Trapezoidal Fuzzy Research Articles

A New Approach of Ranking of Generalized Trapezoidal Fuzzy Numbers and Application in Fuzzy Risk Analysis

In this present work, a new approach for ranking generalized trapezoidal fuzzy numbers has been introduced. This new proposed method is based on a left and right deviation and fuzzyness measure of the generalized trapezoidal fuzzy numbers. Some propositions have been introduced corresponding to the new proposed method. The proposed method has been compared with the different existing methods of ranking generalized trapezoidal fuzzy numbers. Also, it has been shown that the proposed technique succeeds in overcoming the drawbacks of the existing methods. The proposed method has been applied to a risk analysis problem in the selection of a production house by a retailer.

A Novel Operator to Solve Decision-Making Problems Under Trapezoidal Fuzzy Multi Numbers and Its Application

This article investigates solutions to multiple attribute decision-making (MADM) problems in which the attribute values take the form of trapezoidal fuzzy multi-numbers. To do this, this paper proposes a kind of mean aggregation operator called the Bonferroni harmonic mean operator for aggregating trapezoidal fuzzy information. Then, an approach that is a solution algorithm has been developed to find a solution to multi-attribute decision-making problems. Afterwards, an illustrative example has been given to verify the developed approach and to show its usefulness and efficiency. Finally, a comparison table has been presented to compare the proposed method with some existing methods.

A computational method for normalization of Trapezoidal Fuzzy Numbers

A computational method for normalization of Trapezoidal Fuzzy Numbers

Numerical Treatment of Hybrid Fuzzy Differential Equations Subject to Trapezoidal and Triangular Fuzzy Initial Conditions Using Picard’s and the General Linear Method

We study hybrid fuzzy differential equations (HFDEs) under the Hukuhara derivative numerically using Picard’s and the general linear method (GLM). We use trapezoidal and triangular fuzzy numbers as the initial conditions. To demonstrate the efficiency of the proposed methods, the exact as well as the numerical solutions are presented numerically and graphically. In addition, a comparison is made between the results from applying the GLM and those obtained when applying the fifth order Runge–Kutta method as reported in the literature.

Failure Risk Assessment of Coal Gasifier Based on the Integration of Bayesian Network and Trapezoidal Intuitionistic Fuzzy Number-Based Similarity Aggregation Method (TpIFN-SAM)

The coal gasifier is the core unit of the coal gasification system. Due to its exposure to high temperatures, high pressures, and aggressive media, it is highly susceptible to serious accidents in the event of failure. Therefore, it is important for the gasifier to perform failure-risk assessment to understand its safety status and provide safety measures. Bayesian networks (BNs) for risk analysis of process systems has received a lot of attention due to its powerful inference capability and its ability to reflect complex relationships between risk factors. However, the acquisition of basic probability data in a Bayesian network is always a great challenge. In this study, an improved Bayesian network integrated with a trapezoidal intuitionistic fuzzy number-based similarity aggregation method (TpIFN-SAM) is proposed for the failure-risk assessment of process systems. This approach used the TpIFN-SAM to collect and aggregate experts’ opinions for obtaining the prior probabilities of the root events in the BN. In the TpIFN-SAM, the intuitionistic fuzzy analytic-hierarchy-process method (IF-AHP) was adopted to assign the expert weights for reducing subjectivity or the bias caused by individual differences. To clarify the suitability of the proposed method, a case study of a coal gasifier was demonstrated, and both prediction and diagnosis analyses of the BN were performed; finally, the weak links of the gasifier were identified.

Multicriteria group decision making via generalized trapezoidal intuitionistic fuzzy number-based novel similarity measure and its application to diverse COVID-19 scenarios.

