Non-statistical Uncertainty Research Articles

Estimating the Duration of Construction Works Using Fuzzy Modeling to Assess the Impact of Risk Factors

One of the most pressing issues in the implementation of construction projects is the extension of planned deadlines, significantly impacting project costs. This situation often arises due to inaccurate estimation of construction durations, which rely on normative values without accounting for factors hindering construction progress. Consequently, this article aims to develop an innovative approach for assessing construction durations, considering specific risk factors and their influence on construction activities. Given the difficulty of determining risk factors and their effects during the design phase using classical probability theory, characterized by unknown probability distributions, it is highlighted that this scenario represents planning and implementation under conditions of non-statistical uncertainty. Therefore, the article proposes an approach utilizing elements of fuzzy set theory, particularly fuzzy rules and linguistic variables, to determine delays in individual construction tasks. The proposed approach involves estimating extensions of construction timelines based on a specified probability level of occurrence for risk events and their impact. Additionally, the article provides a theoretical description of the proposed approach and practical calculation examples, demonstrating that the authors’ approach significantly enhances the accuracy of construction timeline forecasts, providing more reliable data for project planning and management.

Evaluation and choice of an anti-aircraft missile system under uncertain conditions based on fuzzy-integral calculus and hierarchical cluster analysis

Evaluation and choice of anti-aircraft missile weapon systems (AAMWSs) are a relevant problem in many countries. Estimates are often reduced to one top-level criterion. This is questionable since subordinated criteria are usually difficult to compare and decision-makers excluded from the final decision. The solution to the problem should also take into account non-statistical uncertainty. We propose to use a combination of two algorithms. The first algorithm calculates the estimates of AAMWSs in the criteria hierarchy using fuzzy-integral calculus. The hierarchy relates the characteristics of the AAMWSs to the three top-level criteria. In the space of these criteria, the second algorithm based on hierarchical clustering forms a class of the best AAMWSs equivalent to each other. The decision-maker makes the final choice from the obtained class, taking into account non-formalized factors. These algorithms are tested using the example of medium-range AAMWSs.

Statistical Quality Control: Acceptance Sampling Plans in the Light of Fuzzy Mathematics

Statistical quality control is a productivity enhancing and regulatory technique with three factors––Management, Methods and Mathematics. More precisely, if we want to properly design a self-regulating system for quality, we have to look to the field of cybernetics for design information. Quality improvement management aims to decrease variability, which leads to decrease the costs, the production time, the number of defects, scrap, rework,––and increase the customer satisfaction. Many problems in these scientific investigations generate non-precise data incorporating non-statistical uncertainty. A non-precise observation of a qualitative variable can be described by a special type of membership function defined on the set of all real numbers called a fuzzy number. In this paper, I have thoroughly discussed Acceptance sampling plans (Single, Double, Chain and Sequential) by attributes with the help of fuzzy parameters (mainly by fuzzy Poisson distribution and hypotheses testing). Finally many examples have been used and at last the paper ends with a comparative study.

Методика построения плана диагностического исследования профессионального соответствия кандидатов в системах профессионального отбора

Modern methods of selecting specialists are based on using a whole range of testing tools for candidates. However,
 there are cases when applying the entire complex of means is not appropriate. For instance, such a situation may occur
 during a candidate’s career growth, when his or her psychological and professional characteristics are generally known
 and only specific clarifications are required to make a decision on a new position. In this case, a set of tests can be formed
 taking into account the analysis of the candidate’s previous activities.
 Definitely, such a set of tests also implies a certain sequence of their application in the course of analysing the
 candidates’ potential properties. In this case, the criterion basis for choosing the sequence of applying the tests will be the
 test analysis time (number of steps) and the cost of testing the candidate’s degree of professional compliance. The
 significant non-statistical uncertainty of the candidates’ outcomes of test checks (answers) is also necessary to take into
 account.
 The proposed article considers the problem of a priori planning of the procedure for using test tools for diagnosing the
 candidates’ degree of professional compliance based on a preliminary fuzzy assessment of their professional and personal
 characteristics. Solving the problem is reduced to a sequential (step by step) analysis of fuzzy preference relations of the
 candidates’ degree of professional compliance. At the same time, the composition of diagnostic tools is selected taking into
 account their reliability, followed by determining the most non-dominated alternatives for decisions. The decision-making
 is based on a fuzzy information-cost criterion. Applying this approach allows proposing a methodology for planning
 activities for assessing the candidates’ compliance degree with different levels of competence.

