Neutrosophic theory can effectively and reasonably express indeterminate, inconsistent, and incomplete information. Since Smarandache proposed the neutrosophic theory in 1998, neutrosophic theory and related research have been developed and applied to many important fields. Indeterminacy and fuzziness are one of the main research issues in the field of civil engineering. Therefore, the neutrosophic theory is very suitable for modeling and applications of civil engineering fields. This review paper mainly describes the recent developments and applications of neutrosophic theory in four important research areas of civil engineering: the neutrosophic decision-making theory and applied methods, the neutrosophic evaluation methods and applications of slope stability, the neutrosophic expressions and analyses of rock joint roughness coefficient, and the neutrosophic structural optimization methods and applications. In terms of these research achievements in the four areas of civil engineering, the neutrosophic theory demonstrates its advantages in dealing with the indeterminate and inconsistent issues in civil engineering and the effectiveness and practicability of existing applied methods. In the future work, the existing research results will be further improved and extended in civil engineering problems. In addition, the neutrosophic theory will also have better application prospects in other fields of civil engineering.

The neutrosophic theory was first proposed by Smarandache [

With the development of current engineering science and technology, the complexity, difficulty, and requirements of civil engineering continue to increase. To adapt to these changes and developments in civil engineering, the theoretical research of civil engineering must become more reasonable and scientific. In terms of the characteristics of civil engineering, traditional theoretical research methods are usually difficult to handle indeterminate and inconsistent problems in civil engineering. Although many theoretical studies of civil engineering have considered the uncertainty in actual engineering issues, most theories and methods are difficult to express the uncertain and inconsistent information contained in civil engineering. Therefore, as a theoretical tool that can effectively express indeterminate, incomplete, and inconsistent information, the neutrosophic theory will play a very crucial role in promoting the development of civil engineering theory and applied methods. Currently, neutrosophic sets, neutrosophic numbers, and neutrosophic possibility and statistics have been applied in rock mechanics and engineering management, gradually forming engineering neutrosophic theory and methods [

To review developments and applications of neutrosophic theory in civil engineering fields in recent years, the remainder of this review paper first describes the research achievements of engineering neutrosophic theory and applied methods in four main research areas of civil engineering: the neutrosophic decision-making theory and applied methods, the neutrosophic evaluation methods and applications of slope stability, the neutrosophic expressions and analyses of rock joint roughness coefficient, and the neutrosophic structural optimization methods and applications. Then, we perform a literature analysis of published papers in civil engineering. Finally, the research remarks and future research directions in the field of civil engineering are summarized.

Engineering management usually involves various stages of civil engineering projects and then contains various decision-making issues such as engineering contractors, construction design schemes, building materials, engineering maintenance works, and engineering site selection. With the development of civil engineering, decision-making issues in actual project management reflect complexity, vagueness, and indeterminacy, which require neutrosophic decision-making methods to solve them. Therefore, various studies centered on the neutrosophic theory have proved the advantages of describing and handling indeterminate and inconsistent information in actual decision-making problems. Thus, the neutrosophic theory has achieved many important results in the related research on dealing with decision-making problems.

Decision making is an inevitable and important research topic in the construction and management of engineering projects. Because of the complexity of current decision-making problems, they are often filled with uncertain and inconsistent information. It is particularly important to study how to describe and express this information. For this reason, Zadeh [^{–}0, 1^{+}[. Therefore, many scholars presented the improved neutrosophic theory used for engineering problems to solve complex decision-making problems. In actual engineering decision-making problems, various neutrosophic decision-making theories and methods for decision-making problems have become the research hotspots of civil engineering management.

Regarding complex decision-making problems, multi-attribute/criteria decision-making (MADM/MCDM) is one of the most important research topics. MADM/MCDM is a process of decision makers’ preference assessment of alternatives over multi-attributes and determines the best one among alternatives. In complex MADM problems, how to reasonably express and aggregate relevant information are two main issues that need to be solved. To describe incomplete, indeterminate, and inconsistent information in realistic decision-making problems, Smarandache [^{−}0, 1^{+}[. Thus, the neutrosophic set can better express incomplete, indeterminate, and inconsistent information, which fuzzy sets and (interval-valued) IFSs cannot do.

