Fuzzy Number Approach Research Articles

Exploration of Time-Fractional Cancer Tumor Models with Variable Cell Killing Rates via Hybrid Algorithm

Abstract Cancer is marked by abnormal cell growth that invades healthy tissues, potentially spreading throughout the body through the bloodstream or lymphatic system. It arises when body cells show irregularities in the genes that control cell growth. To treat and minimize the growth of these abnormal cells, different models have been proposed to predict and analyze cancer-tumor. The current study contains analysis of fractional cancer-tumor with different uncertain conditions. To include the uncertainties in the model, Pentagonal fuzzy numbers (PFNs) approach is utilized. A hybrid mechanism, combining homotopies with perturbation technique and a generalized integral transform, is proposed to efficiently handle fractional derivatives with fuzzified conditions. The validity of obtained solutions is checked by calculating residual errors. Graphical analysis assesses the impact of important parameters on the solution profiles, and confirms the reliability of the proposed methodology for complex fractional tumor models and other intricate physical phenomena.

On the Development of Fuzzy Estimators for Life Time Distributions based on Censored Fuzzy Life Times

Lifetime analyses comprise the techniques dealing with observations obtained from the occurrence of a specified event(s). In most of the situations dealing with lifetime observations, some units are recorded as censored observations. Dealing with censored observations makes these techniques unique. Countless standard statistical tools are available for inference based on censored lifetime observations. These classical techniques consider lifetime observations as precise numbers and ignore the uncertainty of single observations. Whereas in practical applications it is not possible to measure life times as precise numbers, they are always more or less nonprecise. The imprecision in measurements can be covered by neutrosophic set. Fuzzy estimators for life time distributions potentially use neutrosophic system to model and analyze the inherent uncertainties and neutalities present in the data and the parameter estimates. This study aimed to obtain estimators for the Weibull parameters and two exponential parameters based on the up-to-date fuzzy number approach, a special case for neutrosophic set. The suggested estimators incorporate fuzziness in addition to random variation, which makes these estimators more realistic. The same techniques need to be extended to fuzzy and neutrosophic sets.

Sub-Contractor Selection in Shipyard Companies Using Fuzzy-AHP Method

Shipyard industries is one of the very complex construction jobs because there is much work to be done in parallel. Activities in the shipyard industry mostly involve sub-contractors. Although many advantages are obtained, involving sub-contractors in the company also has an impact on the company’s performance. The selection of the right sub-contractor is a crucial activity and will determine the company’s performance. This research uses the Fuzzy Analytical Hierarchy Process method (Fuzzy AHP) to solve the problem of selecting sub-contractors in the Shipbuilding Company. Alternative sub-contractors were evaluated and pairwise comparisons were made between these alternatives using Fuzzy AHP with a Triangular Fuzzy Number (TFN) approach. The TFN scale can reduce the ambiguity of expert judgment on AHP. A case study was conducted on the selection of sub-contractors with the bottom cleaning and ship replating project at shipyard company in Surabaya, Indonesia. As a result, one of the sub-contractors selected as the best sub-contractor with a score of 0.167.

Evaluation of emergency evacuation capacity of urban metro stations based on combined weights and TOPSIS-GRA method in intuitive fuzzy environment

Research on emergency evacuations of urban metro stations has become a hot topic in public security applications in recent years. This paper proposes a comprehensive framework for evaluating the emergency evacuation capacity of metro stations. An evaluation indicator system with 16 indicators of human, equipment, environmental, and management factors is established. A triangular intuitionistic fuzzy number (TIFN) approach is used to collect indicator data to express the uncertainty of the language variables and ensure that the data is closer to reality. Subsequently, a combination of the TIFN and the decision-making trial and evaluation laboratory (TIFN-DEMATEL) and the entropy weight method (EWM) are used to combine the weights using game theory to ensure the weights is more scientific and reasonable. Grey relational analysis (GRA) is integrated with the technique for order preference by similarity to an ideal solution (TOPSIS) to improve the ranking results and evaluate metro station emergency evacuation capacity. A case study of eight metro stations in Beijing is conducted to validate the evaluation framework. Sensitivity analysis and comparative analysis demonstrate the reliability and robustness of the proposed method. Finally, the specific measures to improve the emergency evacuation capacity are given.

