Triangular Intuitionistic Fuzzy Numbers Research Articles

On Solving Linear Complementarity Problem using Principal Pivoting Method

Objectives: A rudimentary framework called the linear complementarity problem (LCP) describes a wide range of real-world scenarios in which equilibrium conditions must be met while adhering to constraints. Methods: This study presents the Principal Pivoting Method (PPM), a novel method for solving linear Complementarity problems. PPM is a viable substitute for addressing large-scale complementarity problems. It is a powerful method for handling large-scale challenge circumstances while addressing LCPs. The PPM uses a principle-based pivoting strategy to navigate the solution space. It terminates in a finite number of iterations. It deals with degenerate cases. Findings: Under specific hypotheses, the PPM is guaranteed to converge to a solution if one exists. PPM's pivoting methods account for its numerical stability. In this paper, the process is analyzed using real-life scenarios. The algorithm goes with initialization, iteration, and termination. To ensure numerical stability, a pivot element is selected. Update the basis matrix through pivotal operations. The iterations show how well the algorithm goes perfectly without causing any wrongdoing. Using this method, the solution is obtained accurately in a smaller number of iterations. Novelty: A novelty of the work is finding a solution to a real-life application problem using this method. The comparison of my research work with the existing research work is a novel approach to illustrate the Principal Pivoting method in practical applications. Here, the crisp values are converted into intuitionistic triangular fuzzy numbers for analyzing data in real-life scenarios. This is a novel way to attempt a newly considered problem, which is taken as fuzzy coefficients transforming into a linear complementarity problem. Fuzzy arithmetic operations on the Function principle are utilized. The numerical trials proved the efficacy of the suggested algorithm. Keywords: Fuzzy Linear Complementarity Problem (FLCP), Principle Pivoting Method (PPM), Intuitionistic Fuzzy set (IFS), Triangular Intuitionistic Fuzzy Number (TIFN)

A Multivariate Intuitionistic Fuzzy Grey Model for Forecasting Electricity Consumption

Background: Whether in the short, medium or long term, forecasting electricity consumption has always been an essential study area. In the literature, many methods are used for future forecasting and are being improved daily to achieve better results. Objective: The main objective of this study is to make the most accurate long-term electricity consumption forecast, which is the basis for optimal future planning in the energy sector. Electric consumption forecasting is performed regionally since planning at the regional level is essential for more precise planning. Methods: There may be different variables that affect electricity consumption. This study ex-tends the multivariate grey model for electricity consumption prediction to intuitionistic trian-gular fuzzy numbers for nine regions. In the grey model, population, export, and gross domes-tic product variables were used as independent variables, and future predictions for these vari-ables were obtained through the univariate intuitionistic triangular fuzzy grey model. Results: The results of the proposed method are compared with those of the classical univari-ate grey model, univariate intuitionistic triangular fuzzy grey model, and classical multivariate grey model. The results show that the error values of the proposed method are lower. Conclusion: The study contributes to the development of the grey model. More accurate pre-diction results are obtained with the proposed method compared to similar methods

Enchanting dynamics: Juvenile and adult predators with prey model in an intuitionistic fuzzy environment

This study represents an interaction model including juvenile and adult predators along with prey, involving key characteristics like the inability of juvenile predators to reproduce, the impact of adult predators on juvenile growth rates and the transformation of some juveniles to adulthood. Furthermore, it is supposed that adult predators intake prey for sustenance, and the logistic growth of prey is assumed in the non-appearance of adult predators. Intra-species competition among adult predators, together with predation of juveniles and chasing, is conveyed. To tackle the imprecise biological parameters, most parametric values are considered as triangular intuitionistic fuzzy numbers. The model is further processed into an intuitionistic fuzzy model using the Hukuhara derivative and Yager’s ranking method is implemented to make the model crispified. Non-negativity and boundedness of the model are explored, after that, an investigation of possible equilibrium points is discussed. Local and global stability analyses close to these points are supervised. The study accentuates the significant influence of uncertain model parameters on the solution. Especially, uncertain estimates of intra-species competition among adult predators remarkably regulate the model’s stability. Extended uncertainty in intra-species competition for prey, although, is discovered to stabilize the system. In addition, increased consumption of juvenile predators by adult predators is observed to provide the system’s instability.