Havoc, brutality, economic breakdown, and vulnerability are the terms that can be rightly associated with COVID-19, for the kind of impact it is having on the whole world for the last two years. COVID-19 came as a nightmare and it is still not over yet, changing its form factor with each mutation. Moreover, each unpredictable mutation causes more severeness. In the present article, we outline a decision support algorithm using Generalized Trapezoidal Intuitionistic Fuzzy Numbers (GTrIFNs) to deal with various facets of COVID-19 problems. Intuitionistic fuzzy sets (IFSs) and their continuous counterparts, viz., the intuitionistic fuzzy numbers (IFNs), have the flexibility and effectiveness to handle the uncertainty and fuzziness associated with real-world problems. Although a meticulous amount of research works can be found in the literature, a wide majority of them are based mainly on normalized IFNs rather than the more generalized approach, and most of them had several limitations. Therefore, we have made a sincere attempt to devise a novel Similarity Measure (SM) which considers the evaluation of two prominent features of GTrIFNs, which are their expected values and variances. Then, to establish the superiority of our approach we present a comparative analysis of our method with several other established similarity methods considering ten different profiles of GTrIFNs. The proposed SM is then validated for feasibility and applicability, by elaborating a Fuzzy Multicriteria Group Decision Making (FMCGDM) algorithm and it is supportedby a suitable illustrative example. Finally, the proposed SM approach is applied to tackle some significant concerns due to COVID-19. For instance, problems like the selection of best medicine for COVID-19 infected patients; proper healthcare waste disposal technique; and topmost government intervention measures to prevent the COVID-19 spread, are some of the burning issues which are handled with our newly proposed SM approach.Graphical abstract

Proposal Yager Ranking Function to Solve the Fuzzy Transportation Model via Trapezoidal Fuzzy Number

Transportation theory is the name given to the study of optimal transportation (OT) and resource allocation in mathematics and economics. In any discipline of science and technology, engineering, medicine, and management, uncertainty plays a critical role. Fuzzy Mathematics (FM) and fuzzy logic (FL) are used in Artificial Intelligence (AI) to process natural language and are frequently employed in decision making (DM). In this paper, using three ranking function to treat the fuzzy transportation model, two of them are Yager and Maleki ranking functions and the other is proposal and suggest depend up on of Yager ranking function based on trapezoidal fuzzy membership function when the total demand, cost of transportation, and the total amount of product (supply) are fuzzy, then the fuzzy model shrinkage to traditional or crisp model. Finally solving these models to the real data that we got it from The General Company for Food Products Abo ghreeb / Iraq.

Multiple Attribute Decision Making Based on Interval-Valued Neutrosophic Trapezoidal Fuzzy Numbers and its Application in the Diagnosis of Viral Flu

Decision-making technique (DMT) is mostly used in artificial intelligence and cognitive sciences to elaborate individual and social perception. So, one of the most important strategies in DMT evolved in medical diagnosis scrutiny regarding the connection of symptoms and diagnosis of diseases due to uncertainty and fuzziness in the relevant information. The focus of this article is to develop a diagnostic decision making strategy for the diagnosis of Viral diseases with close related symptoms using the Interval-valued trapezoidal neutrosophic fuzzy Numbers (IVTrNFN) w.r.t multiple attribute decision making (MADM) strategy where, the attribute value is evolved to Interval-valued trapezoidal neutrosophic fuzzy number and the attribute weight is unknown and can be related to the GRA (Grey relational analysis projection) technique. In this research several operational laws are developed as well as the expected value and the hamming distance between two IVTrFNs are introduced. Moreover, the information entropy method is used to determine the attributes weights and the grey relational analysis as well as the projection method are involved too in the proposed framework. The ranks of the alternative decisions are evaluated by their relative closeness to PIS (Positive Ideal Solutions), which combine the grey relational projection values from positive and negative ideal solutions associated with each alternative. Finally, a Viral disease example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application in MCGDM Problems

Compared to previous extensions, the q-rung orthopair fuzzy sets are superior to intuitionistic ones and Pythagorean ones because they allow decision-makers to use a more extensive domain to present judgment arguments. The purpose of this study is to explore the multicriteria group decision-making (MCGDM) problem with the q-rung orthopair trapezoidal fuzzy (q-ROTrF) context by employing Einstein t-conorms and t-norms. Firstly, some arithmetical operations for q-ROTrF numbers, such as Einstein-based sum, product, scalar multiplication, and exponentiation, are introduced based on Einstein t-conorms and t-norms. Then, Einstein operations-based averaging and geometric aggregation operators (AOs), viz., q-ROTrF Einstein weighted averaging and weighted geometric operators, are developed. Further, some prominent characteristics of the suggested operators are investigated. Then, based on defined AOs, a MCGDM model with q-ROTrF numbers is developed. In accordance with the proposed operators and the developed model, two numerical examples are illustrated. The impacts of the rung parameter on decision results are also analyzed in detail to reflect the suitability and supremacy of the developed approach.

