, highly sensitive, and reliable in application results, which opens up a new perspective for the rational determination of the connection number and the difference degree coefficient and provides a new intelligent way to determine the state of a complex set pair system and its causal mechanism analysis and diagnosis of obstacle factors. [ABSTRACT FROM AUTHOR]

In order to enhance the reliability of drought risk assessment results, this study considered the migration and transformation process of the components of connection numbers at the micro-level, providing a more detailed characterization of the relationship between certainty and uncertainty within the continuous semi-partial subtraction set pair potential. The transfer information of partial same potential and partial reverse potential was corrected, and an evolutionary semi-partial subtraction was proposed. A regional drought risk assessment model was constructed based on the continuous evolutionary semi-partial subtraction set pair potential and applied to Jinan City. The results indicate that the modified values of continuous semi-partial subtraction set pair potential are consistent with the values of the five-element subtraction set pair potential concerning both the regional drought risk and the evaluation results of each subsystem in Jinan City. Compared with the five-element subtraction set, the continuous evolutionary semi-partial subtraction set has a slower change in the set pair potential, and the calculated subsystem has obvious differences in the set pair potential change trend of each index value set, which is convenient for identifying the disaster factors affecting the development trends of the subsystems. [ABSTRACT FROM AUTHOR]

The adjoint function of connection number has unique advantages in solving uncertainty problems of water resource complex systems, and has become an important frontier and research hotspot in the uncertainty research of water resource complex problems. However, in the rapid evolution of the adjoint function, some problems greatly limit the application of the adjoint function in the research of water resources. Therefore, based on bibliometric analysis, development, practical application issues, and prospects of the hot directions are analyzed. It is found that the development of the connection number of water resource set pair analysis can be divided into three stages: (1) relatively sluggish development before 2005, (2) a period of rapid advancement in adjoint function research spanning from 2005 to 2017, and (3) a subsequent surge post-2018. The introduction of the adjoint function of connection number promotes the continuous development of set pair analysis of water resources. Set pair potential and partial connection number are the crucial research directions of the adjoint function. Subtractive set pair potential has rapidly developed into a relatively independent and important trajectory. The research on connection entropy is comparatively less, which needs to be further strengthened, while that on adjacent connection number is even less. The adjoint function of set pair potential can be divided into three major categories: division set pair potential, exponential set pair potential, and subtraction set pair potential. The subtraction set pair potential, which retains the original dimension and quantity variation range of the connection number, is widely used in water resources and other fields. Coupled with the partial connection number, a series of new connection number adjoint functions have been developed. The partial connection number can be mainly divided into two categories: total partial connection number, and semi-partial connection number. Among these, the calculation expression and connotation of total partial connection numbers have not yet reached a consensus, accompanied by the slow development of high-order partial connection numbers. Semi-partial connection number can describe the mutual migration movement between different components of the connection number, which develops rapidly. With the limitations and current situation described above, promoting the exploration and application of the adjoint function of connection number in the field of water resources and other fields of complex systems has become the focus of future research.

The information diffusion model is widely used in natural disaster risk assessment because of its operationalization, low data requirements and clear significance of the evaluation results. However, the commonly used normal information diffusion model is based on an average distance assumption, and the diffusion widow with h is directly affected by sample size and extreme values, especially when the sample size is more than 11, which may lead to unstable results of normal diffusion, with typical uncertainty. Considering the influence of the whole samples on the diffusion points, incorporating the connection number method, a connection number structure-based information diffusion model was proposed, and also a relative connection number method is proposed to calculate the connection number, which was applied to the risk assessment of drought disasters in Jianghuai watershed area. The results show that the connection number structure-based information diffusion model reduces the direct influence of sample extremes and sample size, eliminates the constraint of the average distance assumption in the traditional model, and performs more consistently with increasing sample size for risk assessment. And the relative connection number method can contain the traditional connection number expression and offers a wider application. A study of drought risk in the Jianghuai watershed shows that the indices of agriculture drought-suffered, drought-affected and drought-damaged fluctuated greatly, but the trends were generally consistent with each other from 1990 to 2020. It is more likely to suffer from drought in the area, but the disaster rate after drought tends to decrease over time. With the increase in drought intensity, the disaster risk will decrease significantly compared to the drought risk. The connection number structure-based information diffusion model has no two-point proximity principle and the average distance assumption, with better stability in the disaster risk assessment for different samples size compared with the traditional model, which will have more extensive application in risk assessment.

