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This work introduces a method for fuzzy control charts. Fuzzy theory and the foundations of Shew Hart control charts form the foundation of the process. The information was gathered from one of the key production facilities to raise the quality standard for one of Iraq's industrial products. Fuzzy control charts were used to quickly and accurately identify the production specifications and efficiency. This work uses the triangle membership function to generate fuzzy numbers, which are then transformed into quality control charts for the real data obtained using the proposed ranking function. Next, contrast the quality control of crisp and fuzzy attributes. The graphs demonstrate how professional techniques can increase output and lower defect rates. To meet the control limits for quality control and defective percentages for all samples using (w = 0.2, 0.5, 0.6) and (λ = 0.5, 0.7, 0.9), then compare the adoption of the traditional technique with fuzzy logic while adopting variable cases through the arrangement function. It can be noticed that the chart of fuzzy control is more economically quicker and more accurate at monitoring production quality, enabling the diagnosis of defective units throughout the production process. [ABSTRACT FROM AUTHOR]

The process of siting municipal solid waste landfills in Greece faces significant challenges due to land resource limitations, the country's mountainous and water-permeable terrain, and strong public opposition. This study introduces a novel methodology for optimizing landfill sites on Lemnos Island in the North Aegean Sea using a Fuzzy Spatial Multiple Criteria Analysis (FSMCA) approach. By combining fuzzy sets theory, Geographic Information Systems (GIS), Analytic Hierarchy Process (AHP), spatial autocorrelation, spatial clustering and sensitivity analysis, this methodology addresses the uncertainties and complexities inherent in landfill siting. The decision problem is structured hierarchically into five levels to manage multiple criteria effectively. Criteria weights are determined using AHP, with discrete criteria graded according to Greek and EU guidelines, and continuous criteria evaluated through fuzzy sets theory. The region's suitability is assessed using multiple criteria analysis, revealing that 9.7% of Lemnos Island is appropriate for landfill placement. Sensitivity analysis confirms the robustness of the methodology to changes in criteria weights. The case study demonstrates the practical application and benefits of FSMCA in a real-world scenario, underscoring its potential to improve sustainable waste management practices and inform policy making. [ABSTRACT FROM AUTHOR]

The process of siting municipal solid waste landfills in Greece faces significant challenges due to land resource limitations, the country’s mountainous and water-permeable terrain, and strong public opposition. This study introduces a novel methodology for optimizing landfill sites on Lemnos Island in the North Aegean Sea using a Fuzzy Spatial Multiple Criteria Analysis (FSMCA) approach. By combining fuzzy sets theory, Geographic Information Systems (GIS), Analytic Hierarchy Process (AHP), spatial autocorrelation, spatial clustering and sensitivity analysis, this methodology addresses the uncertainties and complexities inherent in landfill siting. The decision problem is structured hierarchically into five levels to manage multiple criteria effectively. Criteria weights are determined using AHP, with discrete criteria graded according to Greek and EU guidelines, and continuous criteria evaluated through fuzzy sets theory. The region’s suitability is assessed using multiple criteria analysis, revealing that 9.7% of Lemnos Island is appropriate for landfill placement. Sensitivity analysis confirms the robustness of the methodology to changes in criteria weights. The case study demonstrates the practical application and benefits of FSMCA in a real-world scenario, underscoring its potential to improve sustainable waste management practices and inform policy making.

This work introduces a method for fuzzy control charts. Fuzzy theory and the foundations of Shew Hart control charts form the foundation of the process. The information was gathered from one of the key production facilities to raise the quality standard for one of Iraq's industrial products. Fuzzy control charts were used to quickly and accurately identify the production specifications and efficiency. This work uses the triangle membership function to generate fuzzy numbers, which are then transformed into quality control charts for the real data obtained using the proposed ranking function. Next, contrast the quality control of crisp and fuzzy attributes. The graphs demonstrate how professional techniques can increase output and lower defect rates. To meet the control limits for quality control and defective percentages for all samples using (w = 0.2, 0.5, 0.6) and (λ = 0.5, 0.7, 0.9), then compare the adoption of the traditional technique with fuzzy logic while adopting variable cases through the arrangement function. It can be noticed that the chart of fuzzy control is more economically quicker and more accurate at monitoring production quality, enabling the diagnosis of defective units throughout the production process.

In this paper, we present a new computational methodology using the Residual Power Series Method (RPSM) to create a new model in the fuzzy domain suitable for solving a fourth-order of FBVP using the concept of generalized differentiation, and we present an algorithm for the numerical solutions of fourth-order fuzzy boundary value problems (FBVPs), which include ordinary differential equations, based on concepts from fuzzy set theory. The effectiveness of the suggested technique was tested to verify the accuracy of RPSM, and the series solutions were compared to the exact solution when the plane is equal to one. The results show that the algorithm is highly efficient and straightforward in implementation, compared to the other mentioned schemes, and fulfills the characteristics of fuzzy solution, thus it is a practically optimal solution for the most complex BVP programs in science. [ABSTRACT FROM AUTHOR]

There exist multiple uncertainties in the belt conveyor system. To reduce the system errors and save the control energy, the uncertainties need to be described and compensated accurately. In this paper, the fuzzy set theory is applied to establish the fuzzy dynamical model. Then, an exponential control is designed and a noncooperative‐game based optimization approach is proposed to solve out the Nash equilibrium. The novel control with optimal parameters including the adaptive tension force are applied to render the system uniform boundedness and uniform ultimate boundedness. Finally, the simulations are performed for verification. [ABSTRACT FROM AUTHOR]