Solving MADM Problems based on Matrix Games with a New Defuzzification Method for Triangular Intuitionistic Fuzzy Numbers

Abstract: The paper discusses about a new defuzzification method called the Comprehensive Li-Samuel ranking for Triangular Intuitionistic Fuzzy Numbers (TrIFNs) which is improved from the Li-Samuel ranking method associated with membership function and Li-Samuel ranking method associated with non-membership function. The Comprehensive Li-Samuel ranking for TrIFNs is utilised to derive the weights for the Multiple Attribute Decision Making (MADM) problems under TrIFN. The MADM problem is solved based on two-person zero-sum game which is converted into a pair of LPP by using Comprehensive Li-Samuel ranking. The process of transforming decision matrix into a matrix game and deriving decision maker’s and attribute weights from the matrix game are discussed. Numerical illustration is given to justify the viability and effectiveness of the proposed method and comparisons are made with existing ranking methods. The comparison study reveals that the proposed method provides the best maximum optimal solution for the decision problem than the existing methods

Ranking of Different States in India Based on Sustainable Women Empowerment Using MCDM Methodology Under Uncertain Environment

In this paper, women’s empowerment in different states of India is considered. Based on considered data sets, the states of India are ranked with Decision-Making (MCDM) methodology. Here, Generalized Triangular Intuitionistic Fuzzy Numbers (GTIFNs) are considered. Here, GTIFNs are taken to deal with the uncertainty and we introduce a new de-fuzzification method for converting the GTIFNs to corresponding crisp values. Here, we have applied two MCDM techniques namely the Entropy-weighted method and Vlekriterijumsko KOmpromisno Rangiranje (VIKOR) method. The entropy-weighted method is used for evaluating the criteria weights and the VIKOR method is applied to rank the alternatives. Last, to verify the stability and vagueness of the system, we perform sensitivity and comparative analysis.

An intuitionistic fuzzy approach for prey–predator harvesting system with toxicity and time delay

This study presents an intuitionistic fuzzy prey–predator model with time delay, where several toxic substances from external sources contaminate the prey and predator species. The system consists of one prey and one predator, with the logistic growth of prey species and predation terms proportional to prey density. This system incorporates Holling type-II functional response and introduces a time delay in harvesting prey species over a precise size or age. The primary focus of this work is to investigate the impact of age or size-selective delay on the system’s stability within the intuitionistic fuzzy environment. The model employs triangular intuitionistic fuzzy numbers to account for imprecise biological parameters, and it is converted into an intuitionistic fuzzy model using the Hukuhara derivative. The fuzziness of the model is then resolved using Yager’s Ranking method. Without delay, the paper delves into the system’s dynamics, examining local and global stability and bionomic considerations. Numerical simulations are performed using MATLAB to validate the theoretical findings.

Reliability analysis of diesel engine cooling system based on improved Bayesian network

For the benefit of solving the problem of absoluteness of conditional probability distribution and difficulty in obtaining basic event probability in Bayesian networks, this paper studies the reliability of diesel engine cooling systems through leakage noise or gate intuitionistic fuzzy Bayesian network. Firstly, the leakage noise or gate is introduced into the intuitionistic fuzzy Bayesian network, which makes the results more realistic. Secondly, prior probability in the Bayesian network is obtained based on the similarity aggregation method of triangular intuitionistic fuzzy numbers. The results show that the introduction of leakage noise or gate, intuitionistic fuzzy set, and Bayesian network can solve the problem that the probability of basic events in a Bayesian network is difficult to obtain. The conditional probability table corrected by leakage noise or gate is more realistic and greatly reduces the workload. It is determined that the two weakest components of the cooling system are the thermostat and the water pump. The results show that the way in this paper can provide support for the reliability analysis of the complex system.

