A novel difference and derivative of linearly correlated fuzzy number-valued functions

In the present paper, the notion of the linearly correlated difference for linearly correlated fuzzy numbers is introduced. Especially, the linearly correlated difference and the generalized Hukuhara difference are coincident for interval numbers or even symmetric fuzzy numbers. Accordingly, an appropriate metric is induced by using the norm and the linearly correlated difference in the set of linearly correlated fuzzy numbers. Based on the symmetry of the basic fuzzy number, the linearly correlated derivative is proposed by the linearly correlated difference of linearly correlated fuzzy number-valued functions. In both non-symmetric and symmetric cases, the equivalent characterizations of the linearly correlated differentiability of a linearly correlated fuzzy number-valued function are established, respectively. Moreover, it is shown that the linearly correlated derivative is consistent with the generalized Hukuhara derivative for interval-valued functions.

Assessment of airside aerodrome infrastructure by SAW method with weights from Shannon's interval entropy

Multi-criteria decision support (MCDM) methods are widely used in many areas of science. This applies to economic, social and technical sciences. Implementing activities at the strategic, tactical or operational level requires appropriate tools to support decision-makers. The use of these tools requires the preparation of a decision model along with the formalization of the goal and the acquisition and preparation of data to make the decision accurate. Due to the wide application of MCDM in engineering practice, the article presents their application in air transport. It is an area that is constantly evolving, and all decisions at the strategic level have long-term effects and must be adequately justified. In the paper a compartmental extension of the classical SAW method with weights obtained using the compartmental Shannon entropy was proposed. This paper presents issues concerning the choice of airport layout and describes the problems that occur in determining the cost and capacity of airports. This paper reviews the literature on airport capacity and operations and airside air transport processes and the application of various multi-criteria decision support methods to airport problems. The main part of the article contains an optimization mathematical model aimed at determining the parameters of the elements comprising the airport, on the basis of which a simulation model was developed and a modified method of multi-criteria evaluation of SAW taking into account the interval numbers was presented, in which the set of weights was estimated by the Shannon entropy method. In the application part for 3 variants of the airport arrangement, the parameters were determined in the form of interval numbers and then evaluated using the presented method. The presented numerical example shows that the proposed method is an excellent tool to assist in solving complex decision problems where the data are imprecise and represented by interval numbers.

NEW IMPROVED METHOD FOR SOLVING THE FUZZY LINEAR PROGRAMMING PROBLEMS WITH VARIABLES GIVEN AS FUZZY NUMBERS

The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random numerical examples has been solved using the proposed approach.

Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management

For the multi-criteria group decision-making problem where the criterion value is a normal interval number and the weight information is incomplete, the normal interval number and its compromise expected value, compromise mean square error, algorithm, weighted arithmetic average of normal interval number (ININWAA) Operator, the ordered weighted average (ININOWA) operator of normal interval numbers and the mixed weighted average (ININHA) operator of normal interval numbers, and a multi-criteria group with incomplete information based on normal interval numbers is proposed. Decision-making methods. This method uses ININWAA operator and INNHA operator to integrate criterion values, uses the compromise mean square error of criterion values, establishes an optimisation model to solve the optimal criterion weights and uses the expectation variance criterion to determine the order of the schemes. The case analysis shows the effectiveness and feasibility of this method.

Evaluation of Transfer Efficiency between Subway and Bus Based on the Interval Number Ranking Method by Employing Probability Reliability: Taking Ningbo for Example

In recent years, the construction and operation of urban subways have been gradually increasing in developing countries. In the next step, more attention should be paid to the transfer efficiency between subway and bus so as to improve the travel efficiency of more urban residents. This paper uses the probability credibility interval number ranking method to evaluate the bus transfer efficiency. Firstly, this study obtains the dynamic transfer time data by matching individual smart card and subway/bus global positioning system (GPS) records, which is used to evaluate the transfer efficiency of corresponding subway stations. Then, we establish a probability density function to represent the characteristic information of transfer time. Accordingly, the probability reliability model of the order relation of interval numbers can be constructed. In the end, the method is applied to evaluate the transfer efficiency between subway and bus stations in Ningbo. Compared to the traditional interval number ranking method, the evaluation result shows that this method can get a more objective transfer efficiency order relation. The reason is that this method can not only consider the random feature of transfer time but also make use of the data distribution characteristics. This method could be applied to obtain the stations with relatively low transfer efficiency and the feedback can be used for bus line operation and station layout improvement.

Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control

This article proposes a distribution function based on normal distribution to express the distribution of criterion values in the interval. This method considers that the economic evaluation target of investment projects is multi-attribute. The economic management risk control environment is divided into information environment, time and space environment, and subject environment. The paper gives the corresponding multi-attribute economic evaluation method for the six possible combinations of project risk environments under the possibility of mutual comparison between interval numbers under the normal distribution. In the end, an example is used to illustrate the practicability and simplicity of the decision-making method.

Decision-Making Optimization of Mine Gas Monitoring Based on Gauss Process Regression and Interval Number Correlation Analysis

For the subjective limitation of gas sensor calibration in coal mines, a decision-making method for gas sensor calibration under monitoring failure was studied based on the Gauss process regression (GPR) and the correlation analysis of interval numbers. Based on the correlation characteristics of gas monitoring data of each monitoring point in the work face area in coal mine, the initial confidence interval of gas concentration in monitoring failure period was obtained by GPR, and then the confidence interval was further optimized by the correlation analysis of interval numbers. According to the correlation characteristics of monitoring data of each monitoring point, its similarity of dynamic variation tendency was measured by using Euclidean distance of interval numbers, and the optimal confidence interval was determined by calculating the correlation degree of interval numbers. The case study shows that making full use of the effective monitoring information of multiple monitoring points ensures the reliability of the initial confidence interval; the dynamic adjustment of model parameters in correlation analysis of interval number avoids the subjectivity defect of similar methods and further obtains the consistency between interval numbers’ reliability and correlation degree, which can ensure the effectiveness of the application of this method.

A Novel Extension of the Technique for Order Preference by Similarity to Ideal Solution Method with Objective Criteria Weights for Group Decision Making with Interval Numbers

This paper presents an extension of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method with objective criteria weights for Group Decision Making (GDM) with Interval Numbers (INs). The proposed method is an alternative to popular and often used methods that aggregate the decision matrices provided by the decision makers (DMs) into a single group matrix, which is the basis for determining objective criteria weights and ranking the alternatives. It does not use an aggregation operator, but a transformation of the decision matrices into criteria matrices, in the case of determining objective criteria weights, and into alternative matrices, in the case of the ranking of alternatives. This ensures that all the decision makers’ evaluations are taken into account instead of their certain average. The numerical example shows the ease of use of the proposed method, which can be implemented into common data analysis software such as Excel.

Risk Analysis of Instability Failure of Earth–Rock Dams Based on the Fuzzy Set Theory

Determining the anti-sliding instability risk of earth–rock dams involves the analysis of complex uncertain factors, which are mostly regarded as random variables in traditional analysis methods. In fact, fuzziness and randomness are two inseparable uncertainty factors influencing the stability of earth–rock dams. Most previous research only focused on the randomness or the fuzziness of individual variables. Moreover, dam systems present a fuzzy transition from a stable state into a failure state. Therefore, both fuzziness and randomness of the influencing factors should be considered in the same framework, where the instability of an earth–rock dam is regarded as a mixed process. In this paper, a fuzzy risk model of instability of earth–rock dams is established by considering the randomness and fuzziness of parameters and the failure criteria comprehensively. We obtained the probability threshold of instability risk of earth–rock dams by Monte-Carlo simulation after the fuzzy parameters were transformed into interval numbers by cut set levels. By applying the proposed model to the instability analysis of the Longxingsi Reservoir, the calculation results showed that the lower limits of risk probability under different cut set levels exceeded the instability risk standard of grade C for earth–rock dams. Compared with the traditional risk determination value, the risk interval obtained with the proposed methods reflects different degrees of dam instability risk and can provide reference for dam structure safety assessment and management.

Evaluation of Vehicle Handling Stability Based on Interval TOPSIS and Entropy Weights

The purpose of this study is to evaluate the handling stability of vehicle from the perspective of users using a multi-criteria decision-making approach with interval numbers. In order to achieve this purpose, the evaluation criteria easy for drivers to understand were constructed based on questionnaire, the interval weights of the criteria were calculated using the entropy weight method with interval numbers, and the interval TOPSIS method was used to evaluate the vehicle handling stability. As the improvement of the method, a new method to determine the crisp value of the interval weight was given, and the relative closeness index used for ranking alternatives was extended to a new additive ranking index. The proposed method was used to evaluate the handling stability of 12 vehicles, and the results may provide some basis for vehicle R & D and design.