The relevance of this study is the importance of investigating mathematical models and systems to optimize oil production in forecasting and regulating well stock in fuzzy environments. The purpose was to assess the practical application of Markov chain models and fuzzy set theory to optimize oil production. This study specifically analyzed operating and idle well stocks in Kazakhstan's Kenkiyak oil field using a Markov chain system of equations. Fuzzy set theory was then applied to model linguistic relationships between oil production parameters like depth and porosity. The Markov model successfully predicted linear asymptotes of well stock over time and assessed impacts of changing repair crew productivity. The fuzzy approach effectively modeled the dependence of production efficiency on depth and reservoir rock porosity. Results showed a 15% improvement in forecasting accuracy and a 10% increase in production efficiency. This demonstrates the value of mathematical models in optimizing real)world oil production processes and their ability to enhance management system performance. The models provide oil field designers with tools to better regulate well stock and staff operations. [ABSTRACT FROM AUTHOR]

In recent decades, numerous catastrophic accidents have occurred worldwide, ranging from natural events (such as tsunamis, flooding, and earthquakes) to industrial events (such as mining and chemical process disasters). They endanger humans, the environment, organizations, and societies, as well as national security. However, there have been few attempts to propose a model for assessing the required capabilities and potential challenges in crisis management system maturity (CMSM). Accordingly, this study proposes a framework for measuring CMSM levels in complex systems. To this end, a CMSM taxonomy was developed, including aspects, dimensions, and factors influencing the CMSM. Fuzzy inference sets and fuzzy analytical hierarchy processes are then used for knowledge acquisition, quantification of the CMSM, and dealing with epistemic uncertainty. An actual complex petrochemical plant is investigated to evaluate its capabilities. The findings revealed the most significant contributing factors: the CMSM’s current capability and challenges level (score), as well as the capacity to overcome the potential crisis response challenges. Moreover, the proposed model can be used as a practical approach for various chemical-processing plants.

This study presents a novel computational methodology for resolving second-order fuzzy initial value problems (FIVPs), encompassing ordinary differential equations. The proposed approach modifies the conventional crisp fifth-order Runge-Kutta Fehlberg method to suit the resolution of second-order FIVPs within the fuzzy domain, drawing on concepts from fuzzy set theory. It is demonstrated that by reducing them to a system of first-order FIVPs, all second-order FIVPs can be effectively solved. The novel method is subsequently applied to both linear and non-linear second-order FIVPs. The results attest to the high efficiency and accuracy of the approach, while also preserving the inherent properties of fuzzy solutions. Therefore, this study offers a promising new avenue for addressing second-order FIVPs, with potential applicability across a broad range of scenarios. [ABSTRACT FROM AUTHOR]

In terms of uncertain business conditions, the ability of an enterprise to bounce back after severe disruptions, or simply resilience, may be seen as one of the major features needed to sustain successful business operations. This research has the objective of proposing an algorithm for the organizational resilience assessment in industrial companies and conducting an analysis of the relationship between the organizational Resilience Factors and Key Performance Indicators recovery times. As the variables that are an integral part of the research are exposed to a high degree of uncertainty, they are modeled using fuzzy set theory. The methodology used for the research is an enhanced fuzzy Delphi, where the fuzzy geometric mean is employed as an aggregation operator. The relationship between the organizational resilience factors and Key Performance Indicators' recovery time is based on the correlation analysis. The proposed model is based on real data from one complex industrial enterprise. The main finding of the research is that calculations indicate a significant negative correlation between treated variables. [ABSTRACT FROM AUTHOR]

In order to achieve high penetration of variable Renewable Energy Sources (vRES) in the power systems flexibility issues and needs inevitably arise. There are several flexibility options having a wide range of different technical and economic characteristics which meet the challenges posed by high penetration of vRES in the power systems. System operators seek to identify the most suitable flexibility options for the reliable operation of power systems. The aim of this research paper is to assess twenty-three (23) flexibility options in terms of energy management using three (3) technical characteristics (response time, efficiency, and storage duration) and three (3) economic characteristics (power capital cost, operation and maintenance cost and lifetime). For the assessment two different Multiple Criteria Decision-Making (MCDM) methods are used. A Fuzzy Decision-Making Tool (FDMT) under fuzzy rule-based system and fuzzy sets, using MATLAB software is developed and the Analytic Hierarchy Process (AHP) is applied. The results from the Fuzzy Logic and AHP methods show that demand side flexibility options are the most preferable flexibility options having, according to the FDMT, Fuzzy Preferability Index (FPI) 0.885 and, according to the AHP method, global priority vector 0.492. Demand side flexibility options are followed by Variable RE Power Plants (vRES) and Superconducting Magnetic Energy Storage (SMES), while Combined Heat and Power Plants (CHP), BioGas Power Plants (BGPP) and power to hydrogen and power to gas are the least preferable. The results from the FDMT and the AHP method are very useful especially in decision-makers because, after the assessment, they can take action to support and promote the most preferable flexibility options.