Multi-attribute decision-making research on investment suitability assessment of hydropower-wind-photovoltaic-storage complementary system based on dynamic social network

The hydropower-wind-photovoltaic-storage (HWPS) complementary system is one of the essential ways for China to build a new type of power system and to realize the dual-carbon goal. However, China's HWPS complementary system is still in the exploratory stage, and it is important to propose a rational multi-attribute decision-making (MADM) framework for investment suitability assessment based on completed hydropower plants. Therefore, this study first established a limitation indicator system for preliminary screening hydropower plants and an HWPS investment suitability assessment indicator system containing six dimensions: nature, market, infrastructure, land, society, and environment. Second, the weights among experts were determined based on the dynamic social network, and a mechanism for updating expert weights was proposed. Again, triangular intuitionistic fuzzy number (TIFN) was used to quantify the qualitative indicators and combined the weights according to the best-worst method (BWM) and criteria importance through intercriteria correlation (CRITIC) methods. Finally, the TODIM (an acronym in Portuguese for interactive and MADM) method was used for scheme suitability assessment with sensitivity analysis and method comparison. The results show that 62 eligible hydropower plants were preliminarily screened out of 647 completed medium- and large-scale hydropower plants in China by combining GIS technology. Natural factors are the most important of the six dimensions, followed by social factors. According to the suitability assessment results of TODIM, #23 hydropower station has the highest suitability for HWPSCS investment, which provides a reference for the layout of China's HWPS complementary system. With different decision makers' risk preferences and different MADM methods, #23 hydropower plant is still the best investment option, which proves the effectiveness of the MADM framework proposed in this study.

Human error probability evaluation based on reference task using intuitionistic fuzzy theory

Human Reliability Analysis (HRA) is a critical issue for addressing human error in system reliability. There are numerous tasks for which human factors-related data are not available, rendering expert knowledge the only basis for assessing such tasks. However, the knowledge obtained from experts is subject to ambiguity and vagueness, which affects the usability of the assessment results. To overcome this challenge, in this paper a reference task based HRA method is proposed and the intuitionistic fuzzy set (IFS) is adopted because of its advantage of being able to handle ambiguous information. Firstly, to analyze the human error probability (HEP) of the target task, a reference task-based human error analysis model is introduced. Two solutions are provided: calculating the performance shaping factors (PSFs) distance between the reference task and the target task and establishing a quantitative relationship between PSFs and HEP. Secondly, the PSFs evaluation and inference methods based on triangular intuitionistic fuzzy numbers (TIFNs) are developed. Finally, the effectiveness and consistency of the two solutions of TIFN-HRA are demonstrated through a spaceflight refueling mission analysis. The distances between the results of the two solutions and the expert linguistic are compared and both results have the shortest distance to “Low”. However, solution I is simpler and the result is clearer.

Pricing Life Contingencies Linked to Impaired Life Expectancies Using Intuitionistic Fuzzy Parameters

Several life contingency agreements are based on the assumption that policyholders have impaired life expectancy attributable to factors, such as lifestyle, social class, or preexisting health issues. Quantifying two crucial variables, augmented death probabilities and the discount rate of projected cash flows, is essential for pricing such agreements. Information regarding the correct values of these parameters is subject to vagueness and imprecision, which further intensifies if impairments must be considered. This study proposes modelling mortality and interest rates using a generalization of fuzzy numbers (FNs), known as intuitionistic fuzzy numbers (IFNs). Consequently, this paper extends the literature on life contingency pricing with fuzzy parameters, where uncertainty in variables, such as interest rates and death probabilities, is modelled using FNs. While FNs introduce epistemic uncertainty, the use of IFNs adds bipolarity to the analysis by incorporating both positive and negative information regarding actuarial variables. Our analysis focuses on two agreements involving policyholders with impaired life expectancies: determining the annuity payment in a substandard annuity and pricing a life settlement over a whole life insurance policy. In particular, we emphasize modelling interest rates and survival probabilities using triangular intuitionistic fuzzy numbers (TIFNs) owing to their ease of interpretation and implementation.

