Triangular Fuzzy Numbers Research Articles

Integrated operational model to analyse policies and socio-demography leading to selection of electric vehicle - A case study on Bihar

In the push for sustainability in the power sector, Electric Vehicles show substantial promise. However, they still face hurdles in replacing traditional combustion engine cars, which have dominated the market for decades. Consumer awareness, especially regarding new technologies like Electric Vehicles, remains a significant barrier to adoption. This study aims to bridge the gap between technical aspects and consumer knowledge and a case study is done on the Indian state of Bihar. Using a hybrid Multi-Criteria Decision-Making approach with Triangular Fuzzy Numbers, a customized model is presented to help residents choose the right Electric Vehicle based on their needs and resources. Results are analyzed from customers’ perspective using Quality Function Deployment and conduct Sensitivity Analysis to explore cost trends. This survey examines seven Electric Vehicle models available in India, with MG ZS Electric Vehicle emerging as a potential standout. It's important to note that this research work does not endorse any specific Electric Vehicle model; rather, a mathematical framework is build to guide customers in selecting an Electric Vehicle that suits their requirements.

Fuzzy-fractional modeling and simulation of electric circuits using extended He-Laplace-Carson algorithm

In literature, most of the electric circuits are found to be at integer order, which are unable to capture the involved uncertainties and memory effects. To understand these effects, the current study is focused on modeling and analysis of fuzzy-fractional L˜C˜ circuit, R˜C˜ circuit, R˜L˜ circuit, and R˜L˜C˜ circuit. Triangular fuzzy numbers (TFNs) are utilized to introduce uncertainties in circuits. The memory effect is considered through fractional derivative in Caputo sense. A hybrid homotopy perturbation method (HPM) is established for solution purpose, in which standard HPM is combined with Laplace-Carson transformation in fuzzy-Caputo sense. This leads to an excellent and well-organized approach to calculate numerical solutions in the aspect of fuzzy logic and fractional calculus. The results obtained through proposed approach are validated by comparing them with already existing results in literature. Residual errors are also calculated across the domain of r at fractional order to determine the convergence and stability of electric circuit models. To study the dynamics of inductor, resistor, and capacitor on current along with fractional and fuzzy parameters involved in the electric circuits, contour and three-dimensional plots are constructed. Several plots specifying the fuzzy membership function of models across various parameter values are also demonstrated. The results achieved through this study indicate that He-Laplace-Carson method can assist engineers and researchers when dealing with electric circuits characterized by fuzzy and fractional dynamics.

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.

Study on hybrid nanofluid flow with heat transfer embedded in a porous medium with uncertain volume fraction

This study examines the heat transfer mechanisms in an MHD Jeffery-Hamel hybrid nanofluid flow with a porous medium in a fuzzy environment. Here, the copper-silver (Cu-Ag) is considered a hybrid nanoparticle. The nanoparticle volume fraction is regarded as a fuzzy variable and is represented with a triangular fuzzy number ranging between 0 − 6 % . A dual parametric homotopy algorithm is used to investigate the impact of Darcy’s number and thermal distribution on the fluid flow’s fuzzy velocities and temperature profiles in ω < 0 and ω > 0 channel positions. Finally, the results are further validated by studying the fuzziness of velocity bounds in different channel positions and providing a comprehensive analysis of heat transfer mechanisms.

A Hybrid Multi-Attribute Decision-Making Approach Considering Correlations Among Indicators

Considering the fuzzy and uncertainty of the evaluation information of the evaluation object, the type of indicators are expanded into five types of mixed evaluation information, namely, exact number, interval number, triangular fuzzy number, hesitant fuzzy number, and probabilistic linguistic term sets, and different types of evaluation information are adopted according to the different characteristics and types of indicators, respectively. When the evaluation information is hybrid information, the generalized Shapley function based on fuzzy measurement is used to analyze the interaction between indicators and determine the weights of indicators, considering that the interaction between indicators is more complicated. In view of the fact that the conversion of mixed information into the same kind of information will lead to the problem of complicated calculation and missing information, the VIKOR method is used to comprehensively evaluate the evaluation objects and select the best ones. Finally, the validity and feasibility of the proposed method is verified by taking the assessment of data literacy level and competence of teachers in a university in a western province of China as an example.