The study of networks by using topological indices (TIs) have been significantly become a useful attention in the physicochemical properties of compounds, pharmacology and drug delivery in the field of experimental sciences. Thus, TIs help us to study the new networks and they also play an essential role in the study of the quantitative structure property and activity relationships. In this paper, we compute the connection number (CN) based Zagreb indices in the form of first general-Zagreb connection index (ZCI), generalized first, second, third and fourth ZCIs of two rhombus type networks such as rhombus oxide and rhombus silicate. In particularly, we also find the first, second, modified first, second, third and fourth ZCIs by using main results of the abovementioned general & generalized connection based Zagreb indices. In addition, a comparison between degree and CN based Zagreb indices is done with the help of their numerical values and graphical demonstration. [ABSTRACT FROM AUTHOR]

A multi-attribute decision-making method based on heterogeneous information and set pair analysis is proposed, considering the balance of the contradictions between information representation and information processing in the decision-making process. The method is applied to decision-making problems in which the attribute weights are completely unknown and the attribute values are characterized as heterogeneous information (including exact numbers, interval numbers, intuitionistic fuzzy numbers, interval intuitionistic fuzzy numbers, neutrosophic numbers, interval neutrosophic numbers, picture fuzzy numbers, and Pythagorean fuzzy numbers). First, various transformation methods for converting heterogeneous information into the connection numbers (CNs) of set pair analysis are introduced and defined, and the heterogeneous information is uniformly converted into CNs for ease of processing. Second, the attribute weights of the heterogeneous information are obtained using the information entropy of the CNs. Thereafter, the alternatives are ranked by the VIKOR method. Moreover, we use the method of setting a threshold for the compromise evaluation value, and the clustering method to group the alternatives to provide more auxiliary decision making. Finally, the feasibility and effectiveness of the proposed method are demonstrated by a typhoon disaster evaluation example, and the advantages of the proposed approach are emphasized by performing a multi-faceted comparative analysis with other methods. Among them, the time complexity of the proposed algorithm can be simplified as O m , which demonstrates an improvement on the simplified time complexity O m 2 of the two existing methods. Particularly in the context of big data, the advantages are apparent. [ABSTRACT FROM AUTHOR]

The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and handle situations more proficiently. Another related theory is the theory of set pair analysis (SPA), which considers both certainties and uncertainties as a cohesive system and represents them from three aspects: identity, discrepancy, and contrary. In this article, we explore the suitability of combining the IHFS and SPA theories in multi-attribute decision making (MADM) and present the hybrid model named intuitionistic hesitant fuzzy connection number set (IHCS). To facilitate the design of a novel MADM algorithm, we first develop several averaging and geometric aggregation operators on IHCS. Finally, we highlight the benefits of our proposed work, including a comparative examination of the recommended models with a few current models to demonstrate the practicality of an ideal decision in practice. Additionally, we provide a graphical interpretation of the devised attempt to exhibit the consistency and efficiency of our approach. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a novel fuzzy multi-criteria decision-making method based on an improved score function of connection numbers and Choquet integral under interval-valued Pythagorean fuzzy environment. To do so, we first introduce a method to convert interval-valued Pythagorean fuzzy numbers into connection numbers based on the set pair analysis theory. Then an improved score function of connection numbers is proposed to make the ranking order of connection numbers more in line with reality in multi-criteria decision-making process. In addition, some properties of the proposed score function of connection numbers and some examples have been given to illustrate the advantages of conversion method proposed in the paper. Then, considering interactions among different criteria, we propose a fuzzy multi-criteria decision-making approach based on set pair analysis and Choquet integral under interval-valued Pythagorean fuzzy environment. Finally, a case of online learning satisfaction survey and a brief comparative analysis with other existing approaches are studied to show that the proposed method is simple,convenient and easy to implement. Comparing with previous studies, the method in this paper, from a new perspective, effectively deals with multi-criteria decision-making problems that the alternatives cannot be reasonably ranked in the decision-making process under interval-valued Pythagorean fuzzy environment.

Currently, the implementation of water resource spatial equilibrium strategy is a fundamental policy of water resource integrated management in China; it is also a considerable challenge to explore the relationship structure features of water resources, society, economy and ecological environment (WSEE) complex system. For this purpose, firstly, we applied information entropy, ordered degree and connection number coupling method to reveal the membership characteristics between different evaluation indicators and grade criterion. Secondly, the system dynamics approach was introduced to describe the relationship features among different equilibrium subsystems. Finally, the ordered degree, connection number, information entropy and system dynamics integrated model was established to conduct relationship structure simulation and evolution trend evaluation of the WSEE system. The application results in Hefei city, Anhui Province, China, demonstrated that: (1) the variation of overall equilibrium conditions of WSEE system in Hefei city, 2020–2029 was higher compared to that of 2010–2019, though the increasing rate of ordered degree and connection number entropy (ODCNE) became slower after 2019; and (2) the annual ODCNE value from 2020 to 2029 of WSEE system under dry year scenarios increased about 0.0812, which indicated that the construction of Yangtze-Huaihe Diversion (YHD) project could play significant positive role in mitigating the equilibrium situation of WSEE system in Hefei city in the future. On the whole, this study is capable of providing the guidance basis for constructing a theoretical framework of structure simulation and equilibrium evaluation analysis of WSEE complex system. [ABSTRACT FROM AUTHOR]

