Use Of Fuzzy Numbers Research Articles

Addressing Fuzzy Linear Programming Problems Through Ranking Functions

In contemporary decision-making, reliance on information is paramount, yet much of it is fraught with uncertainty, making logical decision-making challenging. To tackle this uncertainty, various methods, including the use of fuzzy numbers, have been employed. This paper specifically delves into addressing linear programming (LP) problems characterized by fuzzy coefficients in the objective function, fuzzy values in the right-hand side, and fuzzy coefficients of constraints. The proposed approach involves employing linear ranking functions such as Maleki, Campos, Yager’s F1 and Yager linear ranking functions to solve these fuzzy linear programming (FLP) problems and attain optimal solutions. Furthermore, the paper elucidates the resolution steps through the presentation of numerical examples, in this study, a comprehensive methodology is presented for effectively addressing a wide range of linear programming problems.

Cyclic multi-hoist scheduling with fuzzy processing times in flexible manufacturing lines

This work addresses the problem of scheduling multiple hoists (robots), which arises on real automated electroplating lines. Several hoists operate on a shared track and should not collide with each other. The processing time for each operation is preset in interval form. The problem simultaneously takes into account two criteria: maximum processing quality and maximum line productivity. To do this, we estimate the dependence of the duration of operations on the level of their quality and, in accordance with these estimates, we represent the processing times in the form of fuzzy numbers with triangular membership functions. The novelty of this study is two-fold. First, we propose a new mathematical model based on the use of fuzzy numbers and fuzzy operations on them, which is designed to deal with complex galvanic lines served by multiple hoists. The second new feature is a new combinatorial method developed for scheduling multiple hoists. For this, we modify and refine the so-called “method of prohibited intervals”, which has been actively used in scheduling theory in recent decades to solve problems, but until now was known only for the case of a single hoist. Thus, the second novelty of this work is that it is actually the first attempt to use the powerful technique of fuzzy set theory to solve a practical problem of scheduling multiple hoists. Computational experiments on real and randomly generated instances show that the new algorithm can successfully solve real problems that arise in practice.

Neutrosophic data envelopment analysis based on parametric ranking method

The use of fuzzy numbers and their extensions, especially neutrosophic fuzzy numbers, is inevitable to express the value of the parameters of optimization problems derived from the real world. In this regard, the comparison and ranking of neutrosophic fuzzy numbers as one of the main research topics that can provide a suitable decision to solve optimization problems is of interest to researchers. In this study, we introduce a parametric approach to rank single value trapezoidal neutrosophic numbers which are based on decision–maker aspiration level for degree of the truth membership function and selecting appropriate levels for non-indeterminacy and non-falsity–membership functions. A prominent feature of this method is its high flexibility, which is due to the consideration of acceptable levels for evaluation by the decision maker. Therefore, in most decision issues, it can be used to determine the preferred option. Also, some theorems and reasonable properties are given to demonstrate the effectiveness of our proposed parametric approach. Furthermore, in an example of data envelopment analysis model with neutrosophic information the validity and applicability of the suggested method are examined.

Group decision making in the analytic hierarchy process by hesitant fuzzy numbers

Due to the increasing complexity of decision problems, many managers employ multiple experts to reach a good decision in a group decision making. Now, if there is ambiguity in the evaluation of experts, the use of fuzzy numbers can be useful for each expert. In these situations, the use of hesitant fuzzy numbers (HFNs) which consists of several fuzzy numbers with special conditions can be suggested. HFNs are as an extension of the fuzzy numbers to take a better determining the membership functions of the parameters by several experts. Because of simple and fast calculations, in this paper, we use triangular HFNs in the pairwise comparison matrix of analytic hierarchy process by opinions of a group of decision makers in a hesitant fuzzy environment. We define consistency of the hesitant fuzzy pairwise comparison matrix and use the arithmetic operations on the HFNs and a new method of comparing HFNs to get the hesitant fuzzy performance score. By using score function to hesitant fuzzy score we can get a final score for alternatives. Finally, a practical example is provided to show the the effectiveness of this study. The obtained results from this paper show that new method can get a better answer by keeping the experts’ opinions in the process of solving the problem.