Sensor network control based on randomized and multi-agent approaches

In this paper, a development of randomized and multiagent algorithms is presented. The examples and their advantages are discussed. Different combined algorithms which are applicable for the multi-sensor multitarget tracking problem are shown. These algorithms belong to the class of methods used in derivative-free optimization and has proven efficacy in the problems including significant non-statistical uncertainties. The new algorithm which is an Accelerated consensus-based SPSA algorithm is validated through simulation.The main feature of that algorithm, combining the SPSA techniques, iterative averaging (“Local Voting Protocol”) and Nesterov Acceleration Method, is the ability to solve distributed optimization problems in the presence of signals with fully uncertain distribution; the only assumption is the signal’s limitation.

Value Creation and Investment Projects: An Application of Fuzzy Sensitivity Analysis to Project Financing Transactions

This paper presents a methodology which blends sensitivity analysis (SA) and fuzzy arithmetic for managing uncertainty in project financing transactions. Specifically, we adopt the perspective of the equityholders and use the average return on equity (ROE) to measure shareholder value creation and, in particular, the financial efficiency of the equity investment. We cope with uncertainty via global and local SA and fuzzy arithmetic; we use the fuzzy version of the well-known (global) Gamma indicator and we introduce the fuzzy versions of two (local) importance measures, the differential importance measures (DIM). We then apply them to the pro forma financial statements drawn up by the analyst for measuring and ranking the impact of the key accounting parameters on the resulting values and we show how the uncertain accounting and financial magnitudes of the project company affect the financial efficiency. Among the advantages of this analysis, aimed to enhance the managerial insights generated by the financial model and to lead to appropriate managerial actions, we focus on the attractiveness of fuzzy calculus and possibility theory to represent and compute all relevant financial data that appear in project financing and budgeting, where available information is characterized by incompleteness or nonstatistical uncertainty. In this context, fuzzy computing and appropriate SA techniques, based on application of the extension principle, allow complete investigation of the project characteristics.

Novel Distance and Similarity Measures for Probabilistic Hesitant Fuzzy Set and Its Applications in Stock Selection Problems

The consensus of randomness and ambiguity exists in real world problems. To depict fuzziness, randomness and statistical ambiguity in a single framework, we develop an interactive approach to MCDM method, in which assessment of alternative over attributes are provided by probabilistic hesitant fuzzy elements (PHFEs). This method provides a tool to the decision makers for reasonable ranking of alternatives. The core intention of this paper is to define a series of novel distance and similarity measures and score function for PHFEs. To demonstrate the effectiveness of developed model, a real case study is taken as an example. To completely describe statistical and non-statistical uncertainty, suitable probability distribution function is associated with each element of constructed HFSs. The proposed method is more superior to other MCDM methods, because of introducing probabilistic information in HFEs, which can be helpful to ensure the integrality and accurateness of hesitant fuzzy information.

Possible Scenarios for Reduction of Carbon Dioxide Emissions in Serbia by Generating Electricity from Natural Gas

The main purpose of this paper is to develop possible scenarios for reducing carbon dioxide (CO2) emissions in Serbia by switching from coal-fired to natural gas-fired electricity generation by the end of 2050. Accordingly, the challenges are to establish scenarios and identify measures that are best suited to all Western Balkan countries. In particular, this paper proposes a number of energy mix scenarios that offer some options for reducing CO2 emissions while maintaining an economic way of consumption. Projections of these reduction scenarios are obtained by combining the Kaya identity with the emission factor method. A simplified methodology based on sensitivity analysis is used as a source of data to estimate the nonstatistical uncertainty limits for the projections of the reduction scenarios. The sensitivity analysis is carried out using historical data from Serbia for the period from 1990 to 2019. In addition, a direct verification of the proposed methodology is performed based on historical data for 2020. The developed scenarios 1 and 2 show that CO2 emissions could be reduced by 10.94% and up to 74.44% from baseline in 1990, respectively. The obtained results are also contrasted with the data available for some other countries with similar experiences. Finally, it is found that the developed scenarios are achievable only at significantly decreased levels of coal-fired electricity generation.