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.

An entropy - based fuzzy QFD model on used product remanufacturing design

Compared with new products, consumers put forward higher requirements on remanufactured products. Aimed at effectively transforming customer requirements (CRs) to technical characteristics (TCs) of remanufactured product design, an entropy-based fuzzy quality function deployment (QFD) model is proposed. In this model, triangular fuzzy numbers are suggested to express the vagueness information of CRs first, and then the importance of CRs is determined by an entropy-based algorithm, and the relationship between CRs and TCs is well explained by fuzzy QFD; finally, the importance of TCs is determined to clarify the designing emphasis. A remanufacturing engine is conducted to illuminate the practicability of this model. The results show that “Restorability” and “Reliability” will be treated as the key TCs to control, with the importance degree of 0.16 and 0.15. The entropy-based fuzzy QFD model can also be applied to similar product designs.

Runge-Kutta Method Based on the Linear Combination of Arithmetic Mean, Geometric Mean, and Centroidal Mean: A Numerical Solution for the Hybrid Fuzzy Differential Equation

Objectives: To find the absolute error of the Hybrid fuzzy differential equation with triangular fuzzy number since its membership function has a triangular form. Methods: The third order runge-kuttta method based on the linear combination of Arithmetic mean, Geometric mean and Centroidal mean is introduced to solve Hybrid fuzzy differential equation. Seikkala’s derivatives are considered, and Numerical example is given to demonstrate the effectiveness of the proposed method. Findings: The comparative study have been done between the proposed method and the existing third order runge-kutta method based on Arithmetic mean. The proposed method gives better error tolerance than the third order runge-kutta method based on Arithmetic mean. Novelty: In this study a new formula has been developed by combining three means Arithmetic Mean, Geometric Mean and Centroidal Mean using Khattri’s formula and it is solved by the third order runge-kutta method for the first order hybrid fuzzy differential equation. The error tolerance has been calculated for the proposed method and the Arithmetic mean and it is seen that the error tolerance is better for the proposed method. Keywords: Hybrid fuzzy differential equations, Triangular fuzzy number, Seikkala’s derivative, Third order runge-kutta method, Initial value problem

An optimization of the fully fuzzy transportation problem with triangular type-2 fuzzy parameters using novel ranking technique

This paper focuses on solving the fully fuzzy transportation problem in which the parameters are triangular Type-2 fuzzy numbers due to the instinctive of human imprecision. To deal with uncertainty more precisely, a triangular Type-1 fuzzy transportation problem is reformed as a transportation problem with triangular Type-2 fuzzy parameters in this paper. In order to compare triangular Type-2 fuzzy numbers, a new ranking(ordering) technique is proposed by extending the Yager’s function. However, two efficient algorithmic approaches namely, triangular Type-2 fuzzy zero suffix method (TT2FZSM) and triangular Type-2 fuzzy zero average method (TT2FZAM) are proposed to generate the initial transportation cost of the fully triangular Type-2 fuzzy transportation problem. Both TT2FZSM and TT2FZAM are converging towards an optimal solution. In addition to TT2FZSM and TT2FZAM, the modified distribution method is applied to ensure optimality. Subsequently, we carry out a comprehensive discussion of the obtained results to establish the validation of the proposed approach.

SOLVING FUZZY NONLINEAR PROGRAMMING PROBLEMS WITH EXTERIOR PENALTY FUZZY VALUED FUNCTIONS

In this article, we explore the exterior penalty fuzzy valued function method for Fuzzy Nonlinear Programming Problems (FNLPP). We present methods of penalty fuzzy valued function for solving constrained optimization problems by converting to unconstrained optimization problems. Triangular fuzzy numbers are used to represent the problem’s decision variables and coefficients. Using a new fuzzy arithmetic and fuzzy ranking method on the parametric form of triangular fuzzy numbers, the optimal solution of the FNLPP is found by applying the exterior penalty fuzzy valued function method without changing to its equivalent crisp form. We present a numerical example of the suggested method and compare the results to those produced by existing methods

The Contextuality of Dongdaemun Design Plaza and Park, an Iconic Building in Seoul—A Study Based on Fuzzy Statistical Analysis