This paper proposes a novel fuzzy multi-criteria decision-making method based on an improved score function of connection numbers and Choquet integral under interval-valued Pythagorean fuzzy environment. To do so, we first introduce a method to convert interval-valued Pythagorean fuzzy numbers into connection numbers based on the set pair analysis theory. Then an improved score function of connection numbers is proposed to make the ranking order of connection numbers more in line with reality in multi-criteria decision-making process. In addition, some properties of the proposed score function of connection numbers and some examples have been given to illustrate the advantages of conversion method proposed in the paper. Then, considering interactions among different criteria, we propose a fuzzy multi-criteria decision-making approach based on set pair analysis and Choquet integral under interval-valued Pythagorean fuzzy environment. Finally, a case of online learning satisfaction survey and a brief comparative analysis with other existing approaches are studied to show that the proposed method is simple,convenient and easy to implement. Comparing with previous studies, the method in this paper, from a new perspective, effectively deals with multi-criteria decision-making problems that the alternatives cannot be reasonably ranked in the decision-making process under interval-valued Pythagorean fuzzy environment. [ABSTRACT FROM AUTHOR]

In the modern era, mathematical modeling consisting of graph theoretic parameters or invariants applied to solve the problems existing in various disciplines of physical sciences like computer sciences, physics, and chemistry. Topological indices (TIs) are one of the graph invariants which are frequently used to identify the different physicochemical and structural properties of molecular graphs. Wiener index is the first distance-based TI that is used to compute the boiling points of the paraffine. For a graph F, the recently developed Gutman Connection (GC) index is defined on all the unordered pairs of vertices as the sum of the multiplications of the connection numbers and the distance between them. In this note, the G C index of the operation-based symmetric networks called by first derived graph D 1 (F) (subdivision graph), second derived graph D 2 (F) (vertex-semitotal graph), third derived graph D 3 (F) (edge-semitotal graph) and fourth derived graph D 4 (F) (total graph) are computed in their general expressions consisting of various TIs of the parent graph F, where these operation-based symmetric graphs are obtained by applying the operations of subdivision, vertex semitotal, edge semitotal and the total on the graph F respectively. [ABSTRACT FROM AUTHOR]

In order to quantitatively evaluate and analyze regional water resources carrying capacity (WRCC) and to describe the micro motion between connection number components, a more applicable evaluation model was sought. Firstly, an evaluation index system and grade standards for a regional WRCC were constructed. Then, a method for determining the connection number was proposed, which considered the micro motion between the connection number components in the system structure. Finally, an evaluation model based on set pair analysis (SPA) and partial connection number (PCN) that used subtraction set pair potential (SPP) to identify vulnerability factors was built, and identification results were compared with the total partial connection number (TPCN). The model was applied to Huaibei City, Anhui Province, China. The results showed that: the WRCC grade value was between 2 and 3 which was poor; the support and regulation subsystem grade value was between 2 and 3, and the pressure subsystem grade value was between 1 and 2. SPP identified that the support force and regulation force subsystem were the vulnerable subsystems. Eight indexes, including water resources per capita, rate of ecological water consumption and density of population, were the main indicators causing the poor WRCC, which were in good agreement with the local measured data. In addition, the SPP and TPCN were compared to further verify rationality of the connection number determination method and reliability of the identification results. The model established in this paper has strong applicability and can also be used for the dynamic evaluation of other resources, including the environment and ecological carrying capacity. The results in this study provide a scientific basis for water resources management and decision-making. HIGHLIGHTS Based on partial connection number, a method for calculating the connection number of a regional water resources carrying capacity (WRCC) evaluation sample was proposed.; A dynamic evaluation model of a regional WRCC was constructed based on set pair analysis and partial connection number.; Reasons for poor WRCC in Huaibei City, China are identified and results compared with local measured data.;

