Real-life Numerical Example Research Articles

A two-stage optimization model for relief distribution to disaster survivors under two-fold uncertainty

Disasters are unforeseen occurrences requiring extensive transport deployment to support and relieve victims. Sometimes, this transportation is not feasible directly from some supply points to some destination points. Due to this tragedy, it is unclear precisely what is available at supply points, what is needed at destinations, how much transportation capacity there is, and what the routes are like. In this study, we investigate a two-stage multi-item fixed charge four-dimensional transportation problem using the concept of big data theory under the two-fold uncertainties. Here, the model’s parameters such as unit transportation costs, availabilities of items at the suppliers, fixed charges, capacities of conveyances, and demands of the items at the retailers are considered type-2 zigzag uncertain variables. Using big data theory and based on uncertain programming theory, two novel uncertain models are developed such as chance-constrained programming and expected value programming model. These two uncertain models transformed into the deterministic form via uncertainty inverse distribution theory. A critical value based reduction method with three categories (i.e., expected value, pessimistic value, and optimistic value) is applied to reduce the type-2 zigzag uncertain variable to the type-1 zigzag uncertain variable. The genetic algorithm and particle swarm optimization techniques have been proposed to find the optimal solution for the two deterministic models. The efficiency of our proposed approach is demonstrated with a real-life numerical example.

Performance of load sharing repairable k-out-of-N: G systems

The aim of this research is to explore the performance of load-sharing k-out-of-n: G systems. In such structures, the system operates if at least k components function. Furthermore, in load sharing systems, the load is automatically transferred to the functional components that are still in place whenever one component fails. In this article, asymptotic availability and mean time to failure (MTTF) are used for measuring the system performance assuming exponentially distributed repair times and times between failures. Results indicate that in selecting any configuration over others, we should not only consider the system's performance but also the total cost. For illustrations, the article exhibits a real-life numerical example.

A novel type-2 hexagonal fuzzy logic approach for predictive safety stock management for a distribution business

Safety stock is an important method to overcome variability in inventory management. The classical approach to safety stock decisions relies on historical demand and lead time statistical data, which may not capture the uncertainty and complexity of the real world. Human knowledge and experience are valuable assets for making better decisions, especially when facing unpredictable situations. The fuzzy method is widely used for employing human intuition for decisions. When fuzzy opinions are input, decisions can be made proactively rather than reactively while benefiting from future predictions. The paper aims to integrate human intuition using Hexagonal Type-2 Fuzzy Sets (HT2FS) for safety stock management. HT2FS is a generalization of Interval Type-2 Fuzzy Sets that can represent more uncertainty in the membership functions. Predictions may be integrated into the safety stock models using human intuition. The proposed model uses novel fuzzy approaches to integrate human intuition into the traditional safety stock model. Applying fuzzy sets to safety stock management allowed experts' opinions under fuzzy logic to be integrated into decision-making. The proposed novel approach uses the centre of gravity method of Polygonal Interval Type-2 Fuzzy sets for defuzzification, which is a computationally efficient method that can handle any shape of the footprint of uncertainty. A mathematical model is developed to validate fuzzy opinions that may replace historical data. The data is received from a real-life case, and human intuition is integrated using an expert’s input. After the validation, a real-life numerical example has been considered to illustrate the model and its validity compared to the classical model. The outcomes show that the proposed model may contribute to the classical models, mainly when experts' inputs offer good predictions. When expert opinion on HT2FS is used for a real-life case, the results show that the expert's better representation of future variances lowers total cost by 2.8%. The results, coupled with the sensitivity analysis, underline that the proposed approach may contribute to the literature on safety stock management.

Uncertain maximum likelihood estimation for uncertain Von Bertalanffy regression model with real-life data

Regression analysis is a potent tool to explore the relationship of variables and widely used in many areas. Classical statistics assume that the residual of regression model should follow the Gauss-Markov hypothesis. However, in many cases, the data is not obeying this hypothesis particularly real-life data. Therefore, this paper explores the Von Bertalanffy regression model under the framework of the uncertainty theory, and employs the uncertain maximum likelihood estimation (MLE) to estimate the unknown parameters. Furthermore, the uncertain hypothesis test and an algorithm for data modification which aimed to find outliers and modify data are studied, then the forecast value and confidence interval be formulated. Finally, a real-life numerical example of applying the above theories be given, this example shows that the uncertain MLE has better performance compare with the uncertain least squares and the least absolute deviations methods. Consequently, the uncertain MLE is a better way to deal with the real-life data.