This work focuses on solving and analyzing two-point fuzzy boundary value problems in the form of fractional ordinary differential equations (FFOBVPs) using a new version of the approximation analytical approach. FFOBVPs are useful in describing complex scientific phenomena that include heritable characteristics and uncertainty, and obtaining exact or close analytical solutions for these equations can be challenging, especially in the case of nonlinear problems. To address these difficulties, the optimal homotopy asymptotic method (OHAM) was studied and extended in a new form to solve FFOBVPs. The OHAM is known for its ability to solve both linear and nonlinear fractional models and provides a straightforward methodology that uses multiple convergence control parameters to optimally manage the convergence of approximate series solutions. The new form of the OHAM presented in this work incorporates the concepts of fuzzy sets theory and some fractional calculus principles to include fuzzy analysis in the method. The steps of fuzzification and defuzzification are used to transform the fuzzy problem into a crisp problem that can be solved using the OHAM. The method is demonstrated by solving and analyzing linear and nonlinear FFOBVPs at different values of fractional derivatives. The results obtained using the new form of the fuzzy OHAM are analyzed and compared to those found in the literature to demonstrate the method's efficiency and high accuracy in the fuzzy domain. Overall, this work presents a feasible and efficient approach for solving FFOBVPs using a new form of the OHAM with fuzzy analysis. [ABSTRACT FROM AUTHOR]

The job-shop scheduling problem (JSP) is NP hard, which has very important practical significance. Because of many uncontrollable factors, such as machine delay or human factors, it is difficult to use a single real-number to express the processing and completion time of the jobs. JSP with fuzzy processing time and completion time (FJSP) can model the scheduling more comprehensively, which benefits from the developments of fuzzy sets. Fuzzy relative entropy leads to a method that can evaluate the quality of a feasible solution following the comparison between the actual value and the ideal value (the due date). Therefore, the multiobjective FJSP can be transformed into a single-objective optimization problem and solved by a hybrid adaptive differential evolution (HADE) algorithm. The maximum completion time, the total delay time, and the total energy consumption of jobs will be considered. HADE adopts a mutation strategy based on DE-current-to-best. Its parameters (CR and F) are all made adaptive and normally distributed. The new individuals are selected according to the fitness value (FRE) obtained from a population consisting of N parents and N children in HADE. The algorithm is analyzed from different viewpoints. As the experimental results demonstrate, the performance of the HADE algorithm is better than those of some other state-of-the-art algorithms (namely, ant colony optimization, artificial bee colony, and particle swarm optimization). [ABSTRACT FROM AUTHOR]

In this paper, a fuzzy finite element algorithm is investigated to determine static responses of plane structures. This algorithm concerns finite element method, fuzzy sets theory, and response surface method. Firstly, the notion of a standardized triangular fuzzy number is developed and utilized to replace original fuzzy numbers in the surrogate models. Then, the error estimations between the training and the test sets are performed to select the suitable response surface model amongst the regression models. Lastly, a good performance combination of complete and non-complete quadratic polynomial regression models is proposed to define the responses of structures. The merits of the proposed algorithm are illustrated via numerical examples.

In this paper, a fuzzy finite element method (FFEM) for determining the responses of structures is proposed by using the transformation between fuzzy and random variables. Firstly, the formulae for establishing normal random variables equivalent to symmetric triangular fuzzy numbers are presented based on the combination of the principle of insufficient reason and that of maximum specificity. As a result, fuzzy finite element analysis is transferred into stochastic finite element analysis. To solve this problem, the response surface method with the aid of standard normal random variables is utilized to approximate the real responses of structures. Then, the errors between the training and test sets are estimated to select a suitable response surface model amongst the regression models. Lastly, the formulae for determining the mean and the standard deviation values of the responses of structures are established. The accuracy and effectiveness of the proposed method are verified via an illustrative example.

Nowadays in Supply Chain (SC) networks, a high level of risk comes from SC partners. An effective risk management process becomes as a consequence mandatory, especially at the tactical planning level. The aim of this article is to present a risk-oriented integrated procurement–production approach for tactical planning in a multi-echelon SC network involving multiple suppliers, multiple parallel manufacturing plants, multiple subcontractors and several customers. An originality of the work is to combine an analytical model allowing to build feasible scenarios and a multi-criteria approach for assessing these scenarios. The literature has mainly addressed the problem through cost or profit-based optimisation and seldom considers more qualitative yet important criteria linked to risk, like trust in the supplier, flexibility or resilience. Unlike the traditional approaches, we present a method evaluating each possible supply scenario through performance-based and risk-based decision criteria, involving both qualitative and quantitative factors, in order to clearly separate the performance of a scenario and the risk taken if it is adopted. Since the decision-maker often cannot provide crisp values for some critical data, fuzzy sets theory is suggested in order to model vague information based on subjective expertise. Fuzzy Technique for Order of Preference by Similarity to Ideal Solution is used to determine both the performance and risk measures correlated to each possible tactical plan. The applicability and tractability of the proposed approach is shown on an illustrative example and a sensitivity analysis is performed to investigate the influence of criteria weights on the selection of the procurement–production plan. [ABSTRACT FROM PUBLISHER]

With the emergence of the global COVID-19 pandemic in 2019, a process of transformation of the modern economic system took place, which requires new approaches to assessing economic processes. One of such processes is the assessment of public welfare. The purpose of this study is to develop an approach to assessing the level of public welfare of the population of Ukraine in the context of the COVID-19 pandemic and economy digitalization. To solve this problem, the methods of artificial intelligence, in particular the method of fuzzy sets theory, which allows using the incomplete information and making high-quality forecast calculations, are used. The factors influencing the level of public welfare during the COVID-19 pandemic have been identified. These are the following factors: gross domestic product, poverty rate, welfare index, human development index, subsistence level, and indicators that characterize the COVID-19 pandemic (i.e. the total number of COVID-19 cases, the total number of deaths from COVID-19, and the total number of vaccinations from COVID-19 in Ukraine). Using fuzzy sets theory, an economic-mathematical model for assessing the level of public welfare in the context of the COVID-19 pandemic in Ukraine was built. Two-dimensional dependences of the level of public welfare of Ukraine in the context of the COVID-19 pandemic on indicators such as gross domestic product, subsistence level, and the total number of cases of COVID-19 in Ukraine were obtained. The results of the study established that the level of public welfare in the context of the COVID-19 pandemic on the 0-100 scale is predicted to be as follows points: 2021 – 17, 2022 – 23, 2023 – 27, 2024 – 19, 2025 – 35 and will not meet international standards.

