Trapezoidal Intuitionistic Fuzzy Numbers Research Articles

Functional-Combination-Based Comprehensive Benefit Evaluation of Energy Storage Projects under Source-Grid-Load Scenarios via Super-Efficiency DEA

As an important support for power systems with high penetration of sustainable energy, the energy storage system (ESS) has changed the traditional model of simultaneous implementation of electricity production and consumption. Its installed capacity under the source-grid-load scenario is rising year by year, contributing to sustainable development, but it faces the problems of insufficient utilization and benefits. This study analyzes the functional combination of ESS under source-grid-load scenarios. A comprehensive benefit evaluation method of energy storage projects (ESPs), based on a fuzzy decision-making trial and evaluation laboratory (DEMATEL) and super-efficiency data envelopment analysis (DEA), is proposed. Firstly, the functional requirements of energy storage in source-grid-load scenarios are explored, and the characteristics of various functions are analyzed to form eight functional combination schemes. Secondly, index modeling is carried out from three aspects—the whole life cycle cost, functional combination benefits, and social and environmental benefits—and a comprehensive benefit evaluation index system of ESP is proposed. Then, the intuitionistic trapezoidal fuzzy number (ITFN) is combined with DEMATEL to form an effective analysis method for the input–output relationship of the indices, and the comprehensive evaluation is realized based on the SE-DEA model. Compared with other methods, this model can ensure the objectivity and stability of the evaluation results in ESP evaluation. Finally, the effectiveness of the proposed evaluation method and the rationality of the functional combination are verified under source-grid-load scenarios. The calculation results show that in the application scenario of source-grid-load, after adopting the functional combination scheme formulated in this article, the comprehensive investment benefits of ESPs have been improved. Moreover, the source side effect is at its best, with an efficiency value of 2.209.

An intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model

Intuitionistic fuzzy sets cannot consider the degree of indeterminacy (i.e., the degree of hesitation). This study presents an intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model. We examine the proposed model by assuming generalized trapezoidal intuitionistic fuzzy numbers for the initial condition. Feasible equilibrium points, along with their stability criteria, are evaluated. We describe the characteristics of intuitionistic fuzzy solutions and clarify the difference between strong and weak intuitionistic fuzzy solutions. Numerical simulations are performed in MATLAB to validate the model results.

Evaluating and Ranking Metaverse Platforms Using Intuitionistic Trapezoidal Fuzzy VIKOR MCDM: Incorporating Score and Accuracy Functions for Comprehensive Assessment

The purpose of this study is to develop a new approach for decision-making for addressing multi-attribute decision-making problems within a trapezoidal intuitionistic fuzzy environment, while taking into account decision makers' psychological behavior. As a starting point, we propose and apply a distance metric model for trapezoidal intuitionistic fuzzy numbers. Then, by incorporating the expected value, score function, and accuracy value, we create a novel approach by comparing it with the results obtained from the VIKOR multi-criteria decision-making technique, allowing us to account for decision makers' risk tolerance. Through correlation analysis, we assess the similarities and deviations in the resulting rankings. Finally, we illustrate the practical utility and feasibility of our proposed approach by evaluating the digital marketing capabilities of a few metaverse platforms using standards set in line with marketing mix criteria.

A Novel Method for Finding the Shortest Path With Two Objectives Under Trapezoidal Intuitionistic Fuzzy Arc Costs

The Shortest Path Problem is a core problem in network optimization, with applications in various scientific and engineering fields, such as communication, transportation, routing, scheduling, and computer networks. Many studies and algorithms have been proposed to solve the traditional shortest path problem, but they often fail to provide optimal solutions when dealing with the uncertainties and vagueness that exist in real-world situations. This study aims to address the Bi-objective Shortest Path Problem using intuitionistic fuzzy arc numbers. The main goal is to find the path that minimizes both cost and time between a given source node and destination node. To handle the complexities introduced by trapezoidal intuitionistic fuzzy numbers, an accuracy function is used. The study suggests a simple yet effective method to solve this problem and shows its efficiency through a numerical example. The research tries to offer innovative solutions for optimizing paths in scenarios where cost and time factors are important, navigating the complex landscape of uncertainty inherent in practical applications.

