Trapezoidal Fuzzy Research Articles

Row Column Reduction Method for Solving Trapezoidal Fuzzy Transportation Problem

The primary goal of the transportation issue is to reduce the cost of moving goods from several warehouses to various showrooms. Fuzzy approaches are frequently employed to eliminate uncertainty. When the cost of transportation is uncertain, we sometimes use a fuzzy approach to resolve the issue. In this paper the values used in constraint equation are trapezoidal number and applied our proposed method, row column reduction method to get an optimal transportation cost.

Bipolar Expected Value-based MCDM Technique for Wastewater Management under Trapezoidal Bipolar Fuzzy Environment

: Kolkata is located on western bank of the Hooghly River. Wastewater from the city is discharged into this river and pollutes the river water. It causes maximum negative effects than positive impacts. Many uncertainties and bipolarity occur for this reason. Through the bipolar fuzzy concept, we can easily take the determination for this situation. A bipolar fuzzy expected is an effective tool for illustrating uncertainty and fuzziness in a decision-making problem. There-fore, in this paper, we have invented the bipolar expected value of bipolar fuzzy numbers. In addition, we have invented a few formulae and a theorem based on bipolar expected values. Using this bipolar expected value, we developed a novel MCDM technique, and it's employed for wastewater management problems in Kolkata city under a bipolar environment. Numerically, we have solved the wastewater management problem under a bipolar fuzzy environment.

Fermatean trapezoidal fuzziness average aggregation scheme for selection of infant clothing by group decision-making

The textile industry has gradually increased its use of various chemicals and the quantity of residues produced. Newborn baby apparel should be made of safe materials since it often comes into touch with them. Infant cloth selection is determined via group decision-making in Fermatean trapezoidal fuzzy number (FTFN). This study provides a new score and accuracy function and weighted, ordered, and hybrid averaging aggregation operators on FTFN. The properties of the proposed averaging aggregation operators on FTFN are presented. An algorithm for the multi-attribute group decision-making (MAGDM) approach will be proposed by applying the proposed averaging aggregation operators. The case studies concentrate on choosing newborn clothing with reduced chemical content within the textile sector. The presentation of the sensitivity analysis of the criterion weights is conducted to guarantee the durability and stability of the framework that has been implemented. Furthermore, a comprehensive analysis compares the novel framework with previous models, highlighting its superior performance.

A Novel Method Based on the Fuzzy Entropy Measure to Optimize the Fuzziness in Trapezoidal Strong Fuzzy Partitions

Analyzing the uncertainty of outcomes based on estimates of the data’s membership degrees to fuzzy sets is essential for making decisions. These fuzzy sets are often designated by experts as strong fuzzy partitions of the data domain with trapezoidal fuzzy numbers. Some indices of the fuzzy set’s fuzziness provide an assessment of the degree of uncertainty of the results. It is feasible to bring the fuzzy sets’ fuzziness below a tolerable level by suitably redefining the strong fuzzy partition. Significant differences in the original fuzzy partition, however, result in disparities concerning the decision maker’s approximative reasoning and the interpretability of the results. In light of this, we provide in this study a technique applied to trapezoidal strong fuzzy partitions that, while not appreciably altering the original fuzzy partition, reduces the fuzziness of its fuzzy sets. The fuzziness of the fuzzy sets is assessed using the De Luca and Termini fuzzy entropy. An iterative process is then executed, with the aim of modifying the cores of the trapezoidal fuzzy partitions to decrease their fuzziness. This technique is tested on datasets containing average daily temperatures measured in various cities. The findings demonstrate that this approach strikes a great balance between the goal of lessening the fuzziness of the fuzzy sets and the goal of not appreciably altering the original fuzzy partition.

Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method

In the real world, we are faced with many problems that cannot be easily described by crisp values, as there is always some uncertainty involved in real-life situations and in those situations, we end up receiving fuzzy values rather than crisp ones in those situations. Some preliminary concepts of fuzzy sets and operations on trapezoidal fuzzy numbers incorporated with the membership function have been discussed here. This paper aims to demonstrate the advantages of the newly developed fuzzified newton-raphson method with the help of trapezoidal fuzzy numbers for solving algebraic nonlinear equations arising in fuzzy environments. The algorithm of newton-raphson techniques for solving the same has been described. This paper presents several examples of how the new fuzzified newton-raphson method works.