Complex probabilistic fuzzy set and their aggregation operators in group decision making extended to TOPSIS

Randomness and fuzziness create uncertainty in the system at the same time. To combine randomness and cognitive uncertainty into a single paradigm and incorporate more data, this article focuses on developing complex probabilistic fuzzy set. The main intention of this article is to develop a method that can solve both statistical and non-statistical uncertainties. Statistical uncertainty depicts the type of uncertainty concerning the possibility of a future event occurring and non-statistical uncertainties denote the concept of partial truth and imprecise reason. Here, statistical uncertainty is given through probability and non-statistical uncertainty is denoted via the complex fuzzy sets and are incorporated together to form the complex probabilistic fuzzy set. This combination summarizes the importance of this article as they could depict the real life situations more precisely. Proposing the complex probabilistic fuzzy set and studying its basic operations are the article’s main contributions. Also, various aggregation operators are developed for the same and their essential properties are duely explained. Further on, these operators are extended to TOPSIS which is utilized for a group decision making problem with data obtained in the form of complex probabilistic fuzzy number to find the best site for construction of ethanol plant to produce biofuel. The main reason for considering TOPSIS here is because it is a concept that formulates a scalar value taking into consideration both the best and worst alternatives, it represents the rationale of human choice in a more simplistic and straightforward logic and also, it takes less computation time.

Assessment and Enhancement of Hopf Bifurcation Stability Margin in Uncertain Power Systems

Uncertainties in the forecasted load and generation can have a catastrophic impact on power system stability. For a reliable power supply, a sufficient dynamic stability margin is always desired. This paper introduces a novel boundary eigenvalue-based approach for the determination of Hopf Bifurcation Stability Margin (HBSM), which, explicitly, accounts for the impact of uncertainties in specified renewable generation and loads. Since the Hopf bifurcation stability problem is nondeterministic, it requires large computational efforts to determine the HBSM. Most of the available methods are based on statistical data, which are computationally less efficient for such applications. In this paper, a non-statistical uncertainty based control rescheduling strategy is proposed to enhance the stability margin of the system. To balance the trade-off between solution quality and computation time, the proposed approach is composed of two stages: i) determination of boundaries of critical eigenvalues; and ii) optimal setting of the controllers by minimization of a boundary active power loss based objective function under the given range of uncertainties. The proposed approach is demonstrated on standard IEEE test systems with promising results to show the importance and its reliability.

Probabilistic hesitant fuzzy set based MCDM method with applications in Portfolio selection process

Uncertainty management in decision making problems (DMPs) is a big issue for researchers. To completely depict statistical and non-statistical uncertainty in a single framework a hesitant probabilistic fuzzy set based MCDM method is developed. The developed probabilistic hesitant fuzzy (PHF) based decision-making framework is better than the other MCDM methods. In this work of HFEs, a probabilistic information is introduced which makes this method useful in order to ensure the integrality and the accuracy of hesitant fuzzy information. To illustrate developed method, a real case study is taken to find the ranking of stock organizations using real data.

Estimating the Number of Illnesses Caused by Agents Transmitted Commonly Through Food: A Scoping Review.

Estimates of the overall human health impact of agents transmitted commonly through food complement surveillance and help guide food safety interventions and regulatory initiatives. The purpose of this scoping review was to summarize the methods and reporting practices used in studies that estimate the total number of illnesses caused by these agents. We identified and included 43 studies published from January 1, 1995, to December 31, 2019, by searching PubMed and screening selected articles for other relevant publications. Selected articles presented original estimates of the number of illnesses caused by ≥1 agent transmitted commonly through food. The number of agents (species or subspecies for pathogens) included in each study ranged from 1 to 31 (median: 4.5; mean: 9.2). Of the 40 agents assessed across the 43 studies, the most common agent was Salmonella (36; 84% of studies), followed by Campylobacter (33; 77%), Shiga toxin-producing Escherichia coli (25; 58%), and norovirus (20; 47%). Investigators used a variety of data sources and methods that could be grouped into four distinct estimation approaches-direct, surveillance data scaled-up, syndrome or population scaled-down, and inferred. Based on our review, we propose four recommendations to improve the interpretability, comparability, and reproducibility of studies that estimate the number of illnesses caused by agents transmitted commonly through food. These include providing an assessment of statistical and nonstatistical uncertainty, providing a ranking of estimates by agent, including uncertainties; describing the rationale used to select agents and data sources; and publishing raw data and models, along with clear, detailed methods. These recommendations could lead to better decision-making about food safety policies. Although these recommendations have been made in the context of illness estimation for agents transmitted commonly through food, they also apply to estimates of other health outcomes and conditions.

