Pentagonal Fuzzy Numbers Research Articles

A Stage Structure Prey Predator Model Using Pentagonal Fuzzy Numbers and Functional Response

في هذه الدراسة، قمنا بدراسة نموذج مفترس للفريسة مع هيكل مرحلة للفريسة. الهدف من الدراسة هو إيجاد سلوك النموذج باستخدام قيم المعلمات في وجود أرقام ضبابية خماسية.. يتم التفاعل بين الأنواع باستخدام الاستجابات الوظيفية، مثل تفاعل هولينج من النوع الأول للفريسة الناضجة واستجابة كرولي مارتن الوظيفية للفريسة الناضجة . فكرة المشكلة هي بناء نموذج رياضي في بيئة غامضة باستخدام المعلمات الغامضة والقيم الأولية.. يتم تنفيذ وجود نقاط التوازن. وباستخدام مفهوم قطع ألفا للمعلمات المستخدمة في نموذج الفريسة – المفترس تم التعامل مع الأعداد الغامضة الخماسية. يمكن اعتبار المعلمات التي استخدموها في الصياغة الرياضية قيمة واضحة من خلال تطبيق طريقة إزالة الضبابية. هنا يتم استخدام طريقة تقنية التصنيف القوية. تتم دراسة استقرار كل نقطة توازن عن طريق حساب مصفوفة جاكوبي وإيجاد القيم الذاتية التي تم تقييمها عند كل نقطة توازن. من خلال الاستفادة من تحليل استقرار هيكل مرحلة الفريسة يتم اكتشافه أيضًا. بالنسبة للنظام الديناميكي تم توفير عمليات محاكاة عددية باستخدام برنامج MATLAB للكمبيوتر حتى نتمكن من عرض سلوك النظام وتحديد ما إذا كان مستقرًا أم غير مستقر.

Exploration of Time-Fractional Cancer Tumor Models with Variable Cell Killing Rates via Hybrid Algorithm

Abstract Cancer is marked by abnormal cell growth that invades healthy tissues, potentially spreading throughout the body through the bloodstream or lymphatic system. It arises when body cells show irregularities in the genes that control cell growth. To treat and minimize the growth of these abnormal cells, different models have been proposed to predict and analyze cancer-tumor. The current study contains analysis of fractional cancer-tumor with different uncertain conditions. To include the uncertainties in the model, Pentagonal fuzzy numbers (PFNs) approach is utilized. A hybrid mechanism, combining homotopies with perturbation technique and a generalized integral transform, is proposed to efficiently handle fractional derivatives with fuzzified conditions. The validity of obtained solutions is checked by calculating residual errors. Graphical analysis assesses the impact of important parameters on the solution profiles, and confirms the reliability of the proposed methodology for complex fractional tumor models and other intricate physical phenomena.

Solving Interval Type-2 Fuzzy Pentagonal Polynomial Equation Using Horner-Muller's Method

The recent boom in interval type-2 fuzzy sets has attracted many researchers to the fields of fuzzy numbers, algebraic expressions, and iterative methods. Interval type-2 fuzzy pentagonal polynomial (IT2 FPP) is one of the algebraic expressions that combine the knowledge of interval type-2 pentagonal fuzzy numbers and polynomial equations. Solving IT2 FPP in the absence of an iterative method is becoming a common encounter as the solution is often difficult, expensive, and inexact. This paper defines IT2 FPP and the iterative method Horner-Muller’s used to find the approximate solution of the IT2 FPP. The IT2 FPP is introduced by combining the generalization of interval type-2 pentagonal fuzzy numbers and fuzzy polynomials, whereas the Horner-Muller’s method is a combination of Horner’s method and Muller’s method. A numerical example is presented to illustrate the computational procedures for finding the approximate solution. The approximate solution is obtained after two iterations with zero error. A Comparative analysis is also presented to validate the consistency and efficiency of the proposed method compared to benchmark iterative methods.