An optimization method to solve a fully intuitionistic fuzzy non-linear separable programming problem

This paper presents an optimization method to solve a non-linear separable programming problem with coefficients and variables as generalized trapezoidal intuitionistic fuzzy numbers. Such optimization problems are known as fully intuitionistic fuzzy non-linear separable programming problems. The optimization method is based on the linear approximation of fully intuitionistic fuzzy non-linear separable functions. The concept of an intuitionistic fuzzy line segment between two intuitionistic fuzzy points is introduced to find the required linear approximation. In this way, a fully intuitionistic fuzzy non-linear programming problem is converted into an intuitionistic fuzzy linear programming problem. The defuzzification and component-wise comparison techniques are then used to convert the fully intuitionistic fuzzy linear programming problem to a linear programming problem with crisp coefficients which can then be solved by using traditional optimization techniques. The application of the proposed approach in an investment problem faced by a businessman has been presented.

A prey-refuge harvesting model using intuitionistic fuzzy sets

This study considers the classical Lotka–Volterra model for a prey–predator system with harvesting effort and catchability coefficients for both species incorporating a new prey-refuge parameter. Trapezoidal intuitionistic fuzzy numbers are considered to describe the initial values of the prey and predator population. Generalized Hukuhara intuitionistic fuzzy derivatives of type 1 and type 2 are used to formulate the prey–predator model. Non-negative feasible steady states and stability criteria are analyzed along with strong and weak solutions for the model. Numerical simulations with the help of MATLAB are performed for suitable parameter values, and the results are depicted graphically.

How to improve the rumor-confutation ability of official rumor-refuting account on social media: A Chinese case study

Accelerated by the widespread use of social networks, the propagation of rumors has been a destructive factor in the Internet environment. Chinese governments at different administrative levels have established official rumor-refuting accounts on social media to confute rumors, but the spread of rumors in social networks remains a significant concern due to the immature construction of rumor-refuting accounts. To identify the deficiencies of official rumor-refuting accounts at different administrative levels and how to improve their rumor-confutation ability, this paper applies a multi-criteria decision-making (MCDM) method to evaluate Chinese official rumor-refuting accounts on social media, then discusses the differences among them to provide targeted suggestions for improvement. Based on the 10,253 rumor-refuting articles published by 26 Chinese official rumor-refuting accounts on WeChat (a combined social media of Twitter and WhatsApp in China) in 2021, this paper first proposes a targeted rumor-refuting ability evaluation criteria system based on Source-Message-Channel-Receiver (SMCR) theory of communication. Then it applies the Stochastic Multi-criteria Acceptability Analysis-Analytic Hierarchy Process Sort-II with intuitionistic trapezoidal fuzzy numbers (SMAA-AHPSort-II-ITFN) method to evaluate and compare the official rumor-refuting accounts at different administrative levels. The evaluation results show significant differences in the ability of various rumor-refuting accounts to confute rumors. Finally, specific suggestions are provided for improving the ability of official rumor-refuting accounts.

A Novel Similarity Measure Based on Accuracy Score of Conventional Type of Trapezoidal-Valued Intuitionistic Fuzzy Sets and Its Applications in Multi-criteria Decision-Making Problems

The article aims to investigate the distance measure between any two conventional type trapezoidal-valued intuitionistic fuzzy sets (CTrVIFSs) whose membership and non-membership grades of an element are expressed as conventional trapezoidal intuitionistic fuzzy numbers (CTrIFN). Using the proposed distance measure, the similarity measure of CTrVIFSs is determined and its efficiency is shown by applying it to pattern recognition problems and MCDM problems. The similarity measure propounded in this article can be used to tackle real-world problems involving CTrVIFS as parameters, such as clustering, machine learning, and DNA matching. The application section discusses that this research can help decision-makers to recognize patterns and categorize samples with those patterns. Furthermore, the model of a real-world problem is given which utilizes the suggested similarity measure to solve MCDM problems, demonstrate the usability of the new technique and comprehend its applied intelligence above other methods. Finally, a general conclusion and future scope on this topic are discussed.