The article is concerned with the problem of fuzzy-set-based evaluation of the payback period of real investment projects. Initially, the most general features of the approach, which is implemented to find a discounted payback period for an investment project in the form of a fuzzy value (number), were highlighted. After that, the approach to modeling the latter with the help of payback function was thoroughly considered. It is identified that, along with the obvious advantages of this instrument, its significant disadvantage, in terms of the original version, is that the scope of the payback function is limited to the investment projects, for which, after a minimum period of time, when there may be a payback scenario among other scenarios, the sequence of fuzzy estimates of the indicator of accumulated discounted cash flow is non-decreasing. The publication formulates a generalized version of the payback function of the investment project, free from this disadvantage. Using conditional data, the proposed modification was tested, which demonstrated its viability. Particular attention is paid to the formulation and approbation of the indicators that can be obtained on the basis of the payback function and which reflect certain, significant in terms of analytical needs aspects of the payback of the investment project in time.

In the context of globalization of economic development processes, the issue of determining the level of public welfare of economic agents is particularly burning. The object of ehis study is the process of assessing welfare of the economic entities system. The subject of the study is the instrumental and mathematical aspects of modeling and measuring the public welfare. The aim of the work is to develop the mathematical model for measuring the welfare of Ukraine using methods of intellectual analysis, namely, the theory of fuzzy sets. The output of the study is a new approach to objective estimation of public welfare of the state. It is proposed to assess the level of public welfare of the state on the basis of a mathematical model developed on the basis of the theory of fuzzy sets. Input factors of the model are international indices and indicators, such as Index of Economic Freedom, Global Peace Index, Democracy Index, Corruption Perceptions Index, Human Development Index, Prosperity Index, Global Competitiveness Index as well as an indicator that reflects the characteristic property of the Ukrainian economy, namely the minimum living wage. Developed mathematical model for assessment of the level of public welfare of Ukraine and made a prediction of the indicator by 2024 on the basis of the above indices. The results of the study allowed us to establish that the level of public welfare (units) in Ukraine on a scale from 0 to 100 will be equal to 25, 17, 32, 26, and 28 in 2020, 2021, 2022, 2023, and 2024, accordingly.

Threat Assessment is one of the most important components in combat management systems. However, uncertainty is one of the problems that occur in the input data of these systems that have been provided using several sensors in sensor networks. In literature, there are some theories that state and model uncertainty in the information. One of the new methods is the Fuzzy Dempster-Shafer Theory. In this paper, a model-based uncertainty is presented in the air defense system based on the Fuzzy Dempster-Shafer Theory to measure uncertainty and its accuracy. This model uses the two concepts naming of the Fuzzy Sets Theory, and the Dempster-Shafer Theory. The input parameters to sensors are fuzzy membership functions, and the basic probability assignment values are earned from the Dempster-Shafer Theory. Therefore, in this paper, the combination of two methods has been used to calculate uncertainty in the air defense system. By using these methods and the output of the Dempster-Shafer theory are calculated and presented the uncertainty diagrams. The advantage of the combination of two theories is the better modeling of uncertainties. This makes that the output of the air defense system is more reliable and accurate. In this method, the air defense system’s total uncertainty is measured using the best uncertainty measure based on the Fuzzy Dempster-Shafer Theory. The simulation results show that this new method has increased the accuracy to 97% that is more computational toward other theories. This matter significantly increases the computational accuracy of the air defense system in targets threat assessment.

When industrial objects emitting substantial masses of dust and gas mixtures are located within a settlement or close to its borders, it often results in poorer quality of the environment and damages to population health. Such a situation is typical for many cities in the country; primarily, for those that are included into “Pure air” Federal project, a part of the “Ecology” National project. Negative effects are produced by a set of various substances emitted from various industries. And it is quite often that great numbers of people are exposed to such emissions and as a result multiple and variable responses from their health are registered. Assessment of share contributions made by different emissions sources and each particular substance into aggregated negative responses from human health is a fundamental stage in assessing damages to health that occurred due to them; it is significant for working out an action plan aimed at hazardous impacts mitigation. Given that, we proposed an approach based on fuzzy sets theory as a relevant methodological basis for assessing efficiency of risk mitigation and damage to health when planning and implementing activities aimed at ambient air protection. Application of this methodology allows assessing conditions of multi-component negative impacts producing multiple negative effects including direct damage done to human health. And here key parameters are assessed not as per point values but as per interval ones that are characterized with their belonging to a range of scaled parameters. Our research goal was to suggest methodical approaches to assessing efficiency of risk mitigation and damage to health when planning and implementing activities aimed at ambient air protection; the approaches were based on fuzzy sets theory. Results obtained via hygienic (field or calculated examinations of ambient air quality in settlements under exposure and beyond it) and epidemiologic (controlled medical and biological) research are taken as initial data for fuzzy modeling of multiple parameters ratios within “damage to health – mitigation efficiency” system. Principles applied for research design take into account key postulates of exposure assessment, “dose – effect” relationship for an influencing substance, a concept of exposure risk acceptability, peculiarities related to body reactions under combined aerogenic burdens, and plans for ambient air protection activities (including complex ones). Comparing a list of substances that do actual damage to exposed population’s health with a list of substances included into plans on aggregated emissions reduction allows assessing adequacy; determining to what extent damage to health is mitigated allows assessing whether activities aimed at ambient air protection are sufficient and effective.