A Weighting Method Based on the Improved Hesitation of Pythagorean Fuzzy Sets

The existing expert weight determination method for multi-attribute decision making based on the Pythagorean fuzzy number approach does not make sufficient use of the hesitation involved with the decision information, which may cause biased weight assignment. Therefore, to address the issue of unknown expert weights and attribute evaluation based on Pythagorean fuzzy numbers in multi-attribute group decision-making problems, a weight determination method is proposed that improves the treatment of hesitation in Pythagorean fuzzy sets. Firstly, the proximity of experts and similarity of the modified ones are determined according to the evaluation matrix. Then, the expert weights are integrated from the aspects of proximity and corrected similarity to obtain an assembled comprehensive evaluation matrix. Finally, the alternatives are ranked using the PF-TOPSIS method. The results of expert weight analysis and data verification demonstrate that the proposed method fully utilizes expert decision-making information, leading to a significant improvement in the rationality and accuracy of multi-attribute group decision-making problems.

Behavioral Strategies between Government and Real Estate Developers on Prefabricated Buildings Based on Triangular Fuzzy Matrix Game

The subsidies provided by the local government to real estate developers are an important and common practice to promote the development of prefabricated buildings worldwide. However, there is a lack of current research on how government subsidies affect the decision-making of real estate developers with respect to adopting prefabricated construction methods. This study developed a fuzzy game model integrating classical game theory with the triangular fuzzy number approach between the local government and a real estate developer, with different behavioral strategies regarding whether or not to develop prefabricated buildings. It analyzed the Nash equilibriums under the circumstances of pure and mixed strategies and probed the influencing factors of the game equilibrium results via numerical simulation. The research conclusions are as follows: (1) the government should encourage real estate developers to actively participate in prefabricated building by using financial subsidies, fund rewards, process supervision and economic penalties comprehensively; (2) the pure strategy (no manufacturing process supervision, active development) between the government and real estate developers is feasible when the benefit of “active development” for real estate developers is larger than that of “passive development”; (3) positive incentives, such as offering financial subsidies, reducing the cost of prefabricated building development and improving the popularity of prefabricated construction in the building market, should be taken to motivate real estate developers; and (4) negative incentives, such as increasing economic punishment and enhancing manufacturing process supervision, can also facilitate real estate developers to actively participate in the development of prefabricated buildings. Incentives are more effective when the economic penalties are greater than the incremental costs of developing prefabricated buildings. Some policy implications are given to guide prefabricated building market development. Finally, the main problems that need further study in the future are highlighted.

Aplikasi Fuzzy Analytical Hierarchy Process untuk Menentukan Prioritas Pelanggan Berkunjung Ke Gerai Minuman Choco Late

Choco Late is a beverage outlet in Panam Pekanbaru that sells drinks with various flavors that can be combined with various additional toppings. This study aims to determine the priority criteria for customers visiting the Choco Late beverage outlet using the Fuzzy AHP method. The AHP Fuzzy method combines the AHP method and the Fuzzy method. The AHP Fuzzy approach, especially the triangular fuzzy number approach with the AHP scale, must be able to minimize uncertainty so that the results are accurate. The criteria used in this study are service, goods sold, and the Choco Late environment. Based on the data calculation steps obtained by Fuzzy AHP, the respondent has a CR value = 0.0834, which means it is consistent because it meets the standards set CR < 0.10, and the main priority is service with a criterion weight of 0.7339

Multi-attribute ordered fuzzy numbers approach to transport trolley control

Multi-attribute ordered fuzzy numbers approach to transport trolley control

Generalized fuzzy number and graph theory matrix approach in fuzzy decision making of smartphone selection

A number of studies have proposed a method of ranking a smartphone due to the fact that newly smartphones in the market are offering more features which could give more benefit to the user and thus become increasingly important as a tool in helping them to make everyday decisions. But most of the studies have exhibited shortcoming associated to level of confidence of decision makers’ in giving a judgement, which significantly influences final ranking result. This study proposes Graph Theory and Matrix Approach (GTMA) on ranking smartphone alternatives that ensures consideration of uncertainty and confidence level upon their judgement towards smartphone selection. A Generalized Triangular Fuzzy Number (GTFN) is used in the calculation of interrelation matrix which leads to give more meaningful value of importance weights of the attributes. Selection index is then calculated to rank the smartphone through fuzzy determinant. A numerical example is provided to illustrate the proposed approach whereby five well-known smartphones brand are considered which are apple, Samsung, Huawei, OPPO and Asus. The result shows that Huawei is the most preferred brand followed by OPPO and Apple in selecting the best smartphone.

