Triangular Intuitionistic Fuzzy Numbers Research Articles

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.

A multi-criteria decision-making framework for distributed generation projects investment considering the risk of electricity market trading

Under the background of distributed generation (DG) participating in market trade, the scale of DG has developed rapidly. The investment decision of DG is actually a multi-criteria decision-making (MCDM) problem, nevertheless the current framework rarely considers the risk of market trading. Thus a framework containing scheme attributes and market risks needs to be established. Firstly, an index system including economic benefit, environmental and social benefit and market risk is established. Secondly, subjective and objective weight are combined by using game theory in weighting process. Among them, the subjective weight of each index is determined based on the plus-minus decision-making trial and evaluation laboratory model (plus-minus DEMATEL); the objective weight is determined by the combination of triangular intuitionistic fuzzy number (TIFN) and integrated determination of objective criteria weights (IDOCRIW) model. Finally, the TODIM model is used to rank the alternatives. Taking Shanghai as a case study, the robustness of the proposed framework is verified by sensitivity analysis and comparative analysis. The results show that the weights of index C34 is 0.12, indicating that market participants have a greater influence on market risk. The research will provide an effective tool for investment decision of DG in market trading.

A solution approach for sustainable multi-objective multi-item 4D solid transportation problem involving triangular intuitionistic fuzzy parameters

Sustainability pertains to the interplay between environmental, economic, and social systems at varying scales. In transportation systems, vehicles use different fuels to fulfill their energy requirements. However these fuels emit green house gases that pollute the environment. Taking into account this fact, the present paper delves into the investigation of a multi-objective multi-item fixed cost solid transportation problem with various driving styles. Also, three types of fuels are incorporated in the proposed model. The primary focus of this paper is to maximize profit by reducing breakage of the items along with reducing carbon emission and time of transportation. In real-life situations, the parameters of multi-objective multi-item fixed cost solid transportation problem may not be tackled crisply. Hence triangular intuitionistic fuzzy numbers are introduced in the proposed model. The score function is employed to convert intuitionistic fuzzy problem to deterministic one. Thereafter, a methodology is developed to solve the proposed model involving different driving styles and is extended to consider the optimistic, pessimistic, and mixed view of the decision maker. Comparisons are made among the compromise solutions that are derived from different approaches and are shown by various charts and graphs. A case study is included to illustrate the applicability and validity of the proposed methodology.

Intuitionistic fuzzy fault tree analysis of PCBA using novel arithmetic operations

PurposeThe main goal of this paper is to develop novel Tω(weakest t-norm)-based fuzzy arithmetic operations to analyze the intuitionistic fuzzy reliability of Printed Circuit Board Assembly (PCBA) using fault tree.Design/methodology/approachThe paper proposes a fuzzy fault tree analysis (FFTA) method for evaluating the intuitionistic fuzzy reliability of any nonrepairable system with uncertain information about failures of system components. This method uses a fault tree for modeling the failure phenomenon of the system, triangular intuitionistic fuzzy numbers (TIFNs) to determine data uncertainty, while novel arithmetic operations are adopted to determine the intuitionistic fuzzy reliability of a system under consideration. The proposed arithmetic operations employ Tω(weakest t-norm) to minimize the accumulating phenomenon of fuzziness, whereas the weighted arithmetic mean is employed to determine the membership as well as nonmembership degrees of the intuitionistic fuzzy failure possibility of the nonrepairable system. The usefulness of the proposed method has been illustrated by inspecting the intuitionistic fuzzy failure possibility of the PCBA and comparing the results with five other existing FFTA methods.FindingsThe results show that the proposed FFTA method effectively reduces the accumulating phenomenon of fuzziness and provides optimized degrees of membership and nonmembership for computed intuitionistic fuzzy reliability of a nonrepairable system.Originality/valueThe paper introduces Tω(weakest t-norm) and weighted arithmetic mean based operations for evaluating the intuitionistic fuzzy failure possibility of any nonrepairable system in an uncertain environment using a fault tree.

Intuitionistic fuzzy approach to reliability assessment of multi-state systems

One of the major problems that one encounters within an engineering system is the assessment of its quality, or in other words, reliability. However, conventional reliability tends to ignore the fuzziness in the system, i.e., the lack of precision, vagueness, inaccuracy, or inadequacy in the information obtained. As a result, the integration of fuzzy sets into reliability theory has proven to be incredibly vital. Similarly, the universal generating function (UGF) technique has also been an asset in reliability assessment ever since its inception due to its simplicity. Here, a novel technique involving the intuitionistic fuzzy sets (IFS), specifically using the triangular intuitionistic fuzzy numbers (TIFN) and the UGF method, has been created for the reliability assessment of a fuzzy multi-state system (FMSS). This method is then applied to a system of wireless communication and its intuitionistic fuzzy reliability and availability are evaluated where each performance state and its probability are characterized by a TIFN. The obtained results are also represented graphically for better insights. This work is helpful in getting a clear picture of FMSS and thus, making them more reliable.

A multi-objective transportation problem under quantity dependent credit period and cost structure policies in triangular intuitionistic fuzzy environment

One of the major economic activities of a business concern is transportation of its products without any hassle. Therefore, the research on a transportation problem is very important now-a-days. In a classical transportation problem, the amount incurred for shipping the goods from the source to a destination is determined on the basis of unit transportation cost. But now, in many practical cases, it is seen that the unit transportation cost is settled on the basis of transported amount. In such a direction, this article develops a transportation problem to transport the produced items from a production house to some retailers through some distributors. The system has two cost parameters, one is actual unit transportation cost and other is demanded unit transportation cost. The actual unit transportation cost is the cost incurred during the transportation while the demanded unit transportation cost is the cost demanded by the distributors. Here, the demanded unit transportation cost has been decided depending on the amount of transported item. Since in the system, there are more than one distributor, distributors offer a credit period policy to attract the retailers. On the basis of the deterioration of the loaded amount, the transported items are classified into two categories. For the higher deteriorated items, the transportation cost is relatively larger and for the lower deteriorated items, the transportation cost is relatively lower with the increase in the loading amount. Considering the above two categories, two crisp models are developed. Due to the uncertain information of the actual unit transportation cost, the models are illustrated considering the actual unit transportation cost as a triangular intuitionistic fuzzy number. The main objective of this research is to minimize the total cost of the retailers and to maximize the total profit of the distributors simultaneously under the above circumstances. For crispification, two different methods have been used here — one is an existing method namely ordered weighted average operator and other is a developed average value approach. Also, the elitist non-dominated sorting genetic algorithm (NSGA-II) and the fuzzy programming technique have been used to get the optimal solution of this problem. To justify the impact and significance of the proposed models on this decision making system, some numerical studies have been done and it is observed that distributors and retailers both benefit more under the credit period policy than the policy without credit period. This study discusses the situation under which the uncertain parameters are to be expressed in terms of triangular intuitionistic fuzzy numbers. Also, it is identified that more accurate crispification has been done by the average value approach than the existing approach.