Legendre Operational Differential Matrix for Solving Fuzzy Differential Equations with Trapezoidal Fuzzy Function Coefficients

In this work, we used the Legendre operational differential matrix method based on Tau method to obtain the fuzzy approximate-analytical solutions of the fuzzy differential equations in which the coefficients are trapezoidal fuzzy function. This method allows for the fuzzy solution of the fuzzy initial ( or boundary) value problems to be computed in the form of an infinite fuzzy series .Also, this method enables to approximate the fuzzy exact-analytical solutions with high efficiency, as these solutions can be resorted to if it is not possible to find the exact solutions of these fuzzy problems. We introduced a comparison between the approximate solutions that we computed and the exact solutions of the chosen problem, as we found the absolute error. According to the numerical results, the series solutions that we found are accurate solutions and very close to the exact solutions.

Optimization techniques of Assignment Problem using Trapezoidal Intuitionistic Fuzzy Numbers and Interval Arithmetic

This paper discusses the Assignment problem to optimize the assigning of jobs to workers based on their talents and efficiency. In general, scheduling jobs plays a significant role in manufacturing and is advantageous in real world applications as we face more uncertainty and ambiguity in assigning jobs. The Intuitionistic Fuzzy Assignment problem (IFAP) is employed in circumstances when decision-makers have to deal with uncertainty. The domains are Trapezoidal Intuitionistic Fuzzy Numbers (TrIFNs) and the techniques used are Hungarian Method (HM), Brute Force Method (BFM), and Greedy Method (GM). The suggested model's performance is compared with the existing approach with the help of interval arithmetic operations. Allocating work to the individual is illustrated numerically, the optimal solution of minimizing cost is obtained using R programming and the results of comparative analysis are shown diagrammatically that help viewers to easily understand and generate results from comparisons.

A Decision-Making Framework for Sustainable Highway Restaurant Site Selection: AHP-TOPSIS Approach based on the Fuzzy Numbers

This research work indicates the site selection problem for a restaurant beside the highway. It is really challenging as well as demanding work. It mainly depends on the cost of the selected location, transportation, parking facility, hygienic atmosphere, distance from the city, etc. In this paper, the proposed site selection problem is constructed and solved by using a fuzzy MUlti-Criteria Decision Making (MCDM) process. The two methods of MCDM, that we use here namely the Analytic Hierarchy Process (AHP) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for calculate criteria weight and rank the proposed restaurant locations, respectively. Multiple decision makers (DMs) opinions are considered for data collection and Trapezoidal Fuzzy Numbers (TrFNs) are taken as uncertainty tools to deal with uncertainty. Finally, we perform the sensitivity and comparative analysis performed to verify the system's vagueness and flexibility.

Innovative approaches to multi-attribute decision-making in brain carcinoma diagnosis: a complex q-rung orthopair trapezoidal fuzzy framework and aggregation operator analysis

Innovative approaches to multi-attribute decision-making in brain carcinoma diagnosis: a complex q-rung orthopair trapezoidal fuzzy framework and aggregation operator analysis

Towards green logistics: An innovative decision support model for zero-emission transportation modes development

The transition towards sustainable and eco-friendly transportation modes is a critical step in alleviating the adverse impacts of climate change and reducing carbon emissions. In this aspect, the zero-emission transportation modes development (ZETMD) has received growing interest from policymakers and researchers across the globe. However, developing zero-emission transportation modes is a complex task, as numerous challenges exist in real-life scenarios that must be addressed. Additionally, the identification and modeling of challenges related to ZETMD considering large-scale uncertainty are absent in the literature. Therefore, this study uniquely contributes to the existing literature by identifying and analyzing the critical challenges of ZETMD by offering an integrated and novel decision support method that combines Interval Type-2 Trapezoidal Fuzzy Set (IT2TrFS) Pareto and a generalized IT2TrFS weighted averaging (GIT2TrFSWA) operator-based IT2TrFS-Best-Worst Method (BWM) with lower defuzzification (LD). This integrated model is robust and capable of handling a broader scale of uncertainty during the subjective judgment of challenges. The IT2TrFS-Pareto analysis helps identify the most critical challenges, while GIT2TrFSWA operator-based IT2TrFS-BWM with LD aids in determining the importance of these challenges. The IT2TrFS-Pareto analysis identifies nine challenges as critical challenges from an initially selected sixteen challenges. The findings of the IT2TrFS-BWM-LD analysis suggest that the “High cost of clean technologies development for transport” is the most critical challenge for ZETMD carrying a normalized IT2TrFS defuzzified weight of 0.26067. Further, comprehensive sensitivity, comparative, and statistical correlation analyses confirm the robustness and reliability of the proposed model. The study findings can serve as a benchmark for policymakers and decision-makers to overcome these challenges by formulating and implementing appropriate strategic policies in real-life scenarios that can further mitigate carbon emissions.