A technique to solve Transshipment Problem with Asymmetric Pentagonal Fuzzy Numbers

In order to draw comparison in largely used fuzzy numbers, ranking of fuzzy numbers becomes important. In this paper, a new method for ranking Asymmetric Pentagonal Fuzzy Numbers (APFN) is proposed. In this method, the pentagonal fuzzy numbers are scored by obtaining their centers of gravity using left and right areas associated with them. Further, we propose a direct technique for solving fuzzy Transshipment Problem (TsP) in which costs are represented as Asymmetric Pentagonal Fuzzy Numbers. The solution so obtained is fuzzy optimal solution. The validity of proposed methodology is illustrated through numerical examples.

Optimizing the Economic Order Quantity Using Fuzzy Theory and Machine Learning Applied to a Pharmaceutical Framework

In this article, we present a novel methodology for inventory management in the pharmaceutical industry, considering the nature of its supply chain. Traditional inventory models often fail to capture the particularities of the pharmaceutical sector, characterized by limited storage space, product degradation, and trade credits. To address these particularities, using fuzzy logic, we propose models that are adaptable to real-world scenarios. The proposed models are designed to reduce total costs for both vendors and clients, a gap not explored in the existing literature. Our methodology employs pentagonal fuzzy number (PFN) arithmetic and Kuhn–Tucker optimization. Additionally, the integration of the naive Bayes (NB) classifier and the use of the Weka artificial intelligence suite increase the effectiveness of our model in complex decision-making environments. A key finding is the high classification accuracy of the model, with the NB classifier correctly categorizing approximately 95.9% of the scenarios, indicating an operational efficiency. This finding is complemented by the model capability to determine the optimal production quantity, considering cost factors related to manufacturing and transportation, which is essential in minimizing overall inventory costs. Our methodology, based on machine learning and fuzzy logic, enhances the inventory management in dynamic sectors like the pharmaceutical industry. While our focus is on a single-product scenario between suppliers and buyers, future research hopes to extend this focus to wider contexts, as epidemic conditions and other applications.

A Fuzzy Inventory Model Using Pentagonal Fuzzy Numbers

Transportation expenses may have an effect on significant business sectors. They could affect a company's price of goods as well as its capacity to remain competitive in the market. Another way to maximize transportation expenses is through inventory management. Prevent needless overstocking and incomplete shipments by keeping an accurate inventory and managing stock levels. This lowers the price of shipping extra items or broken shipments. Nonlinear Programming Kuhn Tucker Method is used to find the optimal solution, which has an impact on the monthly payment. The signed distance approach is used for defuzzification in the proposed model, and the Pentagonal fuzzy number is used to find the lowest cost. To test the inventory model, we create a CSV file and use Weka software to analyse the Economic Order Quantity and total cost.

Pascal's triangle graded mean defuzzification approach for solving fuzzy assignment models by using pentagonal fuzzy numbers

Pascal's triangle graded mean defuzzification approach for solving fuzzy assignment models by using pentagonal fuzzy numbers

Investigation of a Fuzzy Production Inventory Model with Carbon Emission using Sign Distance Method

Reducing costs associated with inventory is the primary goal of conventional inventory models like the models of economic order quantity and economic production quantity. However, these models fall short of addressing defective goods or revising them. Imperfections in the manufacturing process result in flawed products alongside the final goods. To convert these flawed components into finished goods, rework is necessary. In manufacturing and reworking process produces carbon emissions which are harmful for the earth. To determine the optimal quantity for a single product manufactured in a single-stage manufacturing system that yields partially defective products that are reworked in the same cycle, is determined in real-life situations, where the inventory characteristics and objectives are not exact. Such a type of uncertainty may be characterized by fuzzy numbers. A pentagonal fuzzy number has been used to define the cost parameters. Due to fuzzy parameters, the model becomes a fuzzy quantity, and it is defuzzied by the sign distance method. this article formulates a model of manufacturing inventories with planned backorders. Furthermore, a closed form for the inventory’s system total cost is determined, and a range of actual values for defective products for which an appropriate method exists is also provided. A proper mathematical model is created to accomplish the goal, and the manufacturing lot size that reduces the overall cost is determined. The ideal amount of a production batch to reduce total cost is established in to attain this goal using an appropriate mathematical model. While formulating and solving the relevant model, the necessary and sufficient conditions for a single globally optimal solution have been determined. Examples used as visualizations are given and confirmed by data.