To further quantitatively assess the water resources carrying capacity (WRCC) system and analyze and identify the regional water resources carrying state and the physical mechanism of the state change, WRCC and obstacle factor diagnosis were carried out. In this paper, we proposed the mobility matrix to determine the connection number components, considered the dynamic attributes of the difference degree coefficient, and calculated it using the semi-partial subtraction set pair potential and triangular fuzzy number, so as to construct the quantitative diagnosis method of regional WRCC obstacle factors based on the connection number and TOPSIS. The results applied to six cities in the Huaibei Plain showed that the WRCC fluctuated around grade 2 and was in a poor state, which was mainly due to the insufficient support force; the water resources carrying state of the six cities gradually improved from 2011 to 2018, but the state became worse in 2019, which was related to the low precipitation in that year, the reduction in water resources, and the high degree of water resource utilization. The WRCC of Fuyang and Huainan was worse than that of the other four cities; over the 9 years, the average grades of Fuyang and Huainan were 2.26 and 2.43, while those of Huainan, Bozhou, Suzhou, and Bengbu were 2.19, 2.12, 2.05, and 2.05, respectively. The key obstacles limiting the improvement in the WRCC of the Huaibei Plain were per capita water resources, annual water production modulus, per capita water supply, vegetation coverage ratio, utilization ratio of water resources, water consumption per 104 yuan value-added by industry, and population density. In time, the key obstacle factors in neighboring years generally tended to have similarity, and conversely appeared as a difference; in space, neighboring regions showed similarity and conversely presented as a difference. The results of this study can offer technical support and a decision-making basis for water resources management in the Huaibei Plain. The method constructed in this paper is extremely interpretive, easy to calculate, highly sensitive, and reliable in application results, which opens up a new perspective for the rational determination of the connection number and the difference degree coefficient and provides a new intelligent way to determine the state of a complex set pair system and its causal mechanism analysis and diagnosis of obstacle factors.

Topological indices (TIs) are functional tools which correlate with a computational value through a undirected, finite and simple networks. Many physicochemical properties and chemical reactions are studied with the help of these TIs. Recently, they are commonly used in the behavior of quantitative structures activity as well as property relationships. In 1972, connection number based TIs are studied by Gutman and Trinajstić to calculate the entire $\pi $ -electron energy of the alternant hydrocarbons. Moreover, the data provided by the website https://www.moleculardescriptors.eu shows that the relations between Zagreb indices and connection based indices that provide the better absolute values of the correlation coefficients for the thirteen physicochemical properties of the octane isomers. In this paper, we discuss the two invariants which are modified indices and modified coindices based on connection number of the resultant networks obtained by the different operations of product such as lexicographic and corona. For the molecular networks such as fence, closed fence, alkene and cycloalkane are depicted in the consequences of the obtained results. The comparisons between two invariants of the aforemention molecular networks are also presented through tables and graphical depictions. In addition, the uses and significance related to product of networks are also included.

【Background】 In previous work, we studied the results of the first-order partial connection coefficient and the subtraction set pair potential of the connection number, where we considered the directionality of the difference coefficient i in the partial positive connection number and the partial negative connection number. 【Objective】 The aim of this paper is to clarify the definition of the total partial coupling coefficient of the five element effect, determine its expression formula, describe its physical connotation, and evaluate its practical application in solving real water problems. 【Method】 This paper uses the method of analogy analysis to determine the calculation formula of the total partial coefficient of the five element effect by analyzing the existing results of the total partial coefficient of the three element effect, and further explains the physical connotation of the total partial coefficient of the five element effect with the help of the area of the trend curve of the partial coefficient, and applies it to the actual analysis of water problems. 【Result】 ①the results of the dynamic evaluation of water resources carrying capacity in Sichuan Province are highly consistent with the results of the full deflection coefficient of five element effect, and the full deflection coefficient of five element effect has the advantages of clearer development trend of the evaluation object, simpler calculation process, more reasonable evaluation results and more consistent with the physical connotation of the deflection coefficient; ②The diagnostic results of the five element effect partial coefficient on the vulnerability index of agricultural drought are consistent with the actual situation. The four indicators have great intraannual changes, and the impact on the comprehensive assessment results of drought vulnerability is more obvious. 【Conclusion】 The proposal of the five element effect total partial coupling coefficient expands the research scope of the effect total partial coupling coefficient, and the application in different cases has drawn more reasonable and credible calculation results, which has a great application prospect in solving similar problems in natural risk research.

To promote the application of entropy concepts in uncertainty analysis of water resources complex system, a quantitative evaluation and obstacle factor diagnosis model of agricultural drought disaster risk was proposed using connection number and information entropy. The results applied to Suzhou City showed that the agricultural drought disaster risks in Suzhou during 2007–2017 were all in middle-risk status, while it presented a decreasing trend from 2010. The information entropy values of the difference degree item bI were markedly lower than those of the difference degree b, indicating that bI provided more information in the evaluation process. Furthermore, the status of drought damage sensitivity and drought hazard were improved significantly. Nevertheless, high exposure to drought and weak drought resistance capacity seriously impeded the reduction of risk. Thus, the key to decreasing risk was to maintain the level of damage sensitivity, while the difficulties were to reduce exposure and enhance resistance. In addition, the percentage of the agricultural population, population density, and percentage of effective irrigation area were the main obstacle factors of risk and also the key points of risk control in Suzhou. In short, the results suggest that the evaluation and diagnosis method is effective and conducive to regional drought disaster risk management. [ABSTRACT FROM AUTHOR]