Sparse subsampling of flow measurements for finite-time Lyapunov exponent in domains with obstacles

We propose an efficient approach to estimate the finite-time Lyapunov exponent (FTLE). Instead of incorporating all available velocity measurements, we develop a sparse subsampling approach to detect relevant flow measurements for velocity reconstruction. This work has two main contributions. We first extend our previous algorithm in Ng and Leung (2019) to reconstruct a flow field with an impermeable condition. To solve the corresponding under-determined system for reconstructing the global velocity field, we propose a L1 optimization framework that can lead to a sparse reconstruction algorithm. Therefore, the overall algorithm can automatically identify and extract a sparse subset of velocity measurements for the FTLE computations. We will provide synthetic and real-life numerical examples to demonstrate the effectiveness of the proposed algorithm.

A Decision-Making Problem for Selecting an optimal Antivirus Mask over COVID-19 Pandemic under Pythagorean Fuzzy Information Based on Hybrid TODIM - Inferior Ratio Method

Yager was the first who developed the concept of Pythagorean fuzzy sets (PFSs) to tackle uncertainty and vagueness. PFSs is applicable when Intuitionistic fuzzy sets are not able to tackle the uncertainty in real life. In the present paper, based on the concept of Gini-Simpson Entropy, a Pythagorean fuzzy entropy measure is introduced under Pythagorean fuzzy environment. The maximality feature and monotonic behaviour of the developed information measure have been presented to satisfy some elegant mathematical properties which prepare the ground for applications in various disciplines. We extend the TODIM-Inferior ratio method for solving the (MCDM) multicriteria decision-making problems where the behaviour of experts, are taken into consideration. The proposed Pythagorean information measure has been established based on the different cases when weights are partially known. A real-life numerical example has been successfully illustrated to demonstrate the flexibility and efficacy of the developed method.

Utilization of biological variation data in the interpretation of laboratory test results - survey about clinicians' opinion and knowledge.

IntroductionTo interpret test results correctly, understanding of the variations that affect test results is essential. The aim of this study is: 1) to evaluate the clinicians’ knowledge and opinion concerning biological variation (BV), and 2) to investigate if clinicians use BV in the interpretation of test results.Materials and methodsThis study uses a questionnaire comprising open-ended and close-ended questions. Questions were selected from the real-life numerical examples of interpretation of test results, the knowledge about main sources of variations in laboratories and the opinion of clinicians on BV. A total of 399 clinicians were interviewed, and the answers were evaluated using a scoring system ranked from A (clinician has the highest level of knowledge and the ability of using BV data) to D (clinician has no knowledge about variations in laboratory). The results were presented as number (N) and percentage (%).ResultsAltogether, 60.4% of clinicians have knowledge of pre-analytical and analytical variations; but only 3.5% of them have knowledge related to BV. The number of clinicians using BV data or reference change value (RCV) to interpret measurements results was zero, while 79.4% of clinicians accepted that the difference between two measurements results located within the reference interval may be significant.ConclusionsClinicians do not use BV data or tools derived from BV such as RCV to interpret test results. It is recommended that BV should be included in the medical school curriculum, and clinicians should be encouraged to use BV data for safe and valid interpretation of test results.

A novel hybrid fuzzy PROMETHEE-IDEA approach to efficiency evaluation

Efficiency evaluation is a desirable kind of a decision making analysis for experts in various fields because if something can be measured, it can also be improved more easily. Measuring efficiency has been a topic of many research studies, and many quantitative methods to deal with this problem under various assumptions have already been established. However, most methods struggle with barriers limiting their use in practice. The aim of this paper is to establish a method for efficiency evaluation which is as traceable as possible, provides a graphical representation of the results, and yields results that are easily interpretable for problems with uncertain input data expressed by fuzzy evaluations. In particular, a new hybrid method for efficiency evaluation is presented. This method is based on a combination of the PROMETHEE (i.e. outranking multi-criteria decision making method) and data envelopment analysis (DEA) under uncertainty, similar to the study published by Ishizaka et al. (Soft Comput 22(22):7325-7338, 2018) who, however, worked only with deterministic data. The PROMETHEE method allows a computationally easy and traceable evaluation of alternatives. The DEA method is currently the most popular method for efficiency evaluation. However, its original version provides a graphical representation only for very simple models. In addition, the results are usually not easy to interpret because it mixes scale-dependent and scale-independent data together. Fuzziness in the DEA model is handled using measures of possibility and necessity, which provide easily interpretable results for a decision maker. In particular, the results reveal to what extent each unit under evaluation can possibly be, or certainly is, efficient. The proposed algorithm is applied to one artificial and one real-life numerical example, and the results are compared with the pure DEA model.