Solving multi-objective linear fractional decentralized bi-level decision-making problems through compensatory intuitionistic fuzzy mathematical method

This study has focused on developing a new method for solving the multi-objective linear fractional decentralized bi-level decision-making (MOLF-DBLDM) problem in an intuitionistic fuzzy decision environment. The main motivation behind this study is to determine a solution approach algorithm that is effective and simple to apply while taking actual decision-making circumstances into account. Real-world decision-making situations involve a bi-level of several decision-makers who use various decision-making processes such as agree, not certain, and disagree. By considering such real-world conditions here, all uncertain coefficients of objectives, constraint functions, and resources are portrayed as trapezoidal intuitionistic fuzzy numbers, and their crisp form is obtained through the (α,β)-cut (confidence level) concept. In the suggested method, we have transformed the crisp (α,β)-MOLF-DBLDM problem into a single objective linear decentralized bi-level decision-making (SOL-DBLDM) model using a modified linearized approach. Additionally, the upper level specified a tolerance region for its decision variables to regulate the lower levels in order to prevent decision lock. Then, the SOL-DBLDM problem is expressed as a single-level model using a new scalar function of membership and non-membership degree for each objective function at all decision-makers and upper level decision control variables. The key advantage of this method over others is that it produces an alternate, preferable compromise solution to the problem of imprecise hierarchical-level optimization. Finally, comparisons to the current methodology and appropriate numerical examples are used to demonstrate the superiority and effectiveness of the suggested method.

Bayesian Uncertainty Inferencing for Fault Diagnosis of Intelligent Instruments in IoT Systems

Intelligent instruments are common components in industrial machinery, and fault diagnosis in IoT systems requires the handling of real-time sensor data and expert knowledge. IoT sensors cannot collect data for the diagnosis of all fault types in a specific instrument, and long-distance data transfer introduces additional uncertainties. However, because industrial equipment has complex fault causes and performances, it is typically difficult or expensive to obtain exact fault probabilities. Therefore, in this study, we proposed an innovative failure detection and diagnosis model for intelligent instruments in an IoT system using a Bayesian network, with a focus on handling uncertainties in expert knowledge and IoT monitoring information. The model addresses the challenge of complex fault causes and performances in industrial equipment, which make the obtainment of exact fault probabilities difficult or expensive. The trapezoidal intuitionistic fuzzy number (TrIFN)-based entropy method was applied in order to aggregate expert knowledge to generate priority probability, and the Leaky-OR gate was used to calculate CPT. The effectiveness of the proposed strategy was demonstrated through its application to an intelligent pressure transmitter (IPT) using the GeNIe software.

A new ranking method for trapezoidal intuitionistic fuzzy numbers and its application to multi-criteria decision making

The ranking of intuitionistic fuzzy numbers is paramount in the decision making process in a fuzzy and uncertain environment. In this paper, a new ranking function is defined, which is based on Robust’s ranking index of the membership function and the non-membership function of trapezoidal intuitionistic fuzzy numbers. The mentioned function also incorporates a parameter for the attitude of the decision factors. The given method is illustrated through several numerical examples and is studied in comparison to other already-existent methods. Starting from the new classification method, an algorithm for solving fuzzy multi-criteria decision-making (MCDM) problems is proposed. The application of said algorithm implies accepting the subjectivity of the deciding factors, and offers a clear perspective on the way in which the subjective attitude influences the decision-making process. Finally, a MCDM problem is solved to outline the advantages of the algorithm proposed in this paper.

A comparative analysis of the fuzzy and intuitionistic fuzzy environment for group and individual equipment replacement Models in order to achieve the optimized results

The main goal of this research is to compare group and individual replacement models based on fuzzy replacement theory and intuitionistic fuzzy replacement theory. The capital costs are assumed to be triangular fuzzy numbers, triangular intuitionistic fuzzy numbers, and trapezoidal intuitionistic fuzzy numbers, respectively. As a result, interpreting the direct relationship between volatility and ambiguity is critical. It is difficult to predict when specific equipment will unexpectedly fail. This problem can be solved by calculating the probability of failure distribution. Furthermore, the failure is assumed to occur only at the end of period t. In this situation, two types of replacement policies are used. The first is the Individual Replacement Policy, which states that if an item fails, it will be replaced immediately. The Group Replacement Policy states that all items must be replaced after a certain time period, with the option of replacing any item before the optimal time. The dimensions of the prosecution are fuzzy, and they are then assessed using mathematical and logical procedures. The fuzzy assessment criteria of the replacement model are provided as a set of outcomes, whereas the intuitionistic fuzzy replacement model has many advantages. A methodological technique is used to determine quality measurements in which fuzzy costs or values are kept without being merged into crisp values, allowing us to draw mathematical inferences in an uncertain setting. A comparison conceptualise is created for each fuzzy number, and in an uncertain environment, a comparison study on group and individual replacement was also conducted.