Arithmetic Operations on Generalized Pentagonal Fuzzy Numbers

Fuzzy concepts have been widely used to treat imprecision in many fields of natural and social sciences. In most of the natural science fields such as applied mathematics, physics, chemistry, and engineering, triangular and trapezoidal fuzzy numbers are commonly used and arithmetic operations on those numbers are studied in detail. On the other hand, in engineering and social science fields such as sociology and psychology, while treating the uncertainties, these numbers are not applicable and fuzzy numbers with more parameters and clear definitions of their arithmetic operations are needed. In order to fill this gap in the literature, in this study we propose the generalized pentagonal fuzzy numbers, and we define fuzzy arithmetic operations based on both extension and the function principle.

Identification of the critical factors in flood vulnerability assessment based on an improved DEMATEL method under uncertain environments

With accelerated urbanization, the expansion of urban construction land and the increase in concrete pavement have led to a continuous decline in the natural permeability of the urban surface. This makes it difficult for rainwater in urban areas to infiltrate quickly into the ground, which may lead to urban flooding disasters in cases of heavy rainfall. In recent years, the frequency of urban flooding disasters has been increasing, posing a great safety threat to communities and residents as well as property damage. Therefore, it is important to build a scientific and reasonable community flooding vulnerability assessment system to improve the community emergency response capacity and reduce the losses caused by flooding disasters. In this paper, 94 indicators for community flooding vulnerability assessment are collected by combining literature research and field surveys. The newly proposed fuzzy language expression method based on pentagonal fuzzy numbers (PFN) and the proportional two-tuple linguistic representation (P2TLR) are used as the first step of indicator evaluation and screening, and PFN-P2TLR with the two-step DEMATEL method are combined as the second step of indicator screening. Finally, 23 representative evaluation indicators belonging to the dependent variable are selected. Following a thorough investigation, it was found that “resident characteristics”, “regional economic strength”, “community precipitation status” and “institutional soundness” are the four most influential factors for community resilience to flooding, and these indicators have a significant impact on other indicators. The research results provide a reliable basis and specific guidance suggestions for community flooding vulnerability assessment, which is crucial for further reducing the occurrence of flooding disasters and mitigating the social and economic losses caused by them.

A possibility-based multi-criteria decision-making approach for artificial recharge structure selection using pentagonal fuzzy numbers

Groundwater recharge is crucial in developing groundwater sources in an area for regional growth. One of the essential natural water resources is groundwater, which differs geographically in quality and amount. Groundwater resources are under great strain due to growing urbanization and population growth. Numerous studies have identified groundwater recharge regions using a geographic information system and Multi-Criteria Decision-Making (MCDM). In this study, we have proposed an Multi-Criteria Decision-Making technique for selecting artificial recharge structures in basaltic terrain. The proposed Multi-Criteria Decision-Making technique is built with possibility theory under a pentagonal fuzzy environment. Additionally, we have developed a possibilistic middle of asymmetric linear pentagonal fuzzy (LPF) number. Through the Multi-Criteria Decision-Making technique, we have selected the best artificial recharge structures from the available ones. To show our Multi-Criteria Decision-Making methods feasibility, we have considered one numerical example under a pentagonal fuzzy environment.

Optimization of a production inventory model of imperfect quality items for three-layer supply chain in fuzzy environment

PurposeGood management strives to align and corporate processes for more attention being paid to supply chain management. Firms realize that greater co-operation and improved coordination can help to manage the entire supply chain more efficiently. The imperfect quality item is one of the most important issues that affect the expected profit of green supply chain. The imprecise cost with screening process of poor quality items posed in supply chain is the subject of this study.Design/methodology/approachThe present study explores production model for imperfect items having uncertain cost parameters with three-layer supply chain encompassing supplier, manufacturer and retailer. The model is considering the impact of business tactics such as order size, production rate, production cost and appropriate times in various sectors on collaborative marketing systems. Due to imprecise cost parameters, the pentagonal fuzzy numbers are set to fuzzify the total cost and defuzzifition by using graded mean integration.FindingsThis study offers an explicit condition in uncertain environment to manage the imperfect quality item to increase the potential profit of the supply chain. The influence of changes in parameter values on the optimal inventory policy under fuzziness is provided managerial insights.Originality/valueThis model makes a significant contribution to fuzzy inference. The results of the study provide a trading strategy for the industry to avoid losses. The prescribed study can be suitable for the industries like sculpture, jewelry, pottery, etc.