A novel Interval Type-2 Fuzzy best-worst method and combined compromise solution for evaluating eco-friendly packaging alternatives

Increasing consumer goods and products has inspired environmental activists and policymakers to demand eco-friendly packaging from retailers and manufacturers. At the same time, consumer attitudes about sustainable packaging have changed significantly. In response to these changing consumer sentiments, the packaging value chain is changing, and businesses are seeking to use environmentally friendly packaging for their products. However, choosing the best packaging is a significant challenge for decision-makers (DMs) who must consider many uncontrollable and unpredictable environmental factors. This study aims to design a new methodology for assessing engineering and ecological challenges and proposing a practical approach for selecting the best eco-friendly packaging alternative. We propose a novel model that integrates the Best-Worst Method (BWM) and Combined Compromise Solution (CoCoSo) within an asymmetric Interval Type-2 Trapezoidal Fuzzy Set (IT2TFS) setting. The new IT2TFS-BWM-CoCoSo method consists of two phases: determining the optimal weights of the evaluation criteria and ranking the alternatives. The asymmetric IT2TFS is used in both phases to interpret DMs’ fuzzy preferences. A new consistency ratio (CR) is defined to assess the consistency level of DMs’ preference comparisons expressed by asymmetric IT2TFSs. The asymmetric features add flexibility to DMs’ evaluations without weakening their accuracy. The proposed methodology is applied to a real-life case study of a US-based company that produces and ships handmade crystals. Recycled cardboard and paper, biodegradable packaging peanuts, and eco-friendly plastic and recycled plastics are found to be the best eco-friendly packaging alternatives. The case study results demonstrate the applicability and efficacy of the proposed method and its flexibility in solving sustainable packaging selection problems of companies with similar characteristics. At the same time, the technical features of the proposed framework open the way to a wide range of applications for sustainable consumption and production.

PUGH Decision Trapezoidal Fuzzy and Gradient Reinforce Deep Learning for Large Scale Requirement Prioritization

Objective: To prioritize requirements for large scale software projects within time involving uncertainty in the opinions among different stakeholders. Methods: We propose Pugh Trapezoidal Fuzzy and Gradient Reinforce Learning (PTF-GRL) methods for large scale software requirement prioritization. A Pugh Decision-based Trapezoidal Fuzzy Requirement Selection model is designed, inputting the functional and non-functional requirements of the corresponding stakeholders. With the assistance of Trapezoidal Fuzzy Inference, the qualitative factors are mapped with the corresponding numeric factors, which increases the computational efficiency. Findings: Performance is analyzed based on four parameters: The first parameter is accuracy and our method showed improvement of 4%, 7% and 3% compared to JRD-SCRUM, IFS and SRPTackle respectively. The second parameter is prioritization time and found that our method had reduced time of 30%, 37% and 39% compared with existing methods. The third parameter is precision and it was found that our method improves precision by 6%, 10% and 5% compared with the other two methods. The final parameter we consider is the test suite execution and our method showed improvement of 12%, 19% and 5% compared with the existing two methods. Novelty/Applications: The originality of this work indicates the better performance along with the optimal test suite execution even considering the uncertainty factor in the proposed method compared with existing similar methods. Keywords: Software Project; Pugh Decision Matrix; Trapezoidal Fuzzy Inference; Gradient Orientation; Reinforce Learning; Requirement Prioritization

Newly Proposed Matrix Reduction Technique Under Mean Ranking Method for Solving Trapezoidal Fuzzy Transportation Problems Under Fuzzy Environment

In this paper, improved matrix Reduction Method is proposed for the solution of fuzzy transportation problem in which all inputs are taken as fuzzy numbers. Since ranking fuzzy number is important tool in decision making, Fuzzy trapezoidal number is converting in to crisp set by using Mean techniques and solved by proposed method for fuzzy transportation problem. We give suitable numerical example for unbalanced and compare the optimal value with other techniques. The Result shows that the optimum profit of transportation problem using proposed technique under robust ranking method is better than the other method. Novelty: The numerical illustration demonstrates that the new projected method for managing the transportation problems on fuzzy algorithms.