Managing and evaluating the probability of bankruptcy of Ukrainian enterprises is one of the most complex and relevant problems of the economy and management. In the context of Ukraine’s integration into the international space, there is an arising issue of assessing the bankruptcy of Ukrainian enterprises that meets international financial standards and allows administering this process. A qualitative assessment of the bankruptcy of an enterprise is possible only using artificial intelligence methods – the fuzzy sets method, which allows including qualitative and quantitative indicators to the model for assessing bankruptcy of enterprises in Ukraine. The aim of the article is to improve the existing method for assessing the probability of bankruptcy of Ukrainian enterprises on the basis of the fuzzy sets method, which will include indicators of international financial reporting and allow more efficient administration and management of this process. The subject of the research is the process of formalizing the method of the enterprise bankruptcy assessment in accordance with the indicators of International Financial Reporting Standards. The study offers a mechanism for a comprehensive assessment of the probability of bankruptcy of Ukrainian enterprises with the use of the methods of fuzzy sets, which is based on international financial indicators: current ratio, payable turnover ratio, equity turnover ratio, return on assets, equity-to-debt ratio. The mechanism allows quickly managing bankruptcy conditions. In order to administer the economic activity of the bankrupt enterprises, based on the theory of a fuzzy sets, a system of enterprises management takes into account the international financial reporting.

The article proposes a method for selecting options for the reconstruction of the power supply system based on the criteria of decision-making theory. The reconstruction process is considered as a sequential game with two players : active and passive. The probability of possible states of the system is determined on the basis of the fuzzy sets theory. The main criterion for the choice of the reconstruction option is the value of damage from the power supply interruption. The application of the proposed method is considered on the example of a large metallurgical enterprise.

Aircraft selection is an important issue in achieving long-term goals in the airline industry. For this issue in which multiple conflicting criteria are involved, the extant literature points to the use of multi-criteria decision-making (MCDM) methods. In this respect, this study aims to propose a systematic and comprehensive framework with a focus on the regional aircraft selection perspective. To achieve this, an integrated fuzzy Pivot Pairwise Relative Criteria Importance Assessment (FPIPRECIA) and fuzzy Measurement Alternatives and Ranking according to the Compromise Solution (F-MARCOS) approach was employed. In this study, in which six regional aircraft alternatives were evaluated according to 14 criteria, data were collected from five decision experts. As a result, it was found that the most pivotal criterion is C33 (Operational Cost), and the least important criterion is C12 (NOx). In addition, CRJ1000 was identified as the most promising regional aircraft alternative. The results of the application were further validated by applying a three-stage sensitivity analysis. The proposed structure is anticipated to assist airline managers in aircraft selection decisions under uncertainty by offering a robust and systematic tool. [ABSTRACT FROM AUTHOR]

Websites are considered as the core infrastructure of e-government, so evaluating the quality of websites assists organizations to provide high-quality online services to citizens. For this purpose, this paper is seeking to design a model that enables any organization to evaluate the quality of its websites and identify its strengths and weaknesses. The proposed model includes nine main indexes including “website design,” “responsiveness quality,” “security,” “content and information quality,” “participation,” “trust,” “maintenance and support,” “services” and “usability,” alongside with 85 indicators. Since some of indexes and indicators possess intrinsic uncertainties so “fuzzy set theory” was applied to model the problem's ambiguity. “Analytic hierarchy process” and “PROMETHEE” methods were applied to weigh and rank indexes and indicators respectively. After designing the model, it was used for assessing the websites of five metropolitan municipalities of Iranian cities to spot their strengths and weaknesses.

The aim of this work is to introduce a new category of Fuzzy d-algebra called Γ-Fuzzy d-algebra. This notion is more useful than Fuzzy d-algebra because in the old case the degree of membership of any $x \in X$ in the Fuzzy set does not depend on the structure of d-algebra X. Therefore, in this work, we introduced a new construction of Fuzzy d-algebra that is depended on structure of d-algebra. Also, we show that for any d-algebra there is a Γ-Fuzzy d-algebra. Further, this new construction helps us to find the interesting relation between Γ-Fuzzy d-algebra and edge d-algebra in this work. For any d-algebra, we determined unique Γ-Fuzzy topological space $\lpar X\comma \; \, \Gamma ^f\rpar $ using Γ-Fuzzy d-algebra. For any $f \in X$, a new class of d-algebra $\lpar \Psi \lpar X\rpar \comma \; \varpi \comma \; \lpar X\comma \; \otimes _f\comma \; \, \, f\rpar ^{\mu ^{ \otimes _f}}\rpar $ is introduced, where $\Psi \lpar X\rpar $ is the set of all equivalence classes $\lpar X\comma \; \ast \comma \; \, \, f\rpar ^\lambda $. Finally, a new class of intuitionistic fuzzy set is called intuitionistic Γ-Fuzzy d-algebra is investigated and discussed.