Seaport Network Efficiency Measurement Using Triangular and Trapezoidal Fuzzy Data Envelopment Analyses with Liner Shipping Connectivity Index Output

Seaport network efficiency is very crucial for global maritime economic trades and growth. In this work, data of three years (2018–2020) with input variables (time in port, age of vessels, size of vessels, cargo carrying capacity of vessels) and output variables (Liner Shipping Connectivity Index (LSCI) and Gross Domestic Product (GDP)) are collected. Few screening tests are performed to ensure the data are fit for further analyses. Since none of the existing studies has ever considered LSCI as an output variable, the main purpose of this study is to measure seaport network efficiency based on LSCI using data envelopment analysis (DEA), both classical and fuzzy. In fuzzy DEA, triangular fuzzy number (TrFN) and trapezoidal fuzzy number (TpFN) are used to construct the fuzzy sets of efficiency scores with DEA. The comparison between DEA and triangular fuzzy data envelopment analysis (TrFDEA) shows the range of differences in the results ranges from −0.0274 to 0.0105, while the comparison between DEA and trapezoidal fuzzy data envelopment analysis (TpFDEA) yields the differences within the range of −0.0307 to 0.0106. Using DEA as the relative reference, it is further revealed that the TpFDEA has smaller standard deviations and variances than the TrFDEA in 2018 and 2019, whereas the opposites hold true during the pandemic year of 2020. With the use of fuzzy numbers, the uncertainty levels in the seaport network efficiency measurement can further be investigated as the minimum, mean, median and maximum values are taken into consideration. Moreover, the proposed TrFDEA and TpFDEA lead new insights on the boundedness concept of the efficiency scores, which were never reported before by any researcher, especially in the maritime industry research. Fuzzy regression modelling based on the Possibilistic Linear Regression Least Squares (PLRLS) method was also performed to determine the interval of minimum and maximum connectivity efficiencies, which gave a better estimation than the regular regression model.

Розв’язання задачі комівояжера на основі методу відпалу з урахуванням нечіткості сприйняття плину часу

This paper investigates the use of fuzzy numbers and the annealing method to improve the results of the traveling salesman problem (TSP) by more accurately representing real-world circumstances, where the value of the objective function represents the subjective perception of the length of the time interval required to travel between cities. TSP is a classic combinatorial optimization problem that involves finding the shortest route between a set of cities. Fuzzy numbers are used to model input inaccuracy and uncertainty, as they allow for a more detailed representation of real-world constraints and factors that may affect the problem. The annealing method is used to optimize the TSP solution by gradually decreasing the temperature of the system, which allows exploring different solutions and avoiding getting stuck in local minima. To demonstrate the effectiveness of this approach, a Python program was developed that was used to compare the results of the TSP problem using crisp and fuzzy numbers using the annealing method. The results show that the use of fuzzy numbers, particularly triangular and parabolic, with the annealing method leads to a significant improvement in the results of the TSP problem compared to the use of crisp numbers, assuming a model is called realistic if it has possible deviations from the expected fixed mean. Computational results of the program are presented and analyzed, demonstrating the potential of this approach for real-world optimization problems involving imprecise or uncertain data and which can be particularly applied to the optimization of processes with subjective time perception.

An Integrated Fuzzy MCDM Hybrid Methodology to Analyze Agricultural Production

A hybrid model was developed by combining multiple-criteria decision-making (MCDM) with the analytic hierarchy process (AHP) and a fuzzy set to give decision support for choosing sustainable solutions to agricultural problems. Six steps were taken to build the suggested hybrid model: identifying and weighing criteria; normalizing data using fuzzy membership functions; calculating the weighting of the criteria using AHP; and selecting the best alternative for the agricultural problem. The objective of this case study is to demonstrate how agricultural production techniques (APTs) are becoming more complex as agricultural production becomes more complex. Organic agriculture aims to protect both the environment and consumer satisfaction by utilizing organic management practices that do not have the negative effects associated with conventional and genetic engineering production. Meanwhile, products obtained through conventional and genetic engineering techniques are more cost-effective. To present the superiority of the proposed fuzzy MCDM hybrid model, this problem is used as the causative agent’s dataset. Because the challenge involves a large number of competing quantitative and qualitative criteria, the assessment approach should improve the ratio of input data to output data. As a result, agricultural productivity should be controlled holistically. However, because the problem may contain both qualitative and quantitative facts and uncertainties, it is necessary to represent the uncertainty inherent in human thinking. To achieve superior outcomes, fuzzy set theory (FST), which enables the expression of uncertainty in human judgments, can be integrated with). The purpose of this study is to present a novel MCDM approach based on fuzzy numbers for analyzing decision-making scenarios. The proposed methodology, which is based on Buckley’s fuzzy analytic hierarchy process (B-FAHP) and the Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (F-TOPSIS), uses Buckley’s fuzzy analytic hierarchy process (B-FAHP) and fuzzy TOPSIS to determine weights and rank alternatives, respectively. As a result, we attempted to include both the uncertainty and hesitancy of experts in the decision-making process through the use of fuzzy numbers. We have three main criteria in this study: Satisfaction (C1), Economy (C2), and Environment (C3). An important objective of the current research is to build a complete framework for evaluating and grading the suitability of technologies. A real-world case study is used to demonstrate the suggested paradigm’s validity.