【Background and Objective】 Carrying capacity of water resources is an important parameter to measure sustainability in regional water resources use, and objectively evaluating its variation and vulnerability can improve water resources management. The purpose of this paper is to evaluate the dynamic carrying capacity of regional water resource, identify and diagnose its vulnerability. 【Method】 Considering significance of the components of five-variable connection numbers and the difference in influence degree of the set on the system situation, and referring to the universal gravitation and damping, a five-variable gravitation subtraction set pair potential model based on the connection numbers was constructed. The model was then applied to evaluate the dynamic water resources carrying capacity in Sichuan and Heilongjiang provinces, and the results were compared with the existing five-variable subtractive set pair potential. 【Result】 Overall, the bearing capacity of water resources in Sichuan province has seen improvement good. Based on the impact of the subsystems, their evaluation index was ranked in the order of ecological environment > social economic> water resource. Subsystems that were persistently potential or partial against-potential are vulnerable, and vigilance over them is thus required. In general, water bearing capacity in Heilongjiang is good, in which “rain” “service industry” are potential of “water production capacity”, while “population density”, “primary industry” are inverse potential. The five-variable gravity subtraction set of potential discrimination system set pair potential value and situational and five-variable subtraction set pair potential calculation results are basically identical, and on the diagnosis, identify vulnerability subsystem and index is more sensitive and effective. 【Conclusion】 Analysis of water resources carrying capacity evaluation, five-variable gravity subtraction sets for system development and diagnosis, identify the potential vulnerability subsystem and the index of the rationality and applicability of the constructed gravity subtraction of set pair potential of five-variable more conform to the calculation results and the actual physical meaning, and simple calculation, strong explanatory. A new set-to-potential method is provided for analyzing dynamically and evaluating the multi-level set pair system.

Connection number-based molecular descriptors are one type of quantitative measure that provides insight into the connectivity of atoms and bonds within a molecule. The investigation of skin cancer treatments based on connection number-based molecular descriptors requires quantifying the structural features of these pharmaceuticals based on their atom and bond connections. By employing connection number-based descriptors, it is possible to understand the chemical structure and connectivity patterns of these drugs. In this article, we calculated a few connection number-based molecular descriptors for skin cancer drugs, particularly Cobimetinib, Picato, Vismodegib, Odomzo, Imiquimod, Vemurafenib, Daurismo, Trametinib, Fluorouracil, Dacarbazine, Dabrafenib, Encorafenib, and Binimeinib. To summarise, the practical implementation of the research findings presented in the paper allows Dermathera Pharmaceuticals to effectively address obstacles in the process of discovering and developing drugs for skin cancer. The organization enhances its workflow by including molecular descriptors based on connection numbers. This allows for improved chemical selection, accurate prediction of therapy results, and the development of more efficient and safer treatments for patients with skin cancer. This application highlights the concrete advantages of the research in practical pharmaceutical engineering environments. [ABSTRACT FROM AUTHOR]

The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and handle situations more proficiently. Another related theory is the theory of set pair analysis (SPA), which considers both certainties and uncertainties as a cohesive system and represents them from three aspects: identity, discrepancy, and contrary. In this article, we explore the suitability of combining the IHFS and SPA theories in multi-attribute decision making (MADM) and present the hybrid model named intuitionistic hesitant fuzzy connection number set (IHCS). To facilitate the design of a novel MADM algorithm, we first develop several averaging and geometric aggregation operators on IHCS. Finally, we highlight the benefits of our proposed work, including a comparative examination of the recommended models with a few current models to demonstrate the practicality of an ideal decision in practice. Additionally, we provide a graphical interpretation of the devised attempt to exhibit the consistency and efficiency of our approach.

A benzenoid is a class of chemical compounds with at least one benzene ring(hexagon as a graph) and resonance bonds in the benzene ring give increased stability in benzenoids. A finite connected subgraph of the infinite hexagonal lattice without cut vertices or non-hexagonal interior faces is said to be a benzenoid system (or a hexagonal system) and these systems are geometric figures. Benzenoid systems are widely used because they are the representations of the skeletons (focussing on the structure induced by the carbon atoms) of molecules of benzenoid hydrocarbons. The first and second Zagreb indices are among the most studied topological indices. We now consider analogous graph invariants, based on the second degrees of vertices, called Zagreb connection indices. The main objective of this paper is to compute these connection indices for six benzenoid systems(three catacondensed and three pericondensed systems). In the end, an application of the obtained results for these indices of some classes of benzenoid systems is also included. Mainly, a comparison among the Zagreb connection indices of some benzenoid systems is performed with the help of numerical tables and 3 D plots. [ABSTRACT FROM AUTHOR]