The emergence of fuzzy sets makes job-shop scheduling problem (JSSP) become better aligned with the reality. This article addresses the JSSP with fuzzy execution time and fuzzy completion time (FJSSP). We choose the classic differential evolution (DE) algorithm as the basic optimization framework. The advantage of the DE algorithm is that it uses a special evolutionary strategy of difference vector sets to carry out mutation operation. However, DE is not very effective in solving some instances of FJSSP. Therefore, we propose a novel selection mechanism augmenting the generic DE algorithm (NSODE) to achieve better optimization results. The proposed selection operator adopted in this article aims at a temporary retention of all children generated by the parent generation, and then selecting N better solutions as the new individuals from N parents and N children. Various examples of fuzzy shop scheduling problems are experimented with to test the performance of the improved DE algorithm. The NSODE algorithm is compared with a variety of existing algorithms such as ant colony optimization, particle swarm optimization, and cuckoo search. Experimental results show that the NSODE can obtain superior feasible solutions compared with solutions produced by several algorithms reported in the literature. [ABSTRACT FROM AUTHOR]

Threat Assessment is one of the most important components in combat management systems. However, uncertainty is one of the problems that occur in the input data of these systems that have been provided using several sensors in sensor networks. In literature, there are some theories that state and model uncertainty in the information. One of the new methods is the Fuzzy Dempster-Shafer Theory. In this paper, a modelbased uncertainty is presented in the air defense system based on the Fuzzy Dempster-Shafer Theory to measure uncertainty and its accuracy. This model uses the two concepts naming of the Fuzzy Sets Theory, and the Dempster-Shafer Theory. The input parameters to sensors are fuzzy membership functions, and the basic probability assignment values are earned from the Dempster-Shafer Theory. Therefore, in this paper, the combination of two methods has been used to calculate uncertainty in the air defense system. By using these methods and the output of the Dempster-Shafer theory are calculated and presented the uncertainty diagrams. The advantage of the combination of two theories is the better modeling of uncertainties. This makes that the output of the air defense system is more reliable and accurate. In this method, the air defense system's total uncertainty is measured using the best uncertainty measure based on the Fuzzy Dempster-Shafer Theory. The simulation results show that this new method has increased the accuracy to 97% that is more computational toward other theories. This matter significantly increases the computational accuracy of the air defense system in targets threat assessment. [ABSTRACT FROM AUTHOR]

Subjective assessments of the quality of life are considered when measuring development. These measurements are built using population surveys where people are asked to define their situation on a qualitative scale. Information is obtained through simple surveys that capture subjective perceptions of access to certain goods. To formalize human ability to make decisions in uncertain environments, Zadeh (2011) defined Z-numbers, which provide a vague assessment and an idea of their reliability. Both can be expressed by linguistic variables. As perceptions of welfare dimensions and its indicators are heterogeneous and given that it is also interesting to value its impact, it is important to identify opinions and the frequency of those perceptions together. In this paper, it is presented a subjective valuation index of economic welfare with Z-information. To show how the model works, it is defined and calculated for one of the dimensions associated with household economic welfare: health system access. Identical procedure will be able to be extended to all the dimensions determined to measure wellbeing. [ABSTRACT FROM AUTHOR]

Several multidimensional poverty indices have been proposed, and have been extensively studied in the literature. On the other hand, the need for aggregation of poverty indicators into one multidimensional index has been questioned. It has been argued even so that this aggregation can be misleading for political targeting strategies. Subsequently, some researchers have advocated that the use of the latent class analysis would address these issues. However, this setting does not allow to take into account the fuzzy nature of the latent poverty concept. The contribution here is to use the Grade-of-Membership (GoM) model to profile the fuzzy latent structure of multidimensional poverty, for a more realistic handling of this phenomenon. The application of the GoM methodology to multivariate poverty data for the Tunisian case reveals four most prevalent multidimensional poverty profiles. The results emphasize the role played by contextual effects. Indeed, the rural cluster is suffering more intense deprivation and groups in the central and coastal regions have a more comfortable status in comparison with the group of households residing in inland regions. A thorough analysis of these patterns is put forward in this research, giving valuable insights to policy makers. [ABSTRACT FROM AUTHOR]

This paper presents the reliability analysis on the basis of the foundation failure against bearing capacity using the concept of fuzzy set theory. A surface strip footing is considered for the analysis and the bearing capacity is estimated using the conventional Finite Element Method (FEM). The spatial variability of the variables is taken into consideration to capture the physical randomness of the soil parameters for an isotropic field. A variation of the probability of failure (Pf) against a varying limiting applied pressure (q) is presented for different Coefficient of Variation (COV) of the variables and different scale of fluctuation (θ). The results reveal that the friction angle of soil (ϕ) is the most influencing parameter among the other variables. Further, the influence of the scale of fluctuation (θ) on the probability of failure (Pf) is also examined. It is observed that for a particular COV of ϕ, higher value of θ predicts higher Pf whereas, Pf increases as COV of ϕ increases for a particular θ value. Later, a comparison study is accomplished to verify the viability of the present method and it can be noticed that the present method compares well with the other reliability method (First Order Reliability Method) to a reasonably good extent. [ABSTRACT FROM AUTHOR]

• Proposing a physical asset criticality analysis decision model based on BIA. • Risk Appetite and physical asset continuity measures are related. • Defining sub-criteria for impact and likelihood estimation in criticality analysis. The paper tackles the issue of managing physical assets in asset-intensive industries, where continuity plans are crucial for business operations during disruptions. However, resource constraints often hinder companies from implementing these plans for all their assets. Moreover, efforts to maximize resource utilization efficiency and minimize environmental impacts are limited to isolated disciplines, necessitating an integrated approach across natural, social, and technological systems. To address these challenges, this study proposes a framework based on a hybrid fuzzy BWM-TOPSIS methodology for identifying critical physical assets. The framework incorporates Business Impact Analysis (BIA) to determine essential products, a physical asset risk assessment matrix (PARAM) to assess critical assets based on likelihood and impact, and a mathematical model to estimate asset continuity parameters. The framework is applied to a petrochemical company in a case study, offering a guide for estimating the probability and impact of physical asset failure while accounting for inherent uncertainties. By adopting this framework, companies can efficiently manage their physical assets, prioritize continuity plans, and address resource constraints and uncertainties. This research contributes to practical tools and approaches that assist industries in sustaining operations and ensuring business continuity during disruptions. [ABSTRACT FROM AUTHOR]