Semi-Analytical Scheme for Solving Intuitionistic Fuzzy System of Differential Equations

The aim of this article is to implement the Generalized Modified Adomian Decomposition Method to compute the semi-numerical solution of the linear system of intuitionistic fuzzy initial value problems. Here, we consider the initial values as generalized trapezoidal intuitionistic fuzzy numbers. The technique is applied to brine tanks problem and coupled mass spring systems.Theoretically, different approaches to solving a system of generalized trapezoidal intuitionistic fuzzy differential equations are discussed in this study under the presumption that the coefficients of the system of the differential equations are associated to generalized trapezoidal intuitionistic fuzzy numbers. The approximate results are compared with exact solutions which shows good efficiency. The corresponding graphs at different levels of uncertainty show the example’s numerical outcomes. The graphical representations further demonstrate the effectiveness and accuracy of the proposed method in comparison to existing semi-numerical methods in the literature.

Trapezoidal Intuitionistic Fuzzy Power Heronian Aggregation Operator and Its Applications to Multiple-Attribute Group Decision-Making

Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used. It is mainly because of the flexibility in capturing the incompleteness that occurs in the data. Aggregation operators play a vital role in real-life decision-making problems (modelled under an intuitionistic fuzzy environment). Different aggregation operators are available in the literature for better decision-making. Various aggregation operators are introduced in the literature as a generalization to the conventional aggregation functions defined on the set of real numbers. Each aggregation operator has a specific purpose in solving the problems effectively. In recent years, the power average (PA) operator has been used to reduce the effect of biased data provided by decision-makers. Similarly, the Heronian mean (HM) operator has a property that considers the inter-relationship among various criteria available in the decision-making problem. In this paper, we have considered both the operators (HM, PA) to introduce a new aggregation operator (on the set of TrIFNs), which takes advantage of both properties of these operators. In this study, firstly, we propose the idea of a trapezoidal intuitionistic fuzzy power Heronian aggregation (TrIFPHA) operator and a trapezoidal intuitionistic fuzzy power weighted Heronian aggregation (TrIFPWHA) operator by combining the idea of the Heronian mean operator and power average operator in real numbers. Secondly, we study different mathematical properties of the proposed aggregation operators by establishing a few essential theorems. Thirdly, we discuss a group decision-making algorithm for solving problems modelled under a trapezoidal intuitionistic fuzzy environment. Finally, we show the applicability of the group decision-making algorithm by solving a numerical case problem, and we compare the proposed method’s results with existing methods.

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

A Study of Foam Bitumen Preparation for Effective Recycling of Pavement Layers

Foamed asphalt recycling technology can effectively recover waste asphalt pavement materials and achieve the sustainable utilization of resources. This technology’s core equipment is asphalt foaming equipment. Since the asphalt foaming device’s fault data are uncertain, this work proposes a method for evaluating the device’s reliability, combining triangular intuitionistic fuzzy numbers, trapezoidal intuitionistic fuzzy numbers, and expert knowledge. Using the proposed evaluation method, the failure probability of the asphalt foaming device and the importance of the bottom event were calculated. The obtained model results were found to be consistent with the actual collected data, verifying the reliability and validity of the model. Furthermore, the asphalt viscosity is one of the key factors affecting the asphalt foaming recycling technology. In this work, the influence of different viscosities on the asphalt foaming mechanism was investigated using a theoretical analysis. Then, a computational fluid dynamics (CFD) analysis method was employed to simulate the different viscosity asphalt foaming processes, aiming to identify the most suitable one for the production of high-quality foam asphalt in the foaming asphalt viscosity range. Finally, experiments were carried out to verify the results of the analysis. The results show that the asphalt foaming device’s failure probability was around 7.512 × 10−2, and the best foaming asphalt viscosity was in the range of 0.3~0.5 Pa·s.