To facilitate science and engineering applications, Ye [

In construction projects, the choice of building materials is usually a MADM problem. The quality of building materials will affect the safety, economy, and reliability of construction projects. Since the quality of clay bricks is affected by various indicators, the MADM problem of clay bricks based on engineering neutrosophic theory is to choose a high-quality clay brick for construction projects in indeterminate and inconsistent situations.

The traditional method of selecting clay bricks is usually just some rough judgments, such as the color, size, and total cost of the clay bricks, but ignores many complex indeterminate factors/useful information regarding the quality of the clay bricks. Therefore, it is particularly important to establish a scientific decision-making method for the quality assessment of clay bricks. In recent years, some scholars have introduced decision-making methods for clay brick selection problems based on the neutrosophic theory. In 2015, Mondal et al. [

In engineering management, the decision making of engineering projects is a vital research topic. In the MADM problem of engineering projects, we usually consider factors such as functionality, economism, and safety as the main indices/attributes of the decision-making problem. Due to the complexity of decision-making problems, there are often the requirements of attributes and sub-attributes in assessment problems of construction projects, then they are considered by the weights of attributes and sub-attributes. To deal with such a decision-making problem, Chen et al. [

The aforementioned neutrosophic decision-making methods and applications of civil engineering management are shown in

Author | Neutrosophic information | MADM method | Application scenario |
---|---|---|---|

Mondal et al. [ |
SvNS | Neutrosophic grey relational analysis | Building materials selection |

Chen et al. [ |
NN | Neutrosophic projection model | Building materials selection |

Chen et al. [ |
RSNS | Weighted vector similarity measures | Construction project selection |

Solang et al. [ |
RSNS | Trigonometric function-based similarity measures | Construction project selection |

Gokasar et al. [ |
T2NN | Hybrid model including WASPAS and TOPSIS | Bridge maintenance project selection |

Deveci et al. [ |
T2NN | Integrated neutrosophic decision-making model | Engineering project location selection |

Bavia et al. [ |
SvNS | Neutrosophic hybrid score and accuracy function | Engineering project location selection |

Slope stability is an important research area of civil engineering, involving many engineering constructions such as rail transit, coal mining, and water conservancy projects. According to the composition of the slope, it can be divided into the soil slope and the rock slope. The slope is affected by various factors. Under the action of shear stress, unstable structural planes are produced. The final failure caused by slippage is the instability failure of the slope. Since most of the rock masses and soil masses in slope stability problems are natural rather than artificial, slope stability problems usually include greater randomness and indeterminacy. Hence, the neutrosophic theory is very suitable for slope stability analysis and assessment.

The damage to slopes usually causes serious consequences, such as road burial and construction damage to result in huge damage to the social economy and human safety. In order to avoid slope instability, the evaluation of slope stability is particularly important and necessary. Therefore, the study of slope stability analysis methods has already become an important topic in geotechnical engineering research. When analyzing and evaluating the stability of a slope, it is usually necessary to consider many influencing factors, such as mechanical properties, geological conditions, construction environment, slope geometric parameters, and human factors. Since there are too many factors to be considered during the analysis and evaluation process, it is impossible to accurately measure and judge many influencing factors in actual engineering problems. Therefore, the problem of slope stability is obviously indeterminate and complicated. The existing slope stability analysis methods can generally be divided into deterministic analysis methods and indeterminate analysis methods. The deterministic analysis methods mainly include the limit equilibrium analysis method [

In fact, the actual slope stability analysis contains a lot of random, discrete, and nonlinear information, so the information indeterminacy cannot be ignored. To make the analysis of slope stability more reasonable and effective, many indeterminate analysis methods, such as the fuzzy mathematical method [

In 2019, Zhou et al. [

Since NNs are used to effectively describe the indeterminacy factor in the assessment of slope stability, Li et al. [

The stability and reliability of the slope have a very significant impact on the safety and economics of open-pit mines. Therefore, ensuring the slope stability of the open-pit mine is a very critical research topic. Compared with other slopes, the open-pit mine slope has stronger indeterminacy and complexity. In addition to objective factors, various factors affecting slope stability will change as mining activity progress, and subjective perceptions and requirements of slope stability will also change over time. Therefore, some scholars regarded it as a kind of “dynamics” [

In view of the aforementioned neutrosophic evaluation methods and applications of slope stability,

Author | Neutrosophic information | Evaluation method | Application |
---|---|---|---|

Zhou et al. [ |
NN | Dice/cosine/exponential similarity measures | Slope stability evaluation |