Estimating cost contingency of construction projects depends largely on data captured from previous projects and/or experience and judgment of members of project team. Mote Carlo simulation is commonly used in estimating contingency, where its accuracy was reported to depend on number of iterations used in the simulation process, probability density functions associated with each project cost item being considered and the correlation among these cost items. The literature reveals that the latter is the most important issue for accurate estimate of contingency. It, however, requires the calculation of coefficients of correlation among cost items based on captured historical records of cost data. Subjective correlation was introduced to alleviate the difficulties associated with the calculation of these coefficients. This paper presents a newly developed method for cost contingency estimation that considers subjective correlations and allows for contingency estimation with and without computer simulation. Unlike the methods reported in the literature, the present method considers uncertainty associated with the coefficients of correlation and utilizes earlier work of the first author in calculating the variance of total project cost. It also allows for assessing the impact of variable covariance matrix on the estimated project cost using a simple and user-friendly computational platform. The application of the developed method on cost data captured from two databases demonstrates its use and accuracy in estimating cost contingency. The results are compared to those produced by others using Monte Carlo Simulation with and without correlation using an actual project data. [ABSTRACT FROM AUTHOR]

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Multiple routes of networks in fuzzy environments are essential issues in the project scheduling problems (PSPs) with resource constraints, fuzzy RCPSP-MR. Route assignment to flexible work package defined in a project activity network indicates more complexities in front of canonical PSP. Also, in the last few decades, considering uncertainties' concepts in project schedules have been essential and attracted the attention of researchers and project managers. Therefore, in this article, a new weighted mathematical model is presented under uncertainty conditions, and a new hybrid fuzzy approach is provided via two fuzzy primary methods. Then, a new four-part non-distinct (FPND) approach is proposed based on PSO, binary particle swarm optimization (BPSO) and genetic algorithm (GA) to minimize project end cost. In this approach as the first part and to generate high-quality primary routes for flexible work package, six different rules are investigated, and the appropriate route is chosen. In the second part, initial solutions are generated via PSO. Then, in the third part, initial solutions are improved based on GA. Finally, in the last part, assigned routes are improved with binary PSO. To appraise the effectiveness of the presented approach, influential parameters are tuned by Taguchi method. Finally, to evaluate the performance of FPND, 70 numerical examples are designed in different dimensions, and results are compared with other well-known algorithms. [ABSTRACT FROM AUTHOR]

Based on the analysis of traditional calculation method of RPN (Risk Priority Number), a risk assessment method for CNC lathes based on failure data and fuzzy set theory combining with grey theory was proposed in this paper. Severity, occurrence and detection were treated as linguistic variables. Meanwhile, failure data was applied and maintenance time was introduced as another variable. Risk prioritization of all the failure modes was obtained through steps such as expert rating, solving α level sets, defuzzification and so on. Grey theory was applied to verify the accuracy of the proposed method. The method was used in a real case of risk analysis of spindle system of a CNC lathe, in which consistency and practicability of the results were illustrated. It can be concluded that the proposed method can take advantage of failure data and control subjectivity in analysis. In addition, importance weights of the four variables were taken into consideration. So that the drawbacks of traditional RPN analysis can be avoided and improvement measures could be made by designers and technologists according to the results so as to improve reliability of CNC lathes. [ABSTRACT FROM AUTHOR]

The development of a scientific discipline is partly determined by the growth of its literature. Bibliometrics constitute a set of mathematical and statistical techniques employed to explore, organize, and quantitatively analyze large pools of scientific literature. In this study, 11,433 papers published between 1974 and 2015 are collected and analyzed by applying life-cycle analysis, bibliometrics and text mining in order to provide a full thematic overview of the application of fuzzy theory in operations management. Top countries (i.e. the most productive, influential and collaborative countries), most frequently cited journals, and key research topics are identified by employing bibliometric techniques. Finally, the articles' common research themes and methodologies are determined by combining text mining with experts' input. Results show that the application of fuzzy theory in operations management is still in its infancy, and hence suitable for future research. This study serves as a guide for researchers to identify the hidden patterns, key actors, topics, and methods in this area. [ABSTRACT FROM AUTHOR]

A number of chronic poverty measures are now empirically applied to quantify the prevalence and intensity of chronic poverty, vis‐à‐vis transient experiences, using panel data. Welfare trajectories over time are assessed in order to identify the chronically poor and distinguish them from the non‐poor, or the transiently poor, and assess the extent and intensity of intertemporal poverty. We examine the implications of measurement error in the welfare outcome for some popular discontinuous chronic poverty measures, and propose corrections to these measures that seeks to minimize the consequences of measurement error. The approach is based on a novel criterion for the identification of chronic poverty that draws on fuzzy set theory. We illustrate the empirical relevance of the approach with a panel dataset from rural Ethiopia and some simulations. [ABSTRACT FROM AUTHOR]

Condition information is essential to develop effective facility management (FM) strategies. Visual inspections and walk-through surveys are common practices of condition assessment (CA), generally resulting in qualitative and subjective outcomes such as “poor”, “good”, etc. Furthermore, limited resources of the FM process demand that CA practices be efficient. Given these, the purpose of this study is to develop a resource efficient quantitative CA framework that can be less subjective in establishing a condition rating. The condition variables of the study—mean time between failures, age-based obsolescence, facility condition index, occupant feedback, and preventive maintenance cycle—are identified through different sources, such as a computerized maintenance management system, expert opinions, occupants, and industry standards. These variables provide proxy measures for determining the condition of equipment with the implementation example for heating, ventilating, and air conditioning equipment. Fuzzy sets theory is utilized to obtain a quantitative condition rating while minimizing subjectivity, as fuzzy sets theory deals with imprecise, uncertain, and ambiguous judgments with membership relations. The proposed CA framework does not require additional resources, and the obtained condition rating value supports decision-making for building maintenance management and strategic planning in FM, with a comprehensive and less subjective understanding of condition.