Diversified behavioral portfolio as an alternative to Modern Portfolio Theory

The traditional mean–variance approach has been complemented by alternative theories that use risk measures different from standard deviation of returns or involve additional distributional features of returns like skewness and kurtosis. We propose a portfolio choice model that combines different distributional characteristics of the returns in the decision-making making process, considering preferences of investors which are modeled as non-statistical uncertainties of investors using fuzzy theory. We use 20 stocks of the S&P500 from January 2013 to December 2017. We assess the obtained portfolios’ performance, and the diversified behavioral portfolios outperform than the mean–variance portfolio. This methodological proposal can be seen as a strong managerial tool to make investment portfolio decisions.

Development of a Multiphase Beryllium Equation of State and Physics-based Variations.

We construct a family of beryllium (Be) multiphase equation of state (EOS) models that consists of a baseline ("optimal") EOS and variations on the baseline to account for physics-based uncertainties. The Be baseline EOS is constructed to reproduce a set of self-consistent data and theory including known phase boundaries, the principal Hugoniot, isobars, and isotherms from diamond-anvil cell experiments. Three phases are considered, including the known hexagonal closed-packed (hcp) phase, the liquid, and the theoretically predicted high-pressure body-centered cubic (bcc) phase. Since both the high-temperature liquid and high-pressure bcc phases lack any experimental data, we carry out ab initio density functional theory (DFT) calculations to obtain new information about the EOS properties for these two regions. At extremely high temperature conditions (>87 eV), DFT-based quantum molecular dynamics simulations are performed for multiple liquid densities using the state-of-the-art Spectral Quadrature methodology in order to validate our selected models for the ion- and electron-thermal free energies of the liquid. We have also performed DFT simulations of hcp and bcc with different exchange-correlation functionals to examine their impact on bcc compressibility, which bound the hcp-bcc transition pressure to within 4 ± 0.5 Mbar. Our baseline EOS predicts the first density maximum along the Hugoniot to be 4.4-fold in compression, while the hcp-bcc-liquid triple-point pressure is predicted to be at 2.25 Mbar. In addition to the baseline EOS, we have generated eight variations to accommodate multiple sources of potential uncertainties such as (1) the choice of free-energy models, (2) differences in theoretical treatments, (3) experimental uncertainties, and (4) lack of information. These variations are designed to provide a reasonable representation of nonstatistical uncertainties for the Be EOS and may be used to assess its sensitivity to different inertial-confinement fusion capsule designs.

On soft set-valued maps and integral inclusions

As an improvement of fuzzy set theory, the notion of soft set was initiated as a general mathematical tool for handling phenomena with nonstatistical uncertainties. Recently, a novel idea of set-valued maps whose range set lies in a family of soft sets was inaugurated as a significant refinement of fuzzy mappings and classical multifunctions as well as their corresponding fixed point theorems. Following this new development, in this paper, the concepts of e-continuity and E-continuity of soft set-valued maps and αe-admissibility for a pair of such maps are introduced. Thereafter, we present some generalized quasi-contractions and prove the existence of e-soft fixed points of a pair of the newly defined non-crisp multivalued maps. The hypotheses and usability of these results are supported by nontrivial examples and applications to a system of integral inclusions. The established concepts herein complement several fixed point theorems in the framework of point-to-set-valued maps in the comparable literature. A few of these special cases of our results are highlighted and discussed.

A novel probabilistic intuitionistic fuzzy set based model for high order fuzzy time series forecasting

The present research proposes a novel probabilistic intuitionistic fuzzy time series forecasting (PIFTSF) model using support vector machine (SVM) to address both uncertainty and non-determinism associated with real world time series data. In this model, the probability of membership values of crisp observation is determined to handle the statistical uncertainty. At the same time, the intuitionistic fuzzy element of crisp observation is determined to handle the non-statistical uncertainty along with non-determinism. Then, both the membership values are aggregated to obtain the probabilistic intuitionistic fuzzy element which handles both statistical and non-statistical uncertainty along with non-determinism due to hesitancy. Additionally, a novel trend-based discretization (TBD) method is proposed to determine the universe of discourse and number of intervals (NOIs) of fuzzy time series (FTS). For the first time, the fuzzy logical relationships (FLRs) are established for the probabilistic intuitionistic fuzzy set by considering the ratio trend variation (RTV) of crisp observation along with the mean of aggregated membership values which is modelled using SVM. The efficiency of the proposed PIFTSF model is demonstrated with sixteen diversified time series datasets and seven existing FTS models. A sensitivity analysis is carried out with respect to different design strategies to ensure the robustness of the proposed model. Extensive statistical analyses on obtained results confirm the superiority of the proposed model over other existing models. Further, Wilcoxon signed rank test, and Friedman and Nemenyi hypothesis test ensures the accuracy, robustness and reliability of the proposed model against its counterparts.