Evaluation of the treatment options for COVID-19 patients using generalized hesitant fuzzy- multi criteria decision making techniques

The breakout of the pandemic COVID-19 has affected numerous countries and territories worldwide. As COVID-19 specific medicines yet to be invented, at present the treatment is case specific, hence identification and evaluation of different prevalent treatment options based on various criteria and attributes are very important not only from the point of view of present pandemic but also for futuristic pandemic preparedness. The present study focuses on identifying, evaluation and ranking of treatment options using Multi Criteria Decision Making (MCDM). In this regard, the existing literature, doctors and scientist were interviewed to know the current treatment options in vogue and the scale of their importance with respect to the criteria. The criteria taken are side effect, regime cost, treatment duration, plasma stability, plasma turnover, time of suppression, ease of application, drug-drug interaction, compliance, fever, pneumonia, intensive care, organ failure, macrophage activation syndrome, hemophagocytic syndrome, pregnancy, kidney problem, age. This study extended Hesitant Fuzzy Set (HFS) to Generalized Hesitant Fuzzy Sets (GHFS). Generalized Hesitant Pentagonal Fuzzy Number (GHPFN) is developed. The properties of GHPFN are demonstrated. Two types of GHPFN has been described. The GHPFN (2nd type) along with MCDM tool Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) has been applied to rank the treatment options. The result of the study ranked ‘Hydroxychloroquine’ as the first alternative followed by, ‘Plasma Exchange’, ‘Tocilizumab’, ‘Remdesivir’ and ‘Favipravir’. To check the robustness and steadiness of the proposed methodology, comparative analysis and sensitivity analysis has been conducted.

A hybrid swarm optimization with trapezoidal and pentagonal fuzzy numbers using benchmark functions

A hybrid swarm optimization with trapezoidal and pentagonal fuzzy numbers using benchmark functions

Fuzzy analytic hierarchy process for pentagonal fuzzy numbers and its application in sustainable supplier selection

Different fuzzy analytic hierarchy process (FAHP) methods are typically developed for conventional fuzzy numbers (FNs), mainly triangular and trapezoidal FNs. The ascending and descending parts of triangular and trapezoidal membership functions (MFs) are straight lines. Therefore, if the value of a member increases by the same values, its membership degrees in ascending (descending) part increase (decrease) equally. These MFs do not necessarily reflect the experts' preferences. Consider two different cases; in the first one, the product quality of supplier A compared to supplier B increases from 2 to 3 times, and in the second case, this quality increases from 8 to 9 times. Triangular and trapezoidal membership degrees in both cases increase equally. However, the quality advantage of supplier A increases by 50% in the first case, while it increases by 12.5% in the second case. Therefore, the experts’ preferences may increase differently for these cases that cannot be reflected accurately by triangular and trapezoidal MFs. To overcome this flaw, we develop four FAHP methods for pentagonal FNs (PFNs). We also use an indirect method to defuzzify the fuzzy local weights. Indirect defuzzification is a simple method equivalent to the center of gravity (COG) method and needs low computations. Numerical examples are used to illustrate the proposed methods. A real example of ranking suppliers in a sustainable framework based on pentagonal fuzzy preferences is also presented. To extract crisp local weights from pentagonal fuzzy comparison matrices, we use the pentagonal FAHP methods presented in this study.