Application of Fuzzy AHP and Fuzzy TOPSIS methods for the new normal problem

The government have new program to deal with the pandemic impact of the Coronavirus, which is said with the new normal. The implementation of the new normal itself requires more attention in terms of the readiness of a region to implement the program. Determination of these areas can be done using the Fuzzy Analytical Hierarchy Process(AHP) and fuzzy technique for Order Performance by Similarity to Ideal Solution(TOPSIS) methods. Fuzzy AHP is used to determine the weight of the existing criteria, while Fuzzy TOPSIS is used to determine the safest area and is ready to implement the new normal. The case study for the problem in this paper is Central Java Province, with alternatives districts and cities. The influencing criterias are the number of People Under Surveillance (PeUS), the number of Patient Under Surveillance (PaUS), the number of patients being treated, the number of positive patients who died, and positive patients who recovered. Triangular fuzzy number approach both methods. The results of this study found that 30% of the total number of districts or cities are ready to implement the New Normal program. This study also explain that the higher of the patient number being treated, the less safe an area will be. While the patients number who recover is increasing, then an area will be ready to implement a New Normal program.

Fuzzy Numerical Solution via Finite Difference Scheme of Wave Equation in Double Parametrical Fuzzy Number Form

The use of fuzzy partial differential equations has become an important tool in which uncertainty or vagueness exists to model real-life problems. In this article, two numerical techniques based on finite difference schemes that are the centered time center space and implicit schemes to solve fuzzy wave equations were used. The core of the article is to formulate a new form of centered time center space and implicit schemes to obtain numerical solutions fuzzy wave equations in the double parametric fuzzy number approach. Convex normalized triangular fuzzy numbers are represented by fuzziness, based on a double parametric fuzzy number form. The properties of fuzzy set theory are used for the fuzzy analysis and formulation of the proposed numerical schemes followed by the new proof stability thermos under in the double parametric form of fuzzy numbers approach. The consistency and the convergence of the proposed scheme are discussed. Two test examples are carried out to illustrate the feasibility of the numerical schemes and the new results are displayed in the forms of tables and figures where the results show that the schemes have not only been effective for accuracy but also for reducing computational cost.

Designing an integrated municipal solid waste management system using a fuzzy chance-constrained programming model considering economic and environmental aspects under uncertainty

In recent decades, municipal solid waste (MSW) management has become one of the major concerns of human societies. Therefore, an efficient MSW system of collecting, recycling, and disposing is required to be designed, maintained and improved continuously. However, designing a proper waste collection management system by controlling the spread of diseases and environmental pollutants is very costly. To provide an efficient MSW management system, this study proposes an integrated location-allocation problem to plan the operations such as collection, recycling, disposal, and transportation under uncertainty. To deal with the problem uncertainty, a triangular fuzzy number approach is employed and finally, a fuzzy chance-constrained programming model is developed. Moreover, the proposed bi-objective mathematical programming model aims to minimize the total costs and the total volume of pollutant emissions simultaneously. To solve and validate the model, a weighted goal programming (WGP) method is employed and solved by CPLEX solver of GAMS software. Finally, a real case study problem was implemented in Qazvin, Iran. The results showed that, in most cases, increasing the confidence level of the case study problem leads to the improvement of objective functions. Managers can take into account the output of this research provided along with a sensitivity analysis under different conditions.

Risk evaluation model for failure mode and effect analysis using intuitionistic fuzzy rough number approach

Risk evaluation model for failure mode and effect analysis using intuitionistic fuzzy rough number approach

Comprehensive Eutrophication Assessment Based on Fuzzy Matter Element Model and Monte Carlo-Triangular Fuzzy Numbers Approach.