Risk Assessment Framework for Reverse Logistics in Waste Plastic Recycle Industry: A Hybrid Approach Incorporating FMEA Decision Model with AHP-LOPCOW- ARAS Under Trapezoidal Fuzzy Set

In this study, a novel risk assessment framework designed for evaluating the challenges of plastic packaging waste management in the context of reverse logistics is introduced. The framework leverages Failure Mode Effect Analysis (FMEA) to address decision-making in a fuzzy environment. To augment the traditional FMEA risk criteria, encompassing severity (S), occurrence (O), and detection (D), three additional essential risk criteria are introduced: cost of failure (C), complexity of failure resolution (H), and impact on business (I). These newly incorporated criteria significantly enhance the capacity to convey the multifaceted risks inherent in reverse logistics for the plastic recycling sector. Furthermore, a comprehensive literature review and expert validation are conducted to identify ten distinct failure modes. To subjectively and objectively determine the risk criteria weightings, a combination of Analytic Hierarchy Process (AHP) and LOgarithmic Percentage Change-driven Objective Weighting (LOPCOW) is employed. Finally, the Additive Ratio Assessment (ARAS) approach is applied to prioritize such failure modes. Recognizing the inherent imprecision and uncertainty associated with human decision-making, the trapezoidal fuzzy set (TrFS) is adopted throughout all decision-making processes. To showcase the proposed framework effectiveness, the framework is applied as a case study to a waste plastic recycling manufacturer in Thailand.

A Study of an EOQ Model of Deteriorated Items with Pentagonal Dense Fuzzy Demand Rate

In this project work, we deal with an economic order quantity inventory model of deteriorating items under non-random uncertain demand. Here we consider the customers screen the fresh items during the selling period. After a certain period of time, the deteriorated items are sold at a discounted price. Firstly, we solve the crisp model, and then the model is converted into a fuzzy environment. Here we consider the pentagonal dense fuzzy, trapezoidal dense fuzzy, and triangular dense fuzzy for a comparative study. We have taken the numerical result using LINGO 18.0 software. Finally, sensitivity analysis and graphical illustration have been given to check the validity of the model.

Trapezoidal fuzzy number methodology for prioritising the predictors of social media addiction

ABSTRACT Numerous studies investigate factors contributing to social media addiction, but few explore their significance and interconnections from psychotherapists’ and researchers’ perspectives. This study used the DEMATEL methodology to examine social media addiction, identifying 50 predictors from literature, categorized into personality traits, comorbid symptoms, and psychosocial components. Data from 115 respondents showed personality traits as the most influential factor. DEMATEL analysis categorized predictors into cause-and-effect groups. Experts assessed direct relationships using Trapezoidal Fuzzy Numbers (TFN), which were then converted and analyzed. The study compared DEMATEL variants, finding Trapezoidal Fuzzy DEMATEL most effective for evaluating predictor interrelationships.

Two-level balancing multi-objective algorithm for trapezoidal type-2 fuzzy flexible job shop problems

Uncertainty remains a critical issue in realistic applications in many fields. However, there is little literature considering trapezoidal interval type-2 fuzzy set (TIT2FS) in scheduling problems. To fill this gap, we propose a two-level balancing multi-objective optimization algorithm for a distributed flexible job shop scheduling problem (DFJSP), wherein two typical constraints are considered: the TIT2FS processing time and the transportation resource limitation. Two objectives are to be minimized: the TIT2FS fuzzy makespan and energy consumption. A two-level evolution mechanism is employed. The first level comprises two populations to optimize the two respective objectives, while the second level is composed of two populations to perform the convergence and diversity balancing tasks. Next, an efficient problem-specific initialization method with several heuristics is presented. Subsequently, different types of mutation and crossover operators are proposed under the consideration of problem knowledge. To further improve the performance of exploration and exploitation abilities, we present a balancing enhanced local search method. Finally, we performed detailed comparisons with four efficient algorithms. The results show that the two-level optimization algorithm was efficient in both convergence and diversity abilities, indicating that our algorithm can efficiently achieve a balance between these abilities.