Triangular intuitionistic fuzzy linear system of equations with applications: an analytical approach

This study extended an existing semi-analytical technique, the Homotopy Perturbation Method, to the Block Homotopy Modified Perturbation Method by solving two n × n crisp triangular intuitionistic fuzzy (TIF) systems of linear equations. In the original system, the coefficient matrix is considered as real crisp, while the unknown variable vector and right hand side vector are regarded as triangular intuitionistic fuzzy numbers. The Block Homotopy Modified Perturbation Method is found to be efficient and practical to solve n × n TIF linear systems as it only requires the non-singularity of the n × n TIF linear system's coefficient matrix, whereas the point Homotopy Perturbation Method and other classical numerical iterative methods typically require non-zero diagonal entries in the coefficient matrix. A set of theorems relevant to this study are presented and demonstrated. We solve an engineering application, i.e. a current flow circuit problem that is represented in terms of a triangular intuitionistic fuzzy environment, using the suggested method. The unknown current is then obtained as a triangle intuitionistic fuzzy number. The proposed semi-analytic method is used to solve some numerical test problems in order to validate their performance and efficiency in comparison to other existing techniques. The numerical results of the example are displayed on graphs with different degrees of uncertainty. The efficiency and accuracy of the proposed method are further demonstrated by comparisons to block Jacobi, Adomain Decomposition method, Successive Over-Relaxation method and the classical Gauss-Seidel numerical method.

Blockchain-Based Inventory System considering Uncertain Carbon Footprints and Pandemic Effects

The global supply chain has been severely impacted with the outbreak of COVID-19. The continuous supply of essential products in the post-COVID-19 world is a truly effective and strategic contest. The security and useability of inventory management are a main burden for industries along with the pressure from the government to fulfil the targets of net-zero economy in an uncertain circumstance. One of the most potential keys to these issues is an accurate demand forecasting process by blockchain technology. This article addresses a basic outline for blockchain-based supply chain (SC) and reveals how blockchain technology (BCT) can aid policymakers to cut carbon footprint during and postpandemic time in a fuzzy environment. This study fuzzifies all the carbon factors as intuitionistic triangular fuzzy numbers and uses a signed distance method to defuzzify the model. We consider that the retailer can embrace BCT to enhance demand forecasting. The planned scenario is modeled as an optimization problem to maximize the profit with low carbon emissions and suggest a solution method to solve it. A numerical example is also given to validate the model. We compare the optimal decisions of the SC with and without BCT. We discover that the pandemic and BCT have considerable influences on the optimal results. The study also shows that practitioners should exercise caution when developing operational strategies for maximizing profit with the least amount of carbon emissions during and postpandemic time.

A two-compartment drug concentration model using intuitionistic fuzzy sets

The intuitionistic fuzzy differential equation (IFDE) is a robust mathematical tool that can deal with problems arising from model uncertainties. Intuitionistic sets are generalized sets of fuzzy sets. They establish that IFDE comprises an intuitionistic number characterized by membership and non-membership functions. This paper deals with generalized Hukuhara derivatives for intuitionistic fuzzy-valued functions. A compartment drug concentration system has been described in a fuzzy, intuitionistic setting to get a more accurate mathematical model. The initial conditions of the proposed drug system are considered triangular intuitionistic fuzzy numbers. The proposed model’s critical points of stability analysis have been explored in an intuitionistic environment. All intuitionistic fuzzy solutions of the proposed system support robust solutions. All results and formulas are confirmed graphically and numerically by MATLAB software.

A novel technique for solving intuitionistic fuzzy DEA model: an application in Indian agriculture sector

Fuzzy DEA is a performance measurement tool that is used to assess the performance of DMUs in highly uncertain environments. In this article, the Intuitionistic fuzzy DEA (IFDEA) model is proposed based on the triangular intuitionistic fuzzy numbers (TIFNs). The weighted Possibility mean for TIFN is used to compare and rank the TIFN. The weighted possibility mean approach is proposed to solve the IFDEA model, and the IFDEA model is converted into its equivalent crisp DEA model to assess the relative efficiencies of the DMUs. One advantage of the proposed approach is that the attitude of the decision-maker is considered while measuring the efficiency of the DMUs. The weight or risk factor delta in [0,1] indicates whether the decision-maker is a risk-taker, neutral, or adverse. The crisp DEA model is a LP problem that is solved by using an existing LP method with different risk factors to determine the efficiency score of the DMUs. The DMUs are ranked based on the overall efficiency score of the DMUs, which is the arithmetic mean of the efficiency scores of the DMUs with different risk factors. Two numerical examples are given here to demonstrate the validity and applicability of the proposed technique and to compare the performance of the DMUs in the proposed approach with the exciting ranking approach and the expected value approach. A case study on the agriculture sector has been conducted in order to evaluate the agricultural performance of Indian states using the IFDEA model. According to the results of the IFDEA model, 15 (53.57%) out of the 28 Indian states were found to be efficient.