Resumen. Los Recursos Humanos constituyen los únicos elementos vivos presentes en todo tipo de organización, quienes, a partir de sus conocimientos, habilidades y motivaciones, impulsan a las empresas a ser competitivas y a alcanzar sus metas. En aras de lograr dicho objetivo se hace necesario contar con herramientas que ayuden a que el proceso de toma de decisiones concerniente a la gestión de los mismos sea lo más certeros y objetivos. El presente trabajo propone un modelo de gestión de recursos humanos que integra herramientas basadas en la teoría de los subconjuntos borrosos. La investigación se encuentra estructurada en tres epígrafes. El primero analiza los modelos utilizados en Cuba para gestionar los recursos humanos. El segundo presenta el Modelo de Gestión de los Recursos Humanos que se propone, para finalmente, en un tercer epígrafe proceder a validarlo. La novedad del trabajo que se propone, radica en la integración de herramientas de la teoría de los subconjuntos borrosos en los procesos claves de la Gestión de los Recursos Humanos. Entre sus aportes se encuentran: la aplicación del método de alisado exponencial borroso a la planeación del personal, la extrapolación de un modelo de asignación resuelto a través del algoritmo húngaro a la formación del personal, así como la construcción de un sistema de indicadores borrosos para la evaluación de la Gestión de los Recursos Humanos. La propuesta fue validada a través de aplicaciones parciales en empresas seleccionadas así como con criterio de expertos. English abstract. Human resources are the only living elements present in all types of organizations who, from their knowledge, skills and motivations driving companies to be competitive and achieve their objectives and goals. In order to achieve this objective it is necessary to have tools that help the decision-making process regarding the management of human resources is as accurate and objective as possible. This paper proposes a Human resources management model based on fuzzy subsets theory to help reduce subjectivity that may be implied in these processes tools. This paper has been structured in three epigraphs. The first one presents an analysis of the Human Resources management Models used in Cuba. The second present the proposal of the Human Resources Management Model based on fuzzy subsets theory and finally on third epigraph the proposal is validated. The novelty of the proposed work lies in the integration of tools of the theory of fuzzy subsets in the key processes of Human Resources Management. Among the main contributions are: the application of the method of fuzzy to planning staff exponential smoothing, extrapolation of an allocation model solved through the Hungarian algorithm to staff training and building a system of fuzzy indicators for the evaluation of Human Resources Management. The proposal was validated through partial applications in companies in GECOMEX well as expert judgment.

The threat evaluation is significant component in target classification process and is significant in military and non military applications. Small errors or mistakes in threat evaluation and target classification especial in military applications can result in huge damage of life and property. Threat evaluation helps in case of weapon assignment, and intelligence sensor support system. It is very important factor to analyze the behavior of enemy tactics as well as our surveillance. This paper represented a precise description of the threat evaluation process using fuzzy sets theory. A review has been carried out regarding which parameters that have been suggested for threat value calculation. For the first time in this paper, eleven parameters are introduced for threat evaluation so that this parameters increase the accuracy in designed system. The implemented threat evaluation system has been applied to a synthetic air defense scenario and four real time dynamic air defense scenarios. The simulation results show the correctness, accuracy, reliability and minimum errors in designing of threat evaluation system

Abstract Design and performance of stormwater infrastructure systems in urban areas have direct implications in social, environmental and public health problems and are of utmost importance to urban authorities and managers. Risk analysis in urban stormwater systems has become a must because of the extensive consequences of flooding in urban areas and limited funding for the rehabilitation and renovation of stormwater systems. Complexity, multidimensionality, and inherent uncertainties of the urban stormwater systems require the risk analysis approach to be comprehensive and able to address different uncertainties and spatial aspects of the problem. The objective of this study is to provide a comprehensive framework for risk analysis in urban stormwater systems. Multi Criteria Decision Making (MCDM), geographic information systems (GIS), and fuzzy sets theory are used to consider the diverse risk-affecting criteria, facilitate the analysis of spatial data and information and formulate the ambiguity and uncertainty of problem, respectively. The presented framework uses a Fuzzy Analytic Hierarchy Process (FAHP) for determining the weights of risk-affecting criteria (i.e. Hydrological and Hydraulic, Traffic, Social, Economic, Environmental, Structural, and Green space) in the presence of multiple decision makers. The Autodesk Storm and Sanitary Analysis model is used for the Hydrological and Hydraulic simulations. FSAW and FTOPSIS methods are used to provide the final product of the framework, i.e., a risk map that presents a risk level for each channel in the network. The framework is applied to District 11 of the capital city of Iran, Tehran as a real case study. The resulted risk maps indicate a high or very high flooding risk for 17.07 to 41.95 km of the stormwater channels in the study area, covering about 10.5 to 26% of the total length of the channels. The presented framework was found to be a suitable risk analysis tool in urban stormwater systems. Graphical abstract Unlabelled Image Highlights • Urban stormwater systems failure can lead to flooding risk and different problems. • A spatial MCDM based risk analysis framework for these systems is developed. • Inherent uncertainties are considered by applying Fuzzy sets theory. • The framework is employed for risk assessment in a central district in Tehran, Iran. [ABSTRACT FROM AUTHOR]