The Use of Fuzzy Linear Regression with Trapezoidal Fuzzy Numbers to Predict the Compressive Strength of Lightweight Foamed Concrete

The Use of Fuzzy Linear Regression with Trapezoidal Fuzzy Numbers to Predict the Compressive Strength of Lightweight Foamed Concrete

Optimization on dual-channel supply chain model with pricing decision and trapezoidal fuzzy demand under a controllable lead time

This paper considers a dual-channel supply chain with one vendor and multiple buyers in which (1) one channel is an offline channel where standard products are produced and shipped to the buyers and (2) the second channel is an online channel with the flow of customized products between the vendor and the online buyers/consumers. The first channel follows a vendor managed inventory with consignment stock (VMI-CS) agreement between the vendor and buyers. The supply lead time between the vendor and the buyer is considered controllable, at a cost. Two models are analyzed: (1) in the first model, the standard and customized product’s demand rate is assumed to be price and lead time-sensitive, and (2) in the second model, the demands are uncertain or ambiguous and are treated as a trapezoidal fuzzy number. It is reasonably complex to obtain analytical solutions. Hence, two algorithms are proposed to obtain the numerical solution with the objective of maximizing total profit. Numerical examples, sensitivity analysis, and managerial insights are given to test the model. Finally, conclusions and directions for future research are provided.

A sustainable dual-channel inventory model with trapezoidal fuzzy demand and energy consumption

Most of the consumers relied heavily on e-commerce for products and services for the past few years due to the recent COVID-19 pandemic. This kind of an unexpected behaviour among the consumer society has taken every industry by surprise so that many industries have begun operating online and offline businesses to ensure future competitiveness. Firms introducing online sales are deplorably facing many challenges in terms of logistics and delivery processes, such as short lead times, flexible delivery, capacity of warehouse, and the production process for controlling carbon emissions. Keeping these challenges in mind, a sustainable dual-channel vendor-buyer supply chain model has considered for a controllable emission under fuzzy demand and energy consumption. The model deals with limitation on warehouse floor-space area, and the warehouse divides into two stages such as one for satisfying online orders and the other for satisfying offline orders. The demand rate and energy consumptions are treated as the trapezoidal fuzzy number, and we use the signed distance method to defuzzify the fuzzy joint expected total cost. The objective focuses on obtaining a trade-off between cost and emissions, thereby determining the optimal production-distribution strategy and a proper sustainable plan for handling both online and offline orders. The aforesaid scenario is mathematically formulated in the form of constrained non-linear programme (NLP) and derive a Lagrangean multiplier method to solve it. An iterative solution algorithm is designed, and for better illustration of the developed theory, numerical analysis is carried out followed by a wide discussion on the sensitivity analysis for various parameters. Our results indicate that the optimal solutions of the sustainable fuzzy model slightly fluctuate from the solutions of the sustainable crisp model. According to results, considering the uncertainty in the system is a crucial factor to achieve the economic and environmental sustainability of the production sector. The research reveals that the practitioners should be careful in accounting flexibility in the input factors demand and energy to tackle the uncertainties that always fit the real situation.

Solving the Trapezoidal Fuzzy Transportation Problems via New Heuristic

The transportation problem is a one of the principal topics in operational research where goods are initially stored at different sources and need to be livered to destination in such a way the total transportation cost is minimum. In this paper, we consider the transportation problem in a trapezoidal fuzzy environment and we introduce the column-row heuristic Dhouib-Matrix-TP1 to solve it in just p iterations (where p is the maximal number between the total number of sources and destinations). The Dhouib-Matrix-TP1 heuristic is enhanced with the robust ranking function and with a new operation for selection based on mean and min metrics. To justify the proposed method, several numerical experiments are given to show the effectiveness of the new technique in solving the trapezoidal fuzzy transportation problems.

Sustainable partner selection and order allocation for strategic items: an integrated multi-stage decision-making model

ABSTRACT Current environmental issues and government requirements, together with pressure from the market and other stakeholders, emphasise the importance of partner selection in constructing and operating sustainable supply chains. Strategic items, which carry both high supply risk and high importance of purchase, are particularly important in sustainable supply chains. This paper presents an integrated decision-making model, which aims to solve the partner selection and order allocation problem for strategic items in sustainable supply chains. In the proposed model, weightings of different decision-makers are first calculated using Trapezoidal Fuzzy Numbers. Then, Taguchi loss function is used to evaluate the relative importance of potential partners, with the weighting results of criteria by Best-Worst Method. Finally, considering the weights of different potential partners, Particle Swarm Optimisation (PSO) is used to solve the multi-objective programming problem, and Technique of Order Preference Similarity to the Ideal Solution (TOPSIS) is applied to identify the most appropriate Pareto solution for sustainable partner selection and order allocation of strategic items. An illustrative application of the proposed model is undertaken in a leading Chinese LED lighting manufacturer to show its effectiveness and applicability.