In order to effectively deal with the uncertainty between evaluation samples and evaluation criteria, and quantitatively identify the water resources carrying capacity (WRCC) and its obstacle factors in the Yellow River irrigation district, a calculation method of dynamic difference degree coefficient varying with evaluation sample was proposed, and then an evaluation and diagnosis model of WRCC was established. The results applied to the Dagong irrigation district showed that the overall WRCC of five counties in the irrigation district were improved from 2010 to 2017, especially since 2013. The improvement magnitudes of Changyuan County, Fengqiu County, and Hua County were significantly higher than those of Xun County and Neihuang County. In 2017, Fengqiu County, Changyuan County, Hua County, Xun County, and Neihuang County were in water resources critical overloaded status, and the connection number values were 0.231, 0.163, 0.120, −0.293, and −0.331, respectively, which is consistent with the fact that their distances become farther from the main stream of the Yellow River. In addition, the utilization ratio of water resources, available water resources amount per capita, GDP per capita, and water deficient ratio in each county belonged to the middle or strong obstacle index over a long period of time. They were the crucial obstacle factors of WRCC in the Dagong irrigation district, as well as the core and difficult points of water resources management. In some counties, the effective irrigation area ratio, effective utilization coefficient of irrigation water, and water consumption ratio of the ecological environment gradually developed from strong obstacle to weak or strong promotion index. These were important reasons for the improvement of their carrying situation, reflecting their control of agricultural and ecological water consumption. In short, the results of the case study suggest that the model established in this study is conducive to the identification of water resources’ carrying status and its key obstacle factors in the Yellow River irrigation district, and can be applied to the evaluation and regulation of resources and environment carrying capacity.

The quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) between the chemical compounds are studied with the help of topological indices (TI’s) which are the fixed real numbers directly linked with the molecular graphs. Gutman and Trinajstic (1972) defined the first degree based TI to measure the total π-electrone energy of a molecular graph. Recently, Ali and Trinajstic (2018) restudied the connection based TI’s such as first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index to find entropy and accentric factor of the octane isomers. In this paper, we study the modified second Zagreb connection index and modified third Zagreb connection index on the T-sum (molecular) graphs obtained by the operations of subdivision and product on two graphs. At the end, as the applications of the obtained results for the modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes are also included. Mainly, a comparision among the Zagreb indices, Zagreb connection indices and modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes is performed with the help of numerical tables, 3D plots and line graphs using the statistical tools.

Dual hesitant fuzzy sets (DHFSs) is the refinement and extension of hesitant fuzzy sets and encompasses fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as a special case. DHFSs have two parts, that is, the membership function and the non-membership function, in which each function is defined by two sets of some feasible values. Therefore, according to the practical demand, DHFSs are more adjustable than the existing ones and provide the information regarding different objects in much better way. The set pair analysis (SPA) illustrates unsureness in three angles, called “identity”, “discrepancy” and “contrary”, and the connection number (CN) is one of its main features. In the present article, the axiom definition of distance measure between DHFSs and CN is introduced. The distance measures are established on the basis of Hamming distance, Hausdorff distance and Euclidean distance. The previous identities and relationship between them are discussed in detail. On the basis of the geometric distance model, the set-theoretic approach, and the matching functions several novel distance formulas of CN are introduced. The novel distance formulas are then applied to multiple-attribute decision making for dual hesitant fuzzy environments. Finally, to demonstrate the validity of the introduced measures, a practical example of decision-making is presented. The benefits of the new measures over the past measures are additionally talked about.

Currently, the implementation of water resource spatial equilibrium strategy is a fundamental policy of water resource integrated management in China; it is also a considerable challenge to explore the relationship structure features of water resources, society, economy and ecological environment (WSEE) complex system. For this purpose, firstly, we applied information entropy, ordered degree and connection number coupling method to reveal the membership characteristics between different evaluation indicators and grade criterion. Secondly, the system dynamics approach was introduced to describe the relationship features among different equilibrium subsystems. Finally, the ordered degree, connection number, information entropy and system dynamics integrated model was established to conduct relationship structure simulation and evolution trend evaluation of the WSEE system. The application results in Hefei city, Anhui Province, China, demonstrated that: (1) the variation of overall equilibrium conditions of WSEE system in Hefei city, 2020–2029 was higher compared to that of 2010–2019, though the increasing rate of ordered degree and connection number entropy (ODCNE) became slower after 2019; and (2) the annual ODCNE value from 2020 to 2029 of WSEE system under dry year scenarios increased about 0.0812, which indicated that the construction of Yangtze-Huaihe Diversion (YHD) project could play significant positive role in mitigating the equilibrium situation of WSEE system in Hefei city in the future. On the whole, this study is capable of providing the guidance basis for constructing a theoretical framework of structure simulation and equilibrium evaluation analysis of WSEE complex system.