Resilient controller synthesis for Markovian jump systems with probabilistic faults and gain fluctuations under stochastic sampling operational mechanism

In this article, by exploiting the sampling communication mechanism (SCM) with probabilistically switching signals, the dissipativity-based resilient reliable control design problem is addressed for Markovian jump systems (MJSs), which simultaneous against the multiplicate stochastic intermittent actuator faults (MSIAFs) and randomly occurring controller gain fluctuations (ROCGFs). The primary objective of this work is to synthesis a resilient controller such that the underlying MJSs is stochastically stable while meeting an expected (Q,S,R)−ϑ dissipative performance index in the presence of ROCGFs. First and foremost, the randomly occurring actuator faults (ROAFs) and their failures rates are characterized by a series of mutually independent stochastic variables that satisfy prescribed probabilistic distributions for each actuator. The distortion degree and failure rate of each actuator can be quantized and calculated with the help of mathematical variance and expectation respectively. Secondly, the sampling controller with stochastically variable operation periods is considered and just assumed to switch between two different values in stochastic circumstances with certain probability. Thirdly, the nonfragile controller gain fluctuations also happens in a random framework which are obedient to Bernoulli distribution sequence (BDS). Fourthly, by resorting to an appropriately Lyapunov–Krasovskii functional (LKF) and adopting matrix inequality decoupling technique, several sufficient conditions for the solvability of the addressed problem are eventually formulated in the shape of linear matrix inequalities (LMIs). Ultimately, three real-life numerical examples are exploited to illustrate the effectiveness and applicability of the presented theoretical findings.

Fuzzy environment replacement model

This paper focuses on replacement of equipment in fuzzy environment. Fuzzy set theory is the main tool to emphatic the vagueness parameters which involving in many real life applications. All imprecise costs involved in this fuzzy replacement model are taken as triangular fuzzy numbers. The proposed method gives the optimal replacement time of the replacement problem in fuzzy nature and it is validated using a real life numerical example.

A new approach for optimality of fully fuzzy assignment problems

In this paper, we developed an efficient approach for the solution of fully fuzzy assignment problems involving imprecise information without transforming to equivalent precise form. Here, the imprecise information are represented as triangular fuzzy numbers and optimal solution is obtained applying branch and bound method and a new type of arithmetic operations, ranking on triangular fuzzy numbers. The proposed method is validated using a real life numerical example.

Uncertain four-dimensional multi-objective multi-item transportation models via GP technique

In this paper, a new type of four-dimensional multi-objective multi-item transportation problem is established using uncertain theory. We formulate and derive the expected value goal programming model and chance-constrained goal programming model based on the uncertain theory, where unit transportation cost, availabilities, capacities of conveyances, demands, unit transportation time, unit loading and unloading time are represented as uncertain matrices. Based on some properties of uncertain theory, the expected value goal programming model and chance-constrained goal programming model are transformed into the corresponding deterministic equivalents form via the soft computing technique, i.e., generalized reduced gradient technique named by LINGO-14.0. After that, a real-life numerical example is given to illustrate the performance of the models. Finally, the sensitivity analysis of the proposed model is presented through chance-constrained goal programming method with respect to different confidence levels.

An EPQ model of substitutable products under trade credit policy with stock dependent and random substitution

Many retailers are trying to attract more customers by offering the different offers to compete for market share. The offer of the similar items implies that the items may be substitutable type. Now a day two equally priced mutually substitutable products are arranged in the similar place such as Coke and Pepsi colas, Colgate and Close up, Progresso soups and Campbell etc. It is usually seen that a large amount of products (tooth paste, perfume, fruits, baked foods, vegetables, etc.) displayed in the market sometimes influenced the customers to purchase more product because of its stock, diversity, and brightness. Hence the items with more stock are preferable by the customers. In a simple meaning demand of one item is positively related to the displayed stock of the item and negatively infected by the stock of other item. In this research work, we are considering the demand of two substitute items. Since the items are substitutable, in case of a stock-out for one of them, a known fraction of its demand can be satisfied by using the stock of the other product. Demand of two substitutable items depends upon the inventory level. Substitutions among random customers are one of the realistic topics. In this paper for the first time we construct an EPQ model of substitutable items under trade credit with stock dependent substitutions and substitutions among random customers. The aim of this research work is to determine the relevant profit of each item. A real life numerical example is set to illustrate this model. Finally the model was solved by LINGO 13.0 software. Managerial insights and implications are also discussed.

Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set

In this article, the crisp, fuzzy and intuitionistic fuzzy optimization problem is formulated. The basic definitions and notations related to optimization problems are given in the preliminaries section. Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set is presented in this article. Then, with the help of the proposed algorithm the optimal solution of the crisp, fuzzy and intuitionistic fuzzy optimization problems are determined. A new theorem related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems is proposed and proved. Some new and concrete results related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems are presented. To illustrate the proposed method, some real-life numerical examples are presented. The proposed article provides seven fully worked examples with screenshots of output summaries from the software used in the computations for better understanding. The advantages of the proposed approach as compared to other existing work are also specified. Detail analyses of the comparative study as well the discussion are given. To show the advantages of the proposed approach, superiority analysis is discussed. Comparison analysis and the advantages of the proposed operators are also discussed. Some managerial applications and the advantages of the proposed approach are given. Finally, conclusion and future research directions are also given.