Li et al. [ |
NN | Vector similarity measures | Slope stability evaluation |

Li et al. [ |
NN | Arctangent/tangent similarity measures | Slope stability evaluation |

Du et al. [ |
SNIS | Weighted aggregation operators of SNIEs | MADM of slope design schemes |

Qin et al. [ |
SvNN | SvNN-ANFIS and score function | Slope stability evaluation |

In addition, the related research of engineering neutrosophic theory has also promoted the development of other uncertainty analysis methods. For example, Wang et al. [

In rock mechanics, joints usually refer to cracks with no obvious relative displacement on both sides of the crack surface caused by rock cracks. It is obvious that rock joints are often one of the important factors affecting the safety and reliability of slopes. Since rock joints only touch the joint surfaces, their mechanical properties are quite different from those of complete rocks. For this reason, many scholars have conducted comprehensive research on many characteristics of rock joints. In actual engineering, the shear strength of rock joints is very important to evaluate the stability of engineering rock mass.

As shown in

In the natural environment, the JRC data of the rock joint surface that we can obtain are usually incomplete and uncertain. Therefore, it is very important to study the mechanical properties of the rock joint surface. Barton first discovered and proposed the scale effect of the JRC values in 1977 [

In order to study the scale effect and anisotropy of the JRC values, Tse et al. [_{2}) for the first time. On this basis, Zhang et al. [

First, Ye et al. [

Due to the complexity and uncertainty of the JRC value in the actual situation, it is usually impossible to give an accurate JRC value in an uncertain situation. Then, NN is composed of a certain part and an indeterminate part. Therefore, Yong et al. [

It is worth mentioning that the NN functions studied above are all fitting functions obtained by fitting the measured value curves. Although they have some fitting accuracy, they still lose 3% to 16% of useful information in the actual fitting process. In addition, the complexity of some fitting functions will also cause inconvenience in practical applications. To make up for the above defects, some scholars have introduced neutrosophic statistics into the uncertainty research of the JRC values. In classic statistical studies on JRC data [

In neutrosophic probability and statistics, Smarandache [

In general, the expression and analysis studies of JRC data are shown in

Authors | Neutrosophic tool | Method | Application |
---|---|---|---|

Ye et al. [ |
Neutrosophic function | Neutrosophic functions of JRC and shear strength | Predicting and estimating JRC values and shear strength |

Yong et al. [ |
NN and Neutrosophic function | Two NN functions |
Analyzing the scale effect and anisotropy of JRC values |

Ye et al. [ |
NN and Neutrosophic function | Two-variable neutrosophic function |
Analyzing the scale effect and anisotropy of JRC values |

Yong et al. [ |
NN and Neutrosophic function | Large-sized joint profile measurement method and NN function |
Analyzing the scale effect of JRC values |

Wang et al. [ |
NN and Neutrosophic function | Calculational method of JRC values based on NN functions and spectral analysis | Determining JRC values |

Chen et al. [ |
NN and Neutrosophic statistics | Neutrosophic statistical analysis of JRC-NNs | Analyzing the scale effect and anisotropy of JRC values |

Aslam [ |
NN and Neutrosophic statistics | NCV based on NEWMA NNs | Determining JRC values and analyzing the anisotropy of JRC values |

Aslam et al. [ |
NN and Neutrosophic statistics | The t-test and F-test under neutrosophic statistics | Analyzing the anisotropy of JRC values |

Chen et al. [ |
NN and Neutrosophic probability | NISN based on combining NN with the confidence degree of NIP | Analyzing the scale effect of JRC values |

Jiang et al. [ |
NN and Neutrosophic probability and statistics | Neutrosophic average value and standard deviation of NISN | Analyzing the scale effect and anisotropy of JRC values |

Song et al. [ |
NN and Neutrosophic probability and statistics | Generalized Dice similarity measures of NISNs | Analyzing the anisotropy of JRC values |

Practical problems in the civil engineering field usually include the information of inevitable uncertainty, incompleteness, and inconsistency. Then, the structural optimization design in structural engineering usually plays a very important role in improving the economy, safety, and applicability of the structure. To improve the structural optimization design, many structural optimization theories have been proposed, such as structural topology optimization [

To solve these indeterminate problems in structural optimization design, some scholars have applied engineering neutrosophic theory to structural optimization design. Jiang et al. [

To overcome the drawbacks of complex calculation and difficult solution in the existing NN optimization model [

It is obvious that the improved NN optimization method provides a new and effective way to optimize the truss structure under an indeterminate environment. However, researchers will continue to improve the existing NN optimization methods and extend them to more application fields in indeterminate environments.