In the modern era, mathematical modeling consisting of graph theoretic parameters or invariants applied to solve the problems existing in various disciplines of physical sciences like computer sciences, physics, and chemistry. Topological indices (TIs) are one of the graph invariants which are frequently used to identify the different physicochemical and structural properties of molecular graphs. Wiener index is the first distance-based TI that is used to compute the boiling points of the paraffine. For a graph F, the recently developed Gutman Connection (GC) index is defined on all the unordered pairs of vertices as the sum of the multiplications of the connection numbers and the distance between them. In this note, the GC index of the operation-based symmetric networks called by first derived graph D1(F) (subdivision graph), second derived graph D2(F) (vertex-semitotal graph), third derived graph D3(F) (edge-semitotal graph) and fourth derived graph D4(F) (total graph) are computed in their general expressions consisting of various TIs of the parent graph F, where these operation-based symmetric graphs are obtained by applying the operations of subdivision, vertex semitotal, edge semitotal and the total on the graph F respectively.

In order to manage and control the subsidence risk of shield tunnel under-passing existing railway comprehensively, and to guarantee the shield construction and the railway train operation safety, according to the construction characteristics of the shield tunneling, the cause of settlement and related construction parameters, by risk identification, 13 secondary evaluation indexes were extracted, creating a structural model for the risk assessment of shield tunnel under-passing existing railway based on set pair analysis (SPA); decision table of rough set (RS) was used to objectively weight each evaluation index to optimize the model; the SPA-RS five-element connection number model was used to realize the risk evaluation of the shield tunnel under-crossing the railway, determine the risk level, and carry out analysis in combination with the project practical case. The research results show that the risk assessment level of a subway shield tunnel under-passing existing railway based on SPA-RS was level II (low risk), which was consistent with the actual situation. [ABSTRACT FROM AUTHOR]

In order to quantitatively evaluate the spatial equilibrium degree of water resources and analyze the distribution characteristics of spatial equilibrium of water resources, aiming at the problem that Gini coefficient can't evaluate the sub regional equilibrium alone, this paper proposed a water resources spatial equilibrium evaluation model combining Gini coefficient and connection number. Based on the Gini coefficient calculated by Lorentz curve, the membership degree of the study area belonging to three different spatial equilibrium levels of equilibrium, critical equilibrium and imbalance was calculated by connection number through hierarchical zoning, and then the vulnerability sub area was diagnosed and identified in combination with subtraction set pair potential. The model was applied to the spatial balance evaluation of water resources in Anhui Province, and the differences between population and water resources, GDP and water resources in 16 prefecture level cities were analyzed respectively. The results show that the Gini coefficient of population, GDP and water resources in Anhui Province from 2011 to 2018 is 0.4 higher than the international warning line, which has been in a relatively unbalanced and unbalanced state for a long time. The spatial balance of water resources gradually deteriorates from south to north. In 2018, the vulnerable areas of spatial balance of water resources in Anhui Province including Hefei, Huaibei, Bozhou, Suzhou, Bengbu, Fuyang, Huainan, Ma'anshan, Wuhu and Tongling, which should be the main control objects of spatial balance of water resources. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Irrigation & Drainage is the property of Journal of Irrigation & Drainage Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To promote the application of entropy concepts in uncertainty analysis of water resources complex system, a quantitative evaluation and obstacle factor diagnosis model of agricultural drought disaster risk was proposed using connection number and information entropy. The results applied to Suzhou City showed that the agricultural drought disaster risks in Suzhou during 2007–2017 were all in middle-risk status, while it presented a decreasing trend from 2010. The information entropy values of the difference degree item bI were markedly lower than those of the difference degree b, indicating that bI provided more information in the evaluation process. Furthermore, the status of drought damage sensitivity and drought hazard were improved significantly. Nevertheless, high exposure to drought and weak drought resistance capacity seriously impeded the reduction of risk. Thus, the key to decreasing risk was to maintain the level of damage sensitivity, while the difficulties were to reduce exposure and enhance resistance. In addition, the percentage of the agricultural population, population density, and percentage of effective irrigation area were the main obstacle factors of risk and also the key points of risk control in Suzhou. In short, the results suggest that the evaluation and diagnosis method is effective and conducive to regional drought disaster risk management.

Copyright of Advanced Engineering Science / Gongcheng Kexue Yu Jishu is the property of Advanced Engineering Science Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Regular plane tessellations can easily be constructed by repeating regular polygons. This design is of extreme importance for direct interconnection networks as it yields high overall performance. The honeycomb and the hexagonal networks are two such popular mesh-derived parallel networks. The first and second Zagreb indices are among the most studied topological indices. We now consider analogous graph invariants, based on the second degrees of vertices, called Zagreb connection indices. The main objective of this paper is to compute these connection indices for the Hex, Hex derived and some honeycomb networks. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give a multi-attribute decision-making (MADM) method for the interval-valued intuitionistic fuzzy (IVIF) set using the set pair analysis (SPA) theory. IVIF set can express the uncertain information in a more valuable manner, while the connection number (CN) based on the "identity," "discrepancy" and "contrary" degrees of the SPA theory handles the uncertainties and certainties systems. Based on these features, in this paper, we develop a new possibility degree measure based on the CNs to rank the different IVIF numbers. The properties and advantages of the measure are described in details. Later on, we present a novel MADM method and illustrate with several examples to validate it. A comparative as well as superiority analysis is performed to show the feasibility and validity of the approach. [ABSTRACT FROM AUTHOR]