For many cities around the world, the construction of iconic buildings is a major strategy to improve their urban space and enhance recognition. Yet, newly built iconic buildings usually spark controversy owing to their relationship with the urban context of the city. In this study, revolving around Dongdaemun Design Plaza and Park, we analyze and evaluate the functional influences of its reconstruction on the urban context of Seoul. We found that though the DPP has a positive effect on the city image and cultural exchange of Seoul, it is barely satisfactory for maintaining and extending the urban context. Through the combination of a random sampling questionnaire and triangular fuzzy number analysis, we transfer previous subjective comments about the DPP into an objective evaluation, analyze its influence on the dimension of culture, and call for consideration of the continuity of the urban context in future urban planning. The results of this study provide a new perspective on quantifying the urban contextual influence of iconic buildings, reminding city planners of the balance between the development of business and the sustainability of the urban context.

Numerical Solution of Hybrid Fuzzy Differential Equation by using Third Order Runge-Kutta Method Based on Linear Combination of Arithmetic Mean, Root Mean Square and Centroidal Mean

Objectives: This article develops the third order Runge-Kutta method, which uses a linear combination of the arithmetic mean, root mean square, and centroidal mean, to solve hybrid fuzzy differential equations. Methods: Seikkala's derivative is taken into account, and a numerical example is provided to show the efficacy of the proposed method. The outcomes demonstrate that the suggested approach is an effective tool for approximating the solution of hybrid fuzzy differential equations. Findings: The comparative analysis was carried out using the third order Runge-Kutta method that is currently in use and is based on arithmetic mean, root mean square, and centroidal mean. Compared to other methods, the suggested method offers a more accurate approximation. Novelty: In this study a new formula has been developed by combining three means Arithmetic Mean, Root Mean Square, and Centroidal Mean using Khattri's formula. And the developed formula is used to solve the third order Runge-Kutta method for the first order hybrid fuzzy differential equation. All real life problems which can be modeled in to an initial value problem can be solved using this formula. Keywords: Hybrid fuzzy differential equations, Triangular fuzzy number, Seikkala's derivative, third order Runge-Kutta method, Arithmetic mean, Root mean square, Centroidal mean, Initial value problem

Risk assessment of deep-sea floating offshore wind power projects based on hesitant fuzzy linguistic term set considering trust relationship among experts.

The development of deep-sea floating offshore wind power (FOWP) is the key to fully utilizing water resources to enhance wind resources in the years ahead, and then the project is still in its initial stage, and identifying risks is a crucial step before promoting a significant undertaking. This paper proposes a framework for identifying risks in deep-sea FOWP projects. First, this paper identifies 16 risk criteria and divides them into 5 groups to establish a criteria system. Second, hesitant fuzzy linguistic term set (HFLTS) and triangular fuzzy number (TFN) are utilized to gather and describe the criterion data to ensure the robustness and completeness of the criterion data. Third, extending the method for removal effects of criteria (MEREC) to the HFLTS environment through the conversion of TFNs, under the influence of subjective preference and objective fairness, a weighting method combining analytic network process (ANP) and MEREC is utilized to calculate criteria weights, and the trust relationship and consistency between experts are used to calculate the expert weights to avoid the subjective weighting given by experts arbitrariness. Fourth, the study's findings indicated that the overall risk level of the deep-sea FOWP projects is "medium." Fifth, sensitivity and comparative analyses were conducted to test the reliability of the assessment outcomes. lastly, this research proposes risk management measures for the deep-sea FOWP project's establishment from economic, policy, technology, environment, and management aspects.

GIS-based floating offshore wind turbine installation site selection using fuzzy analytic hierarchy process in northeast Aegean Sea

The ever-increasing consumption of electrical energy due to increasing requirements arising in parallel with the developing technology forces manufactures and users to seek new and environmentally compatible energy resources. Due to it endless energy potential and continuity, wind energy, which has been used by humanity for various purposes for centuries, continues its journey, which started with windmills that transform one form of mechanical energy into another, with offshore wind energy turbines. In this study, installation site selection, which is the first step for floating offshore wind turbine installation, is carried out. First, a Fuzzy Analytic Hierarchy Process (F-AHP) is applied to obtain the weights of criteria. Transformed alternatives and criteria in a fuzzy decision matrix through triangular fuzzy numbers are used to obtain a database via a Geographic Information System (GIS). Finally, the installation site and study area are determined. This area is located in the Northeast Aegean Sea, between Çanakkale and Gökçeada, 12 km to the northeast of Gökçeada, and 12 square kilometers. The minimum distance of the area to ship routes is 3000 m, and its minimum distance to fault lines is 2000 m. The average sea depth is 110 m, and the average wind speed is 9.26 m/s (18 knots). With this potential, enough energy can be generated for settlements on Gökçeada and the coastlines.