Triangular intuitionistic fuzzy number based backorder and lost sale in production, remanufacturing and inspection process

A method of planning a company's production in advance for the manufacturing process and controlling the raw materials in inventory required for producing finished goods. Remanufacturing is an industrial process that restores usable life to used products or broken-down components known as “cores” through a series of processes. Also, production and remanufacturing process is a desirable concept in the competitive corporate environment because of the globalization of marketing strategy. In this paper, deals with the impact of manufacturing and remanufacturing process with supply changes. Here two models are considered Manufacturing and Remanufacturing with unsatisfied demand, Manufacturing and Remanufacturing with additional one unit under unsatisfied demand. Further cases are discussed with either full backorder and lost sales in commodities and also pure backorder with additional one unit and lost sales in commodities. Along with the both cases are discussed under two types of error in the inspection process. Triangular Intuitionistic fuzzy is applied in this inventory model. The total cost with the maximum profit is calculated using the cost parameters are determined in the inventory control model and the ideal overall cost using triangular intuitionistic fuzzy. The intuitionistic arena yields is the lowest cost. The accuracy function of de-intuitionistic number fuzzification was calculated. Mathematical model, intuitionistic model and four numerical examples are suggested and it reducing the overall inventory cost as well as the existence and uniqueness of the best solutions for both models by the de intuitionistic fuzzification. The solution processes, sensitivity analysis for both models are discussed.

How to promote the sustainable development of strategic emerging industries: Evidence from Guangzhou

The strategic emerging industry (SEI) can effectively cope with high energy consumption, high pollution and low efficiency in traditional production mode, which attracts high attention. However, few studies quantitatively analyze the input-output relationships and the sustainable development level of SEIs. Moreover, existing method frameworks fail to consider both the current situation and development potential of SEIs. To deal with the above research gaps, a novel static-dynamic intuitionistic fuzzy evaluation framework integrating output-oriented data envelopment analysis model, improved Malmquist model, triangular intuitionistic fuzzy number, clustering method and Tobit regression model is first proposed. 120 SEIs from Guangzhou are selected for empirical study. Results reveal that all SEIs have almost no expected movement in operational cost but obvious redundancies in employee expenditure with a standard deviation of 1.771. It's urgent to optimize the employment, assessment and salary systems for staff. Moreover, SEI sustainable development scores vary from 0.473 to 1. It's necessary to strengthen cultivation of excellent SEIs and pay attention to supervision of the weak. Research findings can not only guide local government and industry associations to make scientific evaluation, but also help SEIs carry out self-inspections, which can further promote sustainable development of the entire industry.

A novel group multi-criteria sorting approach integrating social network analysis for ability assessment of health rumor-refutation accounts