Fuzzy portfolio optimization for time-inconsistent investors: a multi-objective dynamic approach

In recent years, fuzzy optimization has been widely adopted to handle the nonstatistical uncertainties in portfolio selection. Meanwhile, various risk measurements, including variance, entropy and value at risk, have been introduced in fuzzy environments to evaluate portfolio risks from different perspectives. In this study, we discuss fuzzy multi-objective dynamic portfolio optimization for time-inconsistent investors. When building the model, variance and value at risk as the representatives of different types of risk measurements are employed together with the expected return. And a dynamic investment policy is developed for time-inconsistent investors, which combines the expected return and value at risk into one objective. Then, the model is established to maximize the cumulative combined objective function and minimize the cumulative portfolio variance simultaneously. In addition, a multi-objective dynamic evolutionary algorithm is designed as a possible solution of the proposed model. The effectiveness of this research is demonstrated by using a real market data-based case study. Experimental results demonstrate that the proposed model matches the practical behavior of time-inconsistent investors and the solution algorithm is feasible to solve the complicated nonlinear problem.

Simulation of live-cell imaging system reveals hidden uncertainties in cooperative binding measurements.

We propose a computational method to quantitatively evaluate the systematic uncertainties that arise from undetectable sources in biological measurements using live-cell imaging techniques. We then demonstrate this method in measuring the biological cooperativity of molecular binding networks, in particular, ligand molecules binding to cell-surface receptor proteins. Our results show how the nonstatistical uncertainties lead to invalid identifications of the measured cooperativity. Through this computational scheme, the biological interpretation can be more objectively evaluated and understood under a specific experimental configuration of interest.

A Multi-Objective Portfolio Selection Model With Fuzzy Value-at-Risk Ratio

Considering nonstatistical uncertainties and/or insufficient historical data in security return forecasts, fuzzy set theory has been applied in the past decades to build portfolio selection models. Meanwhile, various risk measurements such as variance, entropy, and Value-at-Risk have been proposed in fuzzy environments to evaluate investment risks from different perspectives. Sharpe ratio, also known as the reward-to-variability ratio, which measures the risk premium per unit of the nonsystematic risk (asset deviation), has received great attention in modern portfolio theory. In this study, the Sharpe ratio in fuzzy environments is introduced, whereafter, a fuzzy Value-at-Risk ratio is proposed. Compared with Sharpe ratio, Value-at-Risk ratio is an index with dimensional knowledge that reflects the risk premium per unit of the systematic risk (the greatest loss under a given confidence level). On the basis of the two ratios, a multi-objective model is built to evaluate their joint impact on portfolio selection. Then, the proposed model is solved by a fuzzy simulation based multi-objective particle swarm optimization algorithm, where the global best of each iteration is determined by an improved dominance times based method. Finally, the algorithm superiority is justified via comparing with existing solvers on benchmark problems, and the model effectiveness is exemplified by using three case studies on portfolio selection.

Design of Multi-Machine Power System Stabilizers with Forecast Uncertainties in Load/Generation

ABSTRACTOscillatory instability in modern power system has increased due to increasing complexity and integration of dynamic loads. Stability analysis of such interconnected power system is very prominent in the presence of uncertain load/generation. In this paper, a power system stabilizer (PSS) design approach, which aims at enhancing the oscillatory stability of the multi-machine power system over the specified uncertainty range in forecasted load/generation, is presented. With non-statistical uncertainty, problem of selecting design parameters of the PSS is formulated as an optimization problem with minimization of eigenvalues and damping ratios based multi-objective function. In order to account the non-statistical uncertainties, a boundary active power loss (BAPL) based objective function is proposed. This non-linear BAPL objective function is minimized for determining the optimal setting of the generators voltage and taps of the online tap changing transformers (OLTC) under various power system constraints. In this paper, both the objective functions are solved by a new metaheuristic technique known as gray wolf optimization (GWO). Boundary value-based approach is used to minimize the repeated load flows under uncertain load/generation scenarios. Improved small-signal stability (SSS) is achieved with optimal active power loss of uncertain power system. Eigenvalue and time domain analysis for New England system are carried out under wide range of disturbances to demonstrate the potential of the proposed approach.