Fuzzy Framework for Evaluation Strategies of Climate Change Adaptation on Constructing

This study proposes a decision-making model for ranking strategies to eliminate climate change in construction. The triangular fuzzy set deals with uncertain information in the ranking process. Various criteria are used in this study, so the multi-criteria decision-making (MCDM) methodology is used to deal with these criteria. The TOPSIS method is an MCDM methodology used to rank the alternatives. The TOPSIS method is integrated with triangular fuzzy numbers. The criteria weights are computed by using the average method. The application is applied with 12 criteria and 8 options. The results show that alternative 7 is the best and alternative 3 is the worst. The results are tested with sensitivity analysis to show their stability. The sensitivity analysis was conducted with 13 cases of changing the criteria weights. Then, the TOPSIS method is applied under 13 cases in criteria weights. The results show that the ranking is stable in different cases.

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.

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

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

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.

Multi-Attribute Decision-Making Method in Preventive Maintenance of Asphalt Pavement Based on Optimized Triangular Fuzzy Number

By choosing the right pavement maintenance plan, we can reduce resource utilization, reduce environmental pollution, and extend road life, which is important for improving social sustainability. At present, the selection of road maintenance programs mostly adopts multiple attribute decision-making (MADA), in particular, the analytic hierarchy process (AHP) is often used. However, this method needs to use expert scoring data, which leads to strong subjectivity and poor reliability. Therefore, it reduces the science of road maintenance scheme selection. In order to reduce the subjectivity of the score and obtain a more suitable road maintenance scheme, this paper applies a multi-criteria decision-making method that characterizes attribute information by triangular fuzzy numbers (TFN) in the discrete decision space. Firstly, we invite experts to score the importance of the selection of pavement preventive maintenance technical solutions with respect to the indicators affecting the selection of solutions. Secondly, the two indicators of similarity and reliability are used to quantitatively evaluate the indicators and programs, respectively. Finally, we compare the weighted programs according to the overall possibility degree of each program. In actual cases, the overall possibility degree of each scheme obtained by this method is 1.0002–0.0477, and the optimal solution is fog sealing technology. The decision-making model applied in this paper can be considered in multiple dimensions, which can scientifically reduce the subjectivity of expert scoring. The best maintenance plan can also be quickly obtained through the simple calculation method in this paper.

APPLICATION OF FUZZY VECTOR OPTIMIZATION METHODS FOR DIET COMPILATION

The purpose of this work is to study an approach to solving the problem of fuzzy vector optimization for compiling a diet. It is necessary to develop a daily ration that provides human needs in nutrients and energy and is the best in terms of costs and weight. For this purpose the problem of choosing the best alternative from a given fuzzy set of alternatives is solved, while the quality of the alternative is evaluated using several partial efficiency cri- teria. The goal in the task is fuzzily defined. According to the Zadeh – Bellman idea, a fuzzy solution to a problem is the intersection of a fuzzy goal and a fuzzy set of alternatives. The paper considers the problem of fuzzy two-criteria optimization. Partial criteria that are minimized are the weight and cost of the daily ration. Fuzzy needs for nutrients and kilocalories are determined by fuzzy triangular numbers. For an approximate solution of the problem, an algorithm is proposed according to which a sequence of linear programming problems is solved. The computer program was created that implements the solution of this problem in the Wolfram Matematica package. The following results were obtained: a set of products, their weight and cost were determined for the daily diet. The degree of confidence that the found plan is optimal is determined. On the basis of the proposed mathe- matical model and the method of its solution, a software application allowing to choose food products, enter the necessary restrictions in a user- friendly form, and receive one or more options for the daily ration at the output was created. Such an application will be useful for nutritionists, ath- letes, doctors and other people who are concerned with the problems of healthy eating.