A Novel Algorithm to Find the Best Solution for Pentagonal Fuzzy Numbers with Linear Programming Problems

Fuzzy numbers are used in various fields such as fuzzy process methods, decision control theory, problems involving decision making, and systematic reasoning. Fuzzy systems, including fuzzy set theory. In this paper, pentagonal fuzzy variables (PFV) are used to formulate linear programming problems (LPP). Here, we will concentrate on an approach to addressing these issues that uses the simplex technique (SM). Linear programming problems (LPP) and linear programming problems (LPP) with pentagonal fuzzy numbers (PFN) are the two basic categories into which we divide these issues. The focus of this paper is to find the optimal solution (OS) for LPP with PFN on the objective function (OF) and right-hand side. New ranking function (RF) approaches for solving fuzzy linear programming problems (FLPP) with a pentagonal fuzzy number (PFN) have been proposed, based on new ranking functions (N RF). The simplex method (SM) is very easy to understand. Finally, numerical examples (NE) are used to demonstrate the suggested approach's computing process.

Optimal Procurement of COVID-19 Vaccine with Time-Dependent Holding Cost and Shortages under Cloud Fuzzy Demand Rate

COVID-19 vaccine has emerged as the most powerful weapon against the spread of the coronavirus. Therefore, the management of the vaccine inventory is undoubtedly the most influential and important task for the global distribution of the vaccine. This paper is an attempt to model the vaccine inventory system having time-varying holding costs and partially backlogged shortages. The concept of fuzzy set and cloud pentagonal fuzzy number has been incorporated to make the models more realistic and applicable. Models are solved and validated through numerical examples and graphical representation. Further, sensitivity analysis has been done to identify the most sensitive parameters of all. Finally, managerial insights and conclusions have been drawn to make the vaccine inventory system more robust.

OPTIMIZATION OF A FUZZY INVENTORY MODEL WITH PENTAGONAL FUZZY NUMBERS

This paper explores an optimal replenishment strategy for a two-echelon inventory model which has been considered and analyzed in a fuzzy environment. In fuzzy environment, carrying cost, ordering cost and the replenishment processing cost are assumed to be pentagonal fuzzy numbers. The purpose of this model is to minimize the total inventory cost in fuzzy scenario. There are two inventory models proposed in this paper. Crisp models are developed with fuzzy total inventory cost but crisp optimal order quantity. Fuzzy model is also formulated with fuzzy total inventory cost and fuzzy optimal order quantity. Graded mean integration formula is employed to defuzzify the total inventory cost and the Kuhn–tucker condition is used to determine the optimal order quantity. Finally, we develop an algorithm to obtain the optimal order quantity. A comparison of fuzzy model with classical inventory model is being made. Numerical results highlighting the sensitivity of various parameters are also elucidated. The result illustrates that this fuzzy model can be quite useful in determining the optimal order quantity and minimum total inventory cost.

A Novel Approach for Minimizing Processing Times of Three-Stage Flow Shop Scheduling Problems under Fuzziness

The purpose of this research is to investigate a novel three-stage flow shop scheduling problem with an ambiguous processing time. The uncertain information is characterized by Pentagonal fuzzy numbers. To solve the problem, in this paper, two different strategies are proposed; one relies on the idea of a ranking function, and the other on the close interval approximation of the pentagonal fuzzy number. For persons that need to be more specific in their requirements, the close interval approximation of the Pentagonal fuzzy number is judged to be the best appropriate approximation interval. Regarding the rental cost specification, these methods are used to reduce the rental cost for the concerned devices. In addition, a comparison of our suggested approach’s computed total processing time, total machine rental cost, and machine idle time to the existing approach is introduced. A numerical example is shown to clarify the benefits of the two strategies and to help the readers understand it better.

A Multi Objective Epq Model with Uniform Demand and Productıon Rate Along Wıth Shortages Under Intuitioistic Fuzzy Programmıng Approach

In this paper we have described a multi-objective economic production quantity (EPQ) model with uniform demand rate as well as shortages. In this model we have considered the production rate as finite. Due to uncertainty in the various cost parameters, most of the costs parameters are taken as pentagonal fuzzy number. The model has been solved by Fuzzy Non-Linear Programming Problem (FNLP), Fuzzy Additive Goal Programming Problem (FAGP) and Intuitionistic fuzzy programming approach (IFP).To demonstrate the validity of this model some numerical examples have been given lastly. The sensitivity analysis for some cost parameters has also been given.