Evaluation of carbon capture technologies in the oil and gas industry using a socio-technical systems perspective-based decision support system under interval type-2 trapezoidal fuzzy set

Concerns in relation to consequences of global warming and climate change have activated worldwide attempts for mitigating the concentration of carbon dioxide (CO2) produced by the industrial sector. Decarbonizing the oil and gas refining (OGR) industries is a challenging problem for policy-makers owing to its potential to prevent economic, environmental, and health risks. In this regard, CO2 capture, utilization, and storage (CCUS) technologies are the most encouraging options to decarbonize. The technologies related to the part of CO2 capture can play a vital role in solving the mentioned problem. Various technologies have been employed for CO2 capture, and choosing the appropriate technology is a complex multi-criteria decision-making (MCDM) issue. This work develops a novel and robust decision support system (DSS). The DSS integrates MCDM techniques of the Delphi and Entropy integration method (DAEIM) and complex proportional assessment of alternatives (COPRAS) method with the interval type-2 trapezoidal fuzzy (IT2TF) environment. The proposed DSS is used to evaluate, prioritize, and choose technologies for CO2 capture. A hybrid criteria system, which involves elements of socio-technical systems perspective has been used for evaluating the candidate technologies. For implementing the DSS of this work, five capture technologies of post-combustion (A_cc1), pre-combustion (A_cc2), oxy-fuel combustion (A_cc3), direct air capture (A_cc4), and indirect air capture (A_cc5) have been chosen for evaluation. The final value of each technology is A_cc1 (0. 2907), A_cc2 (0.2602), A_cc3 (0.1005), A_cc4 (0.2304), and A_cc5 (0.1181) and the preferences of the technologies are A_cc1> A_cc2> A_cc4> A_cc5> A_cc3. The evaluation findings reveal that post-combustion technology with the value of 0.2907 is the most suitable scenario for the capture of CO2 emissions from Iran's OGR systems. The computation results demonstrate that the suggested DSS is feasible and applicable and give reliable and robust findings for acquiring the optimal CO2 capture technology.

A Novel Ranking Approach to Rank Interval-Valued Trapezoidal Intuitionistic Fuzzy Sets by Using the Concept of Centroids

A Novel Ranking Approach to Rank Interval-Valued Trapezoidal Intuitionistic Fuzzy Sets by Using the Concept of Centroids

Fuzzy Logic In The Digital Travel Era: Enhancing Tourist Experience Through Comprehensive Hotel Reviews And Sentiment Analysis

In today's society, social media is becoming a more and more important part of our everyday lives as it continues to evolve. Lot of of users assess and tourist rate attractions daily, and hotels play a significant part in travel. Following reviews can be implicated to fuzzy logic, which will be beneficial for resolving the fame of tourist attractions and hotel reviews. Tourists can choose their accommodation and travel destinations with ease based on the outcome of the fuzzy control system. In this research, fuzzy logic has been used to implement sentiment analysis. To provide precise pass on relating to a few aspects chosen by the end user, the system uses attributes including food quality, service, locations, and ratings. This method enables customers to assess a certain hotel service's quality using a variety of factors. Additionally, a user can compare various hotels in depth. To accomplish this, a membership task that specifies how a smooth value maps to the term on a scale of 0 to 1 is used in the proposed system of fuzzy logic. It essentially outlines "how good" something is and how to produce complex behaviour from a condensed, understandable set of professional guidelines before passing these variables to a fuzzy control system. Using a set of rules, a fuzzy control system connects fuzzy variables. These laws are merely mappings that explain the relationships between one or more fuzzy variables. After specifying the inputs and obtaining the priority of the alternatives, the control system is finally simulated. As food preferences, service quality, and user-specific amounts vary, the system is scaled for each individual user. As a result, the system offers more accurate outcomes and increased classification method accuracy for the supplied review data set. Future research will use the Trapezoidal Fuzzy Number (TpFNs) as an evaluation tool to reflect clearly the variation of an element from 0 to 1 in order to increase the model's accuracy.