A topological index (TI) is a function from Σ to the set of real numbers, where Σ is the set of finite simple graphs. In fact, it is a final outcome of a logical, systematical and mathematical process that transforms feature encoded in a molecular graph to a fixed real number. Gutman and Trinajstic (1972) first time defined degree based TI named as first Zagreb index to compute the total ?-electron energy of a molecular graph. They also exposed another TI that is renamed as modified first Zagreb connection index in [Ali and Trinajstic; Mol: Inform: 37(2018); 1 - 7]: In this paper, we compute the upper bounds for the Zagreb connection indices i.e. first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index of the resultant graphs which are obtained by applying the tensor and strong product of two graphs. [ABSTRACT FROM AUTHOR]

The objective of the presented paper is to develop a multiattribute decision-making (MADM) method under the intuitionistic fuzzy set (IFS) environment using the set pair analysis (SPA) theory. IFS can express the uncertain information in terms of membership grades, while the connection number (CN) based on the "identity," "discrepancy" and "contrary" degrees of the SPA theory handles the uncertainties and certainties systems. Meanwhile, capturing the relationship between the values during the aggregation is a prominent advantage of the power aggregation operator. Motivated by these primary characteristics, in this paper, we develop some power geometric aggregation operators namely for aggregating the CNs, namely, CN power geometric, CN weighted power geometric and CN ordered weighted power geometric operators. A few properties like idempotency, commutativity and boundedness are established to show the viability and legitimacy of developed operators. Afterward, we develop a decision-making (DM) approach based on the proposed operators for tackling the MADM issues under the intuitionistic fuzzy numbers environment. Finally, real-life case of MADM problem has been discussed to manifest the developed DM approach, and obtained results are compared with the results that are obtained by the existing DM methods for showing the feasibility and validity of the developed DM approach. [ABSTRACT FROM AUTHOR]

• A novel cloud model coupled with connection numbers theory is presented. • Fuzziness and randomness of multiple indexes in finite intervals are discussed. • Proposed model quantitatively expresses the certainty and uncertainty as a whole. • Overcome the shortcoming that indicators must obey normal distribution. Stability evaluation of a slope involves various fuzzy and correlation indicators randomly distributed in finite intervals. A novel multi-dimensional connection cloud model was presented here to address multiple uncertainties and distribution characteristics of indicators, and to depict the randomness and fuzziness of the measured index value belonging to the classification standard in the slope stability analysis. In the model, when simulating fuzzy and random characteristics of evaluation indicators in finite intervals, the numerical characteristics of connection cloud model were assigned on the basis of the analysis of identical-discrepancy-contrary (IDC) relationships between measured indicators and the classification standard to overcome the subjectivity. Considering the effect of indicator correlation in a unified way, the integrated connection degree of a grade was further specified for the evaluation sample. Moreover, case studies and comparisons of the proposed model with one-dimensional normal cloud model, extension model, and support vector machine (SVM) were performed to confirm the validity and reliability. The results indicate that this model employed to evaluate slope stability can clearly depict the random and fuzzy distribution features of measured data in finite intervals, and its calculation process is quicker and simpler than that of one-dimensional normal cloud model. [ABSTRACT FROM AUTHOR]

The evaluation of heavy-metals pollution in soil involves with various uncertainty factors. Although the normal cloud model provides an idea for dealing with the randomness and fuzziness of indicators for the evaluation of heavy-metals pollution in soil, it distorts data fusion and cannot simulate the distribution state of evaluation indicators in a finite interval. Herein, a novel cloud model coupled with connection numbers and Dempster–Shafer evidence theory was discussed to remedy the defects of the normal cloud model. In the model proposed here, the connection cloud model was first presented to simulate the classification standard for each evaluation indicator. Then, the connection degree was calculated to construct the evaluation matrix, and the corresponding basic belief assignment matrix was obtained on the basis of the Dempster–Shafer evidence theory. Next, combining together with the combination weights gained by a distance function and the consistency between the differences in the static and dynamic weights and their coefficients, the classification of heavy-metals pollution in soil was determined according to the mean evidence value. Finally, the case study and comparisons with the fuzzy mathematical method, the extension method, the risk index method and the improved grey clustering method were conducted, respectively, to confirm the validity and reliability of the proposed model. Results show that this novel model can overcome the shortcomings of the normal cloud model and provide a method for comprehensive evaluation of heavy-metals pollution in soil. [ABSTRACT FROM AUTHOR]