Since SvNS contains the advantage of expressing degrees of truth, falsity, and indeterminacy, in addition to NN optimization methods, some scholars have also introduced SvNS into structural optimization design. Das et al. [

In addition, the SvNS optimization method has also been extended to the optimization design of welded beam structures. The optimal design of welded beam structures is often constrained by beam internal stresses, loads on rods, and beam deflections to optimize the durability and economy of welded beams. In this respect, Sarkar et al. used SvNS to express the constraints in the design of welded beams and proposed a single-objective nonlinear SvNS optimization method for welded beams [

Regarding the above neutrosophic optimization methods and applications in structural engineering, existing neutrosophic tools, methods, and applications are shown in

Authors | Neutrosophic tool | Method | Application |
---|---|---|---|

Jiang et al. [ |
NN and Neutrosophic function | General nonlinear NN optimization model | Double-bar truss structure optimization design |

Ye [ |
NN and Neutrosophic function | Improved nonlinear NN optimization model | Three-bar truss structure optimization design |

Das et al. [ |
SvNS and Neutrosophic function | SvNS optimization method for MONLPP | Riser optimization design |

Sarkar et al. [ |
SvNS and Neutrosophic function | SvNS optimization method for SONLPP | Double-bar truss structure optimization design |

Sarkar et al. [ |
SvNS and Neutrosophic function | SvNS optimization method for MONLPP | Three-bar truss structure optimization design |

Sarkar et al. [ |
NN and Neutrosophic function | GSvNN optimization method for MONLPP | Three-bar truss structure optimization design |

Sarkar et al. [ |
SvNS and Neutrosophic function | SvNS optimization method for SONLPP | Welded beam structure optimization design |

Sarkar et al. [ |
SvNS and Neutrosophic function | SvNS optimization method for MONLPP | Welded beam structure optimization design |

In the existing literature, 31 papers have been included in civil engineering, as shown in

Based on research results in the field of civil engineering, we counted the number of publications and researchers in different countries for all 31 papers. As shown in

Finally, we use VOSviewer to analyze the keyword distribution of 31 papers, and give a corresponding keyword density visualization graph in

Through the above analysis, we can find that “Neutrosophic number” and “Neutrosophic set” are the two keywords with the highest frequency and the largest item density in all 31 papers. To clearly and intuitively reflect the relationship between the two keywords and other keywords in the four research areas of civil engineering, we can make a keyword density visualization graph of “Neutrosophic number” related to the published research results in

This review paper mainly introduced the research results and applications of engineering neutrosophic theory and methods in four research areas of civil engineering: (1) the neutrosophic decision-making theory and applied methods, (2) the neutrosophic evaluation methods and applications of slope stability, (3) the neutrosophic expressions and analyses of rock joint roughness coefficient, and (4) the neutrosophic structural optimization methods and applications. They demonstrated the important achievements of engineering neutrosophic theory and methods in civil engineering in recent years.

Since most of the real problems involved in civil engineering usually imply indeterminate, incomplete, and inconsistent information, the neutrosophic theory has achieved significant research results in engineering problems. In addition to the civil engineering problems mentioned in this review paper, there are still many uncertain issues in civil engineering that have not been studied by engineering neutrosophic theory. Therefore, the engineering neutrosophic theory in civil engineering has a very broad range of applications, such as construction cost, construction organization and management, rock shear strength, precast concrete structure, etc.

Due to the significant advantages of the engineering neutrosophic theory in civil engineering, the research results based on the engineering neutrosophic theory in civil engineering have increased drastically in recent years. It is obvious that the neutrosophic theory can better solve various indeterminate problems in civil engineering. In future research directions, in addition to further improving the existing research results of civil engineering problems, it is also necessary to propose more advanced engineering neutrosophic theories and methods according to the applicable characteristics of civil engineering problems. With the development of other uncertain research methods in recent years, combining neutrosophic theory with other uncertain theories [

In general, the existing research results fully reflect the importance and necessity of neutrosophic theory in engineering, which not only effectively solves practical problems in the field of civil engineering, but also greatly promotes the development of neutrosophic theory itself.

_{2}emission based prioritization of bridge maintenance projects using neutrosophic fuzzy sets based decision making approach