A Smart Manufacturing Process for Textile Industry Automation under Uncertainties

Most textile manufacturing companies in the world heavily rely on manual labor, particularly in the fabric inspection section, especially for cotton fabric. Establishing smart manufacturing systems like industrial automation in the textile industry for cotton fabric inspection is important for error-free inspection. The proposed make-to-order (MTO) inventory model focuses on the strategic development of a supply chain network under fuzzy uncertainty. The distinctiveness of this research lies in integrating a methodology that involves human and machine interaction, along with allocating resources to investment in smart manufacturing. This article presents a case study of the Jagatjit Cotton Textiles (JCT) manufacturing company in Punjab, India, as an example to validate the model and check the performance of SMT in the fabric inspection process in cotton TC mills. This paper contributes by developing four distinct textile supply chain models with industrial automation under triangular and trapezoidal fuzzy demand. A numerical analysis is conducted to verify the effectiveness of installing automated fabric inspection machines in the cotton plant. This article proposes an iterative solution algorithm (KDPMG) to obtain the global optimum for the proposed model. A comparative study of the proposed algorithm, KDPMG, and the genetic algorithm (GA) is presented in this study to verify the credibility of the obtained results. It is observed that KDPMG provides more appropriate solutions to the problem compared to the GA. Moreover, the computational time of KDPMG is significantly less than that of the GA. The rigorous analysis reveals that maximum profit can be achieved under trapezoidal fuzzy demand with fully automated fabric inspection technology. Using a triangular fuzzy demand pattern, the model with fully automated smart manufacturing achieves an 8.62% higher profit compared to a traditional system. Similarly, in the case of a trapezoidal fuzzy demand pattern, the adoption of automation in cotton plants can achieve an 8.69% higher profit. Hence, the implementation of smart manufacturing systems in the mending section of the cotton textile industry proves to be more profitable compared to the traditional inspection process.

New algorithm for two-machine fuzzy flow shop scheduling problem with trapezoidal fuzzy processing time

The flow-shop scheduling problem (FSSP) has received a considerable amount of attention due to its wide-ranging applications. However, the omission of uncertainty significantly diminishes the practicality of scheduling results, underscoring its the necessity to address uncertainty in the flow shop problem. In this paper, a fuzzy two-machine flow-shop problem is considered and an effective algorithm with a fuzzy ranking method is proposed to minimize the total waiting time. The processing times are represented using trapezoidal membership functions. Furthermore, a two-stage flow shop scheduling problem is used in the proposed algorithm and various categories of fuzzy mean techniques. The experimental results and statistical comparisons demonstrate that the proposed algorithm exhibits significant advantages in effectively solving the FFSSP (Fuzzy Flow-Shop Scheduling Problem).

SOLVING STOCHASTIC TRANSPORTATION ELECTRICITY PROBLEM WITH FUZZY INFORMATION ON PROBABILITY DISTRIBUTION USING MATLAB PROGRAM

This study focuses on MATLAB code programs of the entire stages of solving Stochastic Transportation Linear Programming Problems with Fuzzy Uncertainty Information on Probability Distribution Space (STLPPFI) with its algorithm outlines. A MATLAB code program of STLPPFI problem solver with algorithm outlines are proposed to solve STLPPFI model problems, and it utilizes many concepts as Alpha-Cut technique, Truth Degrees technique, Linear Fuzzy Membership Function (LFMF), Trapezoidal Fuzzy Number , Triangular Fuzzy Number , Linear Fuzzy Ranking Function (LFRF), Expectation Weighted Summation technique (EWS) and analyzing cases via second condition test of alpha-cut technique. The STLPPFI problem solver is utlized to convert STLPPFI into its corresponding equivalent Deterministic Transportation Linear Programming Problem (DTLPP) via defuzzifying from fuzziness on probability distribution space and derandomization randomness of problem formulation respectively. In addition, Dual-Simplex algorithm method with Vogel Approximation Algorithm Method (VAM) are used to obtain optimal solution from DTLPP. All MATLAB code programs with their proposed algorithm outlines are new except Dual-Simplex and VAM. The MATLAB code program of STLPPFI problem solver are more efficient along with a numerical example on electricity field illustrating practicability of this proposed MATLAB code program with its algorithm. Finally, the solution procedure illustrates the MATLAB code program of the proposed method is practical and applicable in the fields of energy and industry as it facilitates the method of transforming the energy at the lowest cost, least time running and is commercially applicable. Comparative comments are provided between Dual-Simplex and VAM in solution process.