Evaluating the eutrophication level of lakes with a single method alone is challenging since uncertain, fuzzy, and complex processes exist in eutrophication evaluations. The parameters selected for assessing eutrophication include chlorophyII-a, chemical oxygen demand, total phosphorus, total nitrogen, and clarity. Firstly, to deal with the uncertainties and fuzziness of data, triangular fuzzy numbers (TFN) were applied to describe the fuzziness of parameters. Secondly, to assess the eutrophication grade of lakes comprehensively, an improved fuzzy matter element (FME) approach was incorporated with TFNs with weights determined by combination of entropy method and analytic hierarchy process (AHP). In addition, the Monte Carlo (MC) approach was applied to easily simulate the arithmetic operations of eutrophication evaluation. The hybrid model of TFN, FME, and MC method is termed as the TFN–MC–FME model, which can provide more valuable information for decision makers. The developed model was applied to assess the eutrophication levels of 24 typical lakes in China. The evaluation indicators were expressed by TFNs input into the FME model to evaluate eutrophication grade. The results of MC simulation supplied quantitative information of possible intervals, the corresponding probabilities, as well as the comprehensive eutrophication levels. The eutrophication grades obtained for most lakes were identical to the results of the other three methods, which proved the correctness of the model. The presented methodology can be employed to process the data uncertainties and fuzziness by stochastically simulating their distribution characteristics, and obtain a better understanding of eutrophication levels. Moreover, the proposed model can also describe the trend of eutrophication development in lakes, and provide more valuable information for lake management authorities.

Benefit maximization of demand side management operator (DSMO) and private investor in a distribution network

In this paper, the beneficial impact of private investor participation and demand side management operator (DSMO) in planning problem is investigated. All system uncertainties are modeled by fuzzy number approach. Bi-objective optimization model is proposed for the maximum benefit of DSMO and private investor in the planning horizon. To tackle the optimization problem, ε-constraint and fuzzy decision making methods are jointly used. Different scenarios are modeled including and excluding electric vehicles (EVs) charging impact on the daily load curve. The problem is formulated in the general algebraic modeling system (GAMS) environment and solved by its embedded high-performance solvers. The obtained results reveal that the desired benefits of a private investor cannot be satisfied in the no benefit sharing scenario. In non-zero benefit sharing scenario, Pareto optimal front includes non-negative values for both DSMO and private investor which demonstrates the beneficial solutions. Followed by adding EVs charging load to the daily load curve, the total benefits of private investor and DSMO are reduced up to 13.33% and 30.44%, respectively. Furthermore, employing smart charge/discharge behavior increases private investor and DSMO benefits up to 32.04% and 14.76%, respectively.

Human Health Risk Assessment of Contaminants in Drinking Water Based on Triangular Fuzzy Numbers Approach in Yinchuan City, Northwest China

Access to safe drinking water is one of the fundamental human rights and an important component of healthy life. In this paper, the triangular fuzzy numbers approach has been used for recognizing uncertainties in the estimation of health risks proposed by the United States Environmental Protection Agency in Yinchuan city, northwest China. The levels of As, Cd, Cr, Mn, Cu, Zn, Hg, Pb, F, NO3-N, and NH4-N in drinking water were within the permissible limits except for Fe. The results showed that the health risks were primarily attributed by Cr, As, and F in drinking water. When the confidence level was 0.8, the total carcinogenic and noncarcinogenic risks values were less than the acceptable risk levels (10−4 and 1.0) set by the USEPA, respectively. The health risk of drinking water in Yinchuan city is as follows: Nanjiao water source > Beijiao water source > Dongjiao water source. Furthermore, the total noncarcinogenic risks were more sensitive with respect to different confidence levels. The spatial distribution of As and F levels in drinking water sources is urgently needed to be ascertained in drinking water, especially for Nanjiao water source. The health risk assessment model based on the triangular fuzzy numbers approach is effective to quantify uncertainty in risks with less complexity. The findings in this paper will help managers minimize the potential health risks and provide a new insight for solving uncertainties in water management.