Blooming social media platforms provide breeding ground for health rumors. Despite the establishment of accounts by numerous organizations to counter health rumors, the effectiveness of these endeavors exhibits considerable variability. Thus, there exists a pressing need to refine the framework and operation of rumor-refutation accounts. Aiming at enhancing the proficiency of accounts in refuting health rumors on social media platforms and exploring the factors affecting it, this paper proposes a novel group multi-criteria sorting approach integrating social network analysis (SNA) to classify accounts’ health rumor-refutation ability. To commence, an evaluation indicator system for accounts’ health rumor-refutation ability is established using SNA. Subsequently, the indicator values are computed, incorporating methods such as triangular fuzzy number (TFN), a lite bert (ALBERT) pre-trained language model, and PageRank. Furthermore, hesitant fuzzy linguistic term set (HFLTS) and triangular intuitionistic fuzzy number (TIFN) are used to determine the expert weights and indicator weights. After that, on the basis of original best worst method-sort (BWM-Sort), classification boundaries are discovered creatively using optimal clustering (OC), and minimum discrimination information (MDI) is adopted as the objective function for priority assignment. Consequently, an OC-MDI-BWM-Sort method is newly proposed which offers distinct advantages in computational efficiency, information integration, decision-making objectivity, and result effectiveness. Lastly, regarding to four cases of widely circulated rumors, health rumor-refutation ability of 35 accounts on Weibo platform is classified using the proposed method. The findings underscore that merely 8.57% of accounts exhibit stable and good health rumor-refutation ability, while up to 28.57% and 80.00% display poor and inconsistent ability in certain instances. Tailored to accounts with excellent or good, satisfactory or fair, and poor health rumor-refutation ability, respectively, managerial suggestions are provided regarding information expression standards, account operator proficiency, and account cooperation, and all accounts are advised to watch audience behavior.

Development of intuitionistic fuzzy cost efficiency model in data envelopment analysis

Data envelopment analysis (DEA) is a non-parametric linear programming (LP) based technique to measure the relative efficiencies of decision-making units (DMUs). The conventional DEA models assume that input-output data is crisp, which may not always be feasible in practical situations due to the presence of ambiguity and imprecision. Therefore, to handle uncertain and imprecise data, the concept of intuitionistic fuzzy sets (IFS) has been introduced. In this study, the relative efficiencies of DMUs with uncertain data will be determined. For this reason, the conventional cost efficiency (CE) model of DEA is extended to IF environment. Also, the lower and upper-cost efficiency models are developed using α-cut and β-cut approach. The data for inputs, outputs and input prices are considered intuitionistic fuzzy numbers (IFNs), in particular triangular intuitionistic fuzzy numbers (TIFNs). To demonstrate the practical application of the proposed intuitionistic fuzzy cost efficiency models (IFCEMs), a numerical example is presented.

Intuitionistic fuzzy multi-objective transportation model during pandemic COVID-19

The given paper discusses an intuitionistic fuzzy discrete time-space optimization model while taking into account the COVID-19 pandemic. The novelty of this study is characterized by the proposal of a distinctive multi-objective intuitionistic fuzzy transportation model in which the demand function varies with time as the number of infected, exposed and susceptible persons increase. Forecasting of demand is executed using the epidemic diffusion model. Also, a new approach to defuzzify triangular intuitionistic fuzzy numbers, depending upon the concept of the golden ratio, is presented. Intuitionistic fuzzy programming approach is used to obtain the pareto-optimal solution. A real-life numerical illustration is explained using the proposed methodology to examine its practical suitability. Outperforming the existing traditional method of solving a transportation problem verifies its proficiency.

Evaluation of emergency evacuation capacity of urban metro stations based on combined weights and TOPSIS-GRA method in intuitive fuzzy environment

Research on emergency evacuations of urban metro stations has become a hot topic in public security applications in recent years. This paper proposes a comprehensive framework for evaluating the emergency evacuation capacity of metro stations. An evaluation indicator system with 16 indicators of human, equipment, environmental, and management factors is established. A triangular intuitionistic fuzzy number (TIFN) approach is used to collect indicator data to express the uncertainty of the language variables and ensure that the data is closer to reality. Subsequently, a combination of the TIFN and the decision-making trial and evaluation laboratory (TIFN-DEMATEL) and the entropy weight method (EWM) are used to combine the weights using game theory to ensure the weights is more scientific and reasonable. Grey relational analysis (GRA) is integrated with the technique for order preference by similarity to an ideal solution (TOPSIS) to improve the ranking results and evaluate metro station emergency evacuation capacity. A case study of eight metro stations in Beijing is conducted to validate the evaluation framework. Sensitivity analysis and comparative analysis demonstrate the reliability and robustness of the proposed method. Finally, the specific measures to improve the emergency evacuation capacity are given.