An [formula omitted]-cut interval based IF-importance measure for intuitionistic fuzzy fault tree analysis of subsea oil and gas production system

The subsea production system is very important for having deep water oil and gas production. The leakage of the oil and gas in the subsea production system may result in enormous adverse consequences on marine lives, high production loss, and serious deadly disasters to humans. For the safety analysis of subsea production system, importance measures play an important role to rank the components of the system according to their contribution to the leakage of oil and gas for preventive and corrective purposes. In conventional fault tree analysis and fuzzy fault tree analysis, various importance measures are developed for criticality analysis of the system. The objective of the present study is to develop a novel IF-importance measure by employing the concept of α-cut interval under intuitionistic fuzzy environment. The failure possibilities of basic events in fault tree analysis are quantified by triangular and trapezoidal intuitionistic fuzzy numbers. The presented research study applies α-cut intervals of intuitionistic fuzzy numbers, intuitionistic fuzzy fault tree analysis and interval arithmetic operations. The validation is carried out by comparing the developed importance measure with some pre-existing importance measures.

The decision making method of financial institutions in industrial cluster upgrading based on interval-valued intuitionistic trapezoidal fuzzy number game matrix

The decision problem of financial institutions supporting the upgrading of industrial clusters is ambiguous, and it is difficult to satisfy the basic feature of uncertainty by the payment function constructed by precise values. To cope with the fuzziness and uncertainty of game matrix, this paper firstly proposes a basic theory of interval-valued intuitionistic trapezoidal fuzzy number (IITFN) based on score function and accuracy function to construct an IITFN fuzzy matrix game (FMG) model. Next, expected utility theory is used to offer the acquisition of mixed strategy optimal solution of IITFN-FMG. Finally, it is applied to analyze the conditions and strategies of financial institutions to support the upgrading of industrial clusters. The main innovations of this paper are: The introduction of interval-valued intuitionistic trapezoidal fuzzy number to characterize the fuzzy features in the decision-making process of financial institutions and cluster enterprises, the proposed construction of a game matrix based on IITFN, and the corresponding solution method to obtain the conditions and strategies for financial institutions to support the upgrading of industrial clusters, and the proposed method and countermeasures to break the “prisoner’s dilemma” in the cooperation between financial institutions and cluster enterprises.

An Improved EDAS Method for the Multi-Attribute Decision Making Based on the Dynamic Expectation Level of Decision Makers

The improved evaluation based on the distance from average solution (EDAS) of the interval-valued intuitionistic trapezoidal fuzzy set is proposed. At first, we propose a new distance between interval-valued intuitionistic trapezoidal fuzzy numbers according to their interval endpoints and centroid point, and its properties are also discussed. Furthermore, we apply the proposed distance measure to calculate the expectation level of the emergency plan, and the optimal dynamic expectation level of the emergency plan is obtained by solving the programming model. Then, we improve the EDAS method based on the dynamic expectation level of the decision makers and apply it to calculate the optimal emergency plan. Finally, a numerical example about flood disaster rescue is given to verify the feasibility and effectiveness of the proposed method, which is also compared with the existing methods.

Intuitionistic fuzzy MAUT-BW Delphi method for medication service robot selection during COVID-19

Coronavirus Disease 2019 (COVID-19), a new illness caused by a novel coronavirus, a member of the corona family of viruses, is currently posing a threat to all people, and it has become a significant challenge for healthcare organizations. Robotics are used among other strategies, to lower COVID’s fatality and spread rates globally. The robot resembles the human body in shape and is a programmable mechanical device. As COVID is a highly contagious disease, the treatment for the critical stage COVID patients is decided to regulate through medication service robots (MSR). The use of service robots diminishes the spread of infection and human error and prevents frontline healthcare workers from exposing themselves to direct contact with the COVID illness. The selection of the most appropriate robot among different alternatives may be complex. So, there is a need for some mathematical tools for proper selection. Therefore, this study design the MAUT-BW Delphi method to analyze the selection of MSR for treating COVID patients using integrated fuzzy MCDM methods, and these alternatives are ranked by influencing criteria. The trapezoidal intuitionistic fuzzy numbers are beneficial and efficient for expressing vague information and are defuzzified using a novel algorithm called converting trapezoidal intuitionistic fuzzy numbers into crisp scores (CTrIFCS). The most suitable criteria are selected through the fuzzy Delphi method (FDM), and the selected criteria are weighted using the simplified best–worst method (SBWM). The performance between the alternatives and criteria is scrutinized under the multi-attribute utility theory (MAUT) method. Moreover, to assess the effectiveness of the proposed method, sensitivity and comparative analyses are conducted with the existing defuzzification techniques and distance measures. This study also adopt the idea of a correlation test to compare the performance of different defuzzification methods.