Forecasting Motorcycle Sales Using Nearest Symmetric Trapezoidal Fuzzy Number

A business activity aimed at obtaining forecasting as an initial step in planning activities helps provide an overview of sales in a business for the coming period based on data available. This research aims to design and develop a motorcycle sales forecasting application using Fuzzy Time Series with Nearest Symmetric Trapezoidal Fuzzy Number approach to predict the next period sales of PT Mutiara Motor. To test the accuracy of the method used in application, we used the MSE and MAPE criteria. Based on the results of three experiments taken: (1) monthly ‘All Category’-’All Type’ with MSE = 54.42 and MAPE = 4.28%, (2) monthly ‘Beat CW Fuel Injection’ with MSE = 3.67 and MAPE = 4.04%, and (3) daily ‘All Category’- ’All Type’ with MSE = 1.42 and MAPE = 27.36% we indicate that Fuzzy Time Series with Nearest Symmetric Trapezoidal Fuzzy Number approach could give higher accuracy than the Single Exponential Smoothing method as comparison in forecasting motorcycle sales.
 Index Terms—fuzzy time series, nearest symmetric trapezoidal fuzzy number, sales forecasting

Assessment of arsenic and fluoride pollution in groundwater in Dawukou area, Northwest China, and the associated health risk for inhabitants

Exposure to arsenic and fluoride through contaminated drinking water can cause serious health effects. In this study, the sources and occurrence of arsenic and fluoride contaminants in groundwater are analyzed in Dawukou area, northwest China, where inhabitants rely on groundwater as the source of drinking water. The triangular fuzzy numbers approach is adopted to assess health risk. The fuzzy risk assessment model incorporates the uncertainties that are caused by data gaps and variability in the degree of exposure to contaminants. The results showed that arsenic and fluoride in groundwater were mainly controlled by the dissolution–precipitation of Ca-arsenate and fluorite under weakly alkaline conditions. The arsenic and fluoride concentrations were higher in the shallow groundwater. The most probable risk values for arsenic and fluoride were 4.57 × 10−4 and 0.4 in the shallow groundwater, and 1.58 × 10−4 and 0.3 in the deep groundwater. Although the risks of fluoride were almost within the acceptable limit (<1.0), the risk values of arsenic were all beyond the acceptable levels of 10−6 for drinking water. Further, the local administration should pay more attention to the potential health risk through dietary intake and to the safety of deep water by ensuring it is not contaminated under prolonged pumping conditions. The fuzzy risk model treats the uncertainties associated with a quantitative approach and provides valuable information for decision makers when uncertainties are explicitly acknowledged, particularly for the variability in contaminants. This study can provide a new insight for solving data uncertainties in risk management.

Comparing A Bayesian and Fuzzy Number Approach to Uncertainty Quantification in Short-Term Dissolved Oxygen Prediction

A new autoregressive-type, updating fuzzy linear regression method is proposed to predict daily dissolved oxygen (DO) concentration in a highly urbanized riverine environment. Results of this model are compared to results from an updating Bayesian regression model. Both methods use lagged daily DO (at four different lags) as the independent variable. Uncertainty in the models is represented by a fuzzy number based approach in the first case, and by a Bayesian framework in the second. Real-time data from the Bow River in Calgary, Canada is used to calibrate the models sequentially to mimic a real-time updating model. Four different performance metrics were used to measure the performance of each model. Lastly, the input data resolution is reduced to measure the impact on model performance. Results show that the physical system can be adequately characterized using only one year of data. Both approaches can capture the general trend of daily DO, but the fuzzy number based method can better capture the changes in observed variability. The metrics for both models are comparable, with the one-day lag case categorized as “very good”; however, the performance reduces at higher lags. The fuzzy number method captures more low DO events than the Bayesian approach, with a much lower mean squared error. A possibility to probability transformation is used to highlight the risk of low DO days for the fuzzy case. Lastly, reducing the input data resolution from 96 to 6 points per day has a minimal impact on model performance, suggesting the limited efficacy or utility in increasing sampling rates.

Using A Fuzzy Number Error Correction Approach to Improve Algorithms in Blind Identification

As part of a detailed study on blind identification of Gaussian channels, the main purpose was to propose an algorithm based on cumulants and fuzzy number approach involved throughout the whole process of identification. Our objective was to compare the new design of the algorithm to the old one using the higher order cumulants, namely Alg1, Algat and the Giannakis algorithm. We were able to demonstrate that the proposed method -fuzzy number error correction- increases the performance of the algorithm by calculating the ratio of squared errors of ALGaT and AlgatF. The method can be applied to any algorithm for more improvement and effinciency.