Convergence Analysis Hilbert Space Approach for Fuzzy Integro‐Differential Models

In this paper, we present and demonstrate an innovative numerical method, which makes use of fuzzy numbers and fuzzy parameters that is effective in the solution of fuzzy type Volterra integro‐differential equations, which was previously thought to be impossible using conventional methods. The first application of a technique for solving Volterra integro‐differential equations of the fuzzy type, which was devised and tested in this paper, is shown here. This is the first time that this approach has been used. This system’s overall quality may be improved as a consequence of the use of the Hilbert space replicating kernel idea, which is a possibility. Separate evaluations are made of the algorithms’ correctness and sloppiness, as well as their foundations in the computationally effective kernel Hilbert space, which has been extensively researched in the past. Numerical examples are provided of the article to demonstrate how the technique outlined before may achieve convergence and accuracy. Here are a few illustrations to help understand that it is possible to deal with physical issues that require complicated geometric calculations with the assistance of the method explained in this article.

A novel method for ranking generalized fuzzy numbers with two different heights and its application in fuzzy risk analysis

Due to the large use of fuzzy numbers, the ranking of these numbers is very important.In this paper, we propose a new method for ranking generalized fuzzy numbers with different left and right heights.The proposed method, at first obtains the centers of gravity of fuzzy numbers and left and right side crisp numbers; then by computing left and right areas associated with them, ranks the fuzzy numbers. The proposed method can overcome the flaws and defects of some ranking methods, and the provided examples are evidence of this. Finally this method is applied to the fuzzy risk analysis problem.

Fuzzy Numbers and Fractional Programming in Making Decisions

This study surveys the use of fuzzy numbers in classic optimization models, and its effects on making decisions. In a wide sense, mathematical programming is a collection of tools used in mathematical optimization to make good decisions. There are many sectors of economy that employ it. Finance and government, logistics and manufacturing, the distribution of the electrical power are worth to be first mentioned. When real life problems are modeled mathematically, there is always a trade-off between model’s accuracy and complexity. By this survey, we aim to present in a concise form some mathematical models from the literature together with the methods to solve them. We will focus mainly on fuzzy fractional programming problems. We will also refer to but not describe in detail the multi-criteria decision-making problems involving fuzzy numbers and linear fractional programming models.

From MCDA to Fuzzy MCDA: violation of basic axiom and how to fix it

The use of fuzzy numbers (FNs) for managing uncertainty in multi-criteria decision analysis (MCDA) demands a thorough exploring multi-criteria decision problem under fuzzy environment. Fuzzy MCDA (FMCDA) model implies comparison, choice or ranking alternatives based on assessing corresponding functions with subsequent ranking of FNs. Despite the wide use of FMCDA in recent decades, the effect of the violation of axioms for fuzzy ranking methods on FMCDA models has not been explored yet. This paper aims at demonstrating the violation of the basic MCDA axiom, associated with ranking of dominating and dominated in Pareto alternatives, by fuzzy TOPSIS and fuzzy MAVT models as an example. The suggestion to implement FMCDA models in applications without violation of the basic axiom is elicited based on the use of distinguishable fuzzy numbers.

Assessing Supply Chain Risks in the Automotive Industry through a Modified MCDM-Based FMECA

Supply chains are complex networks that receive assiduous attention in the literature. Like any complex network, a supply chain is subject to a wide variety of risks that can result in significant economic losses and negative impacts in terms of image and prestige for companies. In circumstances of aggressive competition among companies, effective management of supply chain risks (SCRs) is crucial, and is currently a very active field of research. Failure Mode, Effects and Criticality Analysis (FMECA) has been recently extended to SCR identification and prioritization, aiming at reducing potential losses caused by lack of risk control. This article has a twofold objective. First, SCR assessment is investigated, and a comprehensive list of specific risks related to the automotive industry is compiled to extend the set of most commonly considered risks. Second, an alternative way of calculating the Risk Priority Number (RPN) is proposed within the FMECA framework by means of an integrated Multi-Criteria Decision-Making (MCDM) approach. We give a new calculation procedure by making use of the Analytic Hierarchy Process (AHP) to derive factors weights, and then the fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL) to evaluate the new factor of “dependence” among the risks. The developed joint analysis constitutes a risk analysis support tool for criticality in systems engineering. The approach also deals with uncertainty and vagueness associated with input data through the use of fuzzy numbers. The results obtained from a relevant case study in the automotive industry showcase the effectiveness of this approach, which brings important value to those companies: When planning interventions of prevention/mitigation, primary importance should be given to (1) supply chain disruptions due to natural disasters; (2) manufacturing facilities, human resources, policies and breakdown processes; and (3) inefficient transport.