A comparison of some modified confidence intervals based on robust scale estimators for process capability index

This paper aims to compare the performances of modified confidence intervals based on robust scale estimators with classical confidence interval for process capability index (Cp) when the process has a non-normal distribution. The estimated coverage probability and the average width of the confidence intervals were obtained by a Monte-Carlo simulation under different scenarios. Simulation results showed that the modified confidence intervals performed well in terms of coverage probability and average width for all cases. Two real-life numerical examples from industry are analyzed to illustrate the performance and the implementation of the classical and modified confidence intervals for the process capability index (Cp) which also supported the results of the simulation study to some extent.

Regularized Local Multivariate Reduced-Order Models With Nonaffine Parameter Dependence

This paper addresses a singular problem, not yet discussed in the literature, which occurs when parametric reduced-order models are created using a subspace projection approach with multiple concatenated projection bases. We show that this technique may lead to the appearance of localized artifacts in the frequency characteristics of a system, even when the reduced-order projection basis is rich enough to describe the original system. These artifacts are found to be related to nonphysical poles of the transfer function that emerge whenever more than one projection basis is used, each spanning is a similar space, and these bases are directly put together to build multivariate reduced-order models. These unwanted poles are identified using the Bauer–Fike theorem and then the parametrized reduced-order model is regularized with a simple deflation procedure that completely removes the artifacts due to nonphysical resonances from the circuit characteristics. Finally, real-life numerical examples illustrate the accuracy and abilities of the proposed approach.

A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory

The objective of this work is to present a novel multi-attribute decision making (MADM) method under interval-valued intuitionistic fuzzy (IVIF) set environment by integrating a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. Set pair analysis (SPA) theory is the modern uncertainty theory which is composed by the three components, namely “identity”, “discrepancy” and “contrary” degrees of the connection number (CN) and overlap with the various existing theories for handling the uncertainties in the data. Thus, motivated by this, in the present work, an attempt is made to enrich the theory of information measure by presented some exponential based distance measures using CNs of the IVIF sets. The supremacy of the proposed measure is also discussed. Afterward, a TOPSIS method based on the proposed distance measures is developed to solve MADM problem under IVIF environment where each of the element is characteristics by IVIF numbers. The utility, as well as supremacy of the approach, is confirmed through a real-life numerical example and validate it by comparing their results with the several existing approaches results.

A Simple and Efficient Algorithm for Solving Type-1 Intuitionistic Fuzzy Solid Transportation Problems

This article describes how in solving real-life solid transportation problems (STPs) we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation, many authors have suggested the intuitionistic fuzzy (IF) representation for the data. In this article, the author tried to categorise the STP under uncertain environment. He formulates the intuitionistic fuzzy solid transportation problem (IFSTP) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The STP has uncertainty and hesitation in supply, demand, capacity of different modes of transport celled conveyance and when it has crisp cost it is known as IFSTP of type-1. From this concept, the generalized mathematical model for type-1 IFSTP is explained. To find out the optimal solution to type-1 IFSTPs, a single stage method called intuitionistic fuzzy min-zero min-cost method is presented. A real-life numerical example is presented to clarify the idea of the proposed method. Moreover, results and discussions, advantages of the proposed method, and future works are presented. The main advantage of the proposed method is that the optimal solution of type-1 IFSTP is obtained without using the basic feasible solution and the method of testing optimality.

Economic Optimization of an Underground Power Cable Installation

This paper presents a mathematical model for the selection of an optimal power cable conductor cross section and the dimensions of a corrective backfill. To this end, a detailed model for the calculation of the life-cycle cost of cable ownership is presented. The formula considers the material and labor costs in the production of a power cable as well as the cost of losses during its operation. Simultaneously, the procedure seeks the optimal size of the corrective backfill, taking ampacity constraints into account. Since the formulation is complex, a genetic algorithm is proposed to solve the optimization problem. A real-life numerical example is presented.

Linear Programming Approach for Solving Balanced and Unbalanced Intuitionistic Fuzzy Transportation Problems

In this article, two methods are presented, proposed method 1 and proposed method 2. Proposed method 1 is based on linear programming technique and proposed method 2 is based on modified distribution method. Both of the methods are used to solve the balanced and unbalanced intuitionistic fuzzy transportation problems. The ideas of the proposed methods are illustrated with the help of real life numerical examples which is followed by the results and discussion and comparative study is given. The proposed method is computationally very simple when compared to the existing methods, it is shown to be and easier form of evaluation when compared to current methods.