Optimum harnessing of solar energy with proper selection of phase changing material using integrated fuzzy-COPRAS Model

ABSTRACT Thermal Energy Storage (TES) devices can assist in storing the energy during the sunlight hours which can be used later on non-availability of solar power. Implementation of Phase Changing Material (PCM) can enhance efficiency of TES devices. Selection of resourceful and efficient PCM plays an essential role such that it can be successfully implanted nearly with all solar thermal devices. Assortment of the material involves selection of certain characteristics and properties associated with the performance of material as well as their physical, mechanical, economic and environmental properties. This study deals with a methodological analysis by integrating techniques for finding optimum PCM among various selected materials. Hybridization involves integrating Triangular Fuzzy Number (TFN) with Complex Proportional Assessment (COPRAS) method. In general, Fuzzy set comprises of three or more numbers, denoting it as TFN, Gaussian Fuzzy numbers, Trapezoidal Fuzzy Numbers, and so on. Although alternatives are many to design a fuzzy set depending on elements count, the TFNs are the ones considered as actual representations of a Fuzzy number. COPRAS is a well-known robust MCDM technique chosen to carry out the work of selection. Eight PCM have been compared on the parameters like Latent Heat, Cost, Melting points and others. Calcium Chloride Hexahydrate is the optimum material found as PCM. The result of this study would help planners and designers for an optimum selection of PCM in efficient harnessing of solar energy.

Obtaining Crisp Priorities for Triangular and Trapezoidal Fuzzy Judgments

This paper proposes anoptimal fuzzy-based model for obtaining crisp priorities for Fuzzy-AHP comparison matrices. Crisp judgments cannot be given for real-life situations, as most of these include some level of fuzziness and complexity. In these situations, judgments are represented by the set of fuzzy numbers. Most of the fuzzy optimization models derive crisp priorities for judgments represented with Triangular Fuzzy Numbers (TFNs) only. They do not work for other types of Triangular Shaped Fuzzy Numbers (TSFNs) and Trapezoidal Fuzzy Numbers (TrFNs). To overcome this problem, a sum of squared error (SSE) based optimization model is proposed. Unlike some other methods, the proposed model derives crisp weights from all of the above-mentioned fuzzy judgments. A fuzzy number is simulated using the Monte Carlo method. A threshold-based constraint is also applied to minimize the deviation from the initial judgments. Genetic Algorithm (GA) is used to solve the optimization model. We have also conducted casestudiesto show the proposed approach’s advantages over the existingmethods. Results show that the proposed model outperforms other models to minimize SSE and deviation from initial judgments. Thus, the proposed model can be applied in various real time scenarios as it can reduce the SSE value upto 29% compared to the existing studies.

Generating Type 2 Trapezoidal Fuzzy Membership Function Using Genetic Tuning

Fuzzy inference system (FIS) is a process of fuzzy logic reasoning to produce the output based on fuzzified inputs. The system starts with identifying input from data, applying the fuzziness to input using membership functions (MF), generating fuzzy rules for the fuzzy sets and obtaining the output. There are several types of input MFs which can be introduced in FIS, commonly chosen based on the type of real data, sensitivity of certain rule implied and computational limits. This paper focuses on the construction of interval type 2 (IT2) trapezoidal shape MF from fuzzy C Means (FCM) that is used for fuzzification process of mamdani FIS. In the process, upper MF (UMF) and lower MF (LMF) of the MF need to be identified to get the range of the footprint of uncertainty (FOU). This paper proposes Genetic tuning process, which is a part of genetic algorithm (GA), to adjust parameters in order to improve the behavior of existing system, especially to enhance the accuracy of the system model. This novel process is a hybrid approach which produces Genetic Fuzzy System (GFS) that helps to enhance fuzzy classification problems and performance. The approach provides a new method for the construction and tuning process of the IT2 MF, based on the FCM outcomes. The result is compared to Gaussian shape IT2 MF and trapezoid IT2 MF generated by the classic GA method. It is shown that the proposed approach is able to outperform the mentioned benchmarked approaches. The work implies a wider range of IT2 MF types, constructed based on FCM outcomes, and an optimum generation of the FOU so that it can be implemented in practical applications such as prediction, analytics and rule-based solutions.