A novel approach for the next software release using a binary artificial algae algorithm

In software incremental development methodology, the product develops in several releases. In each release, one set of the requirements is suggested for development. The development team must select a subset of the proposed requirements for development in the next release such that by consideration the limitation of the problem provides the highest satisfaction to the customers and the lowest cost to the company. This problem is known as the next release problem. In complex projects where the number of requirements is high, development teams cannot choose an optimized subset of the requirements by traditional methods, so an intelligent algorithm is required to help in the decision-making process. The main contributions of this study are fivefold: (1) The customer satisfaction and the cost of every requirement are determined by use of fuzzy numbers because of the possible changing of the customers’ priorities during the product development period; (2) An improved approximate approach is suggested for summing fuzzy numbers of different kinds, (3) A new metaheuristic algorithm namely the Binary Artificial Algae Algorithm is used for choosing an optimized subset of requirements, (4) Experiments performed on two fuzzy datasets confirm that the resulted subsets from the suggested algorithm are free of human mistake and can be a great guidance to development teams in making decisions.

AN OPTIMIZATION OF FEOQ MODEL FOR WEIBULL DETERIORATING ITEMS WITH INFLATIONARY CONDITION

The economic instability is a haunting situation in the present era for the economy. There is a monetary depreciation due to the tremendous increase in the price of the commodities. Present study basically deals with the investigation of the inventory system considering the case of perishable products under inflationary environment under condition of partial backorder. The rate of demand is a function which exponentially increases with increase in inflation and deterioration is taken as a Weibull distributed two parameter function. In the state of shortage when the inventory system runs out of stock an assumption is made that the demands are backlogged or lost. There is a variation in the rate of backlogging which shows this variation as a consequence of lead time required for the arrival of the next replenishment. The deterioration of commodities begins after a fixed interval of time. Present model aims at minimizing the average total cost considering both the crisp and fuzzy environments considering both inflationary effect as well as the time value of money. For the fuzzy economic order quantity (FEOQ) model of the inventory system fuzzification has been done by the use of fuzzy number of the trapezoidal nature. Defuzzification has been done by the use of centroid method. The primary motive of this work is to determine and compare the cost in total of the system of inventory in both crisp and fuzzy environments. The main inference that we can draw from this study is that fuzzy economic order quantity (FEOQ) model has more accuracy as in this model the total cost has been reduced as compared to the crisp model. Thus fuzzy economic order quantity (FEOQ) model is highly beneficial to any sort of inventory system and this result can be further generalized to any sector for enhancing the total profit of the system. Appropriate example has been provided for the illustration of both the models.

Influence of Managers’ Subjective Judgments on Project Abandonment Decision Making

Real option valuation with flexibility under uncertainty has been proposed as an alternative and advantageous complement to the traditional net present value (NPV) method for capital budgeting decisions, yet the problem with unrealistic expectations on precision has still not been solved. It appears clearly that a high level of precision in cash flow estimates can be misleading for the decision makers with sentiments. To the extent that precision surrounds a decision, we introduce a fuzzy process into an abandonment option approach, which is built on the use of fuzzy numbers, to investigate the effects of managerial optimism and pessimism when a manager considers whether or not to abandon capital budgeting decisions under imprecision and uncertainty. From the numerical analyses of the proposed model, we find that an optimistic manager tends to continue executing the project, while a pessimistic manager tends to give up the project and liquidate it as the value of the abandonment option is within the range of a fuzzy sentiments interval. In addition, if the project value is below the lower bound of the fuzzy sentiments interval, then it is better to exercise the abandonment option rather than to continue holding it, for both optimistic and pessimistic managers. Finally, this paper also examines why managers may still continue a project, even if its Tobin’s [Formula: see text] value is smaller than one.

Quality of Project Team in Traditional Project Management Using Fuzzy Numbers

This paper is a continuation and development of the same authors paper which has been published recently. The presented paper pertains to the notion of quality of project team in traditional project management. A paradox is observed in the state of art of the project team quality in project management. All specialists recognize the exceptional importance of the parameter “quality” for the final result of the project. On the one hand, one can easily find definitions of project quality, quality of product of the project, quality of the project management processes, and so on. On the other hand, a huge number of bibliographical sources considers the project team functioning, as a sine qua non condition of the project success. The notion “project team quality” is quasi absent in the literature. In this paper an approach is proposed to fill in this gap, in the form of a proposal of the model, which defines the project team quality and allows to measure it. The main results of the previous paper of the authors, particularly guidelines for the quality model of the project team, are briefly presented. The paper presented here has a conceptual character. The main part of the paper are guidelines for the quality model of the project team: general assumptions, measure of the quality of team – classical and with use of fuzzy numbers, based on Myers-Briggs method and Belbin test, and finally, an impact of the quality of the project team on the team management is discussed. The objective of this paper is to show the possibility to define the project team quality process, which ensures not only the optimal level of the team quality, but also allows undertake valuable managerial decisions during the project life cycle.

University Website Quality Ranking using Logarithmic Fuzzy Preference Programming

The current tight competition in developing University websites forces developers to create better products that meet users needs and convinient. There are at least two factors representing university websites; accessibility and usability. We test three criteria of accessibility and usability that are called stickiness, backlink, and web page loading time. Usability and accessibility are closely related to subjective user judgments. Human judgment cannot be valid. Thus the use of fuzzy numbers are expected to provide solutions in calculating the results. In this research, the question of usability is a multi criteria decision-making problem that is caused by its complex structure. We use the Logarithmic Fuzzy Preference Programming (LFPP) method, which is a refinement of the Fuzzy Analytical Hierarchy Process method, to solve this problem. This research aims to re- assess the rank of five Indonesian university websites. Based on LFPP method, we obtain that the equation of model gets high consistency of the set priority matching to fuzzy pairwise comparison matrix of three selection criteria. The calculation results show that stickiness is the most significant factor that affects the quality of the websites.

Optimal solution of full fuzzy transportation problems using total integral ranking

Full fuzzy transportation problem (FFTP) is a transportation problem where transport costs, demand, supply and decision variables are expressed in form of fuzzy numbers. To solve fuzzy transportation problem, fuzzy number parameter must be converted to a crisp number called defuzzyfication method. In this new total integral ranking method with fuzzy numbers from conversion of trapezoidal fuzzy numbers to hexagonal fuzzy numbers obtained result of consistency defuzzyfication on symmetrical fuzzy hexagonal and non symmetrical type 2 numbers with fuzzy triangular numbers. To calculate of optimum solution FTP used fuzzy transportation algorithm with least cost method. From this optimum solution, it is found that use of fuzzy number form total integral ranking with index of optimism gives different optimum value. In addition, total integral ranking value using hexagonal fuzzy numbers has an optimal value better than the total integral ranking value using trapezoidal fuzzy numbers.

Generation Rescheduling and Load Shedding in Distribution Systems Under Imprecise Information

Microgrids represent a smart solution to increase power system reliability through the development of self-supplied islands that integrate distributed power generation and other smart technologies. In this paper, we formulate and solve an optimal generation rescheduling and load shedding problem in microgrids to determine a stable equilibrium state following outages. To address this problem, focused on MV distribution systems, we use a new methodology based on the use of fuzzy numbers is proposed. The approach allows representing the sources of uncertainty in the data or approximations made during the computation and considering many possible scenarios in case of outages. In order to demonstrate the performance and the effectiveness of the proposed method, several simulations have been carried out on a 69-bus radial distribution system, and results have been compared with those obtained by using a stochastic optimization approach. The encouraging results are presented and discussed.

Fuzzy Regression Prediction and Application Based on Multi-Dimensional Factors of Freight Volume

Based on the reality of the development of air cargo, the multi-dimensional fuzzy regression method is used to determine the influencing factors, and the three most important influencing factors of GDP, total fixed assets investment and regular flight route mileage are determined. The system’s viewpoints and analogy methods, the use of fuzzy numbers and multiple regression methods to predict the civil aviation cargo volume. In comparison with the 13th Five-Year Plan for China’s Civil Aviation Development (2016-2020), it is proved that this method can effectively improve the accuracy of forecasting and reduce the risk of forecasting. It is proved that this model predicts civil aviation freight volume of the feasibility, has a high practical significance and practical operation.