Triangular Intuitionistic Fuzzy Research Articles

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.

Triangular Intuitionistic Fuzzy Linear Programming Problem with a New Ranking Method based on Correlation Coefficient

Triangular Intuitionistic Fuzzy Linear Programming Problem with a New Ranking Method based on Correlation Coefficient

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.

Correction: Skin Cancer Segmentation Based on Triangular Intuitionistic Fuzzy Sets

Correction: Skin Cancer Segmentation Based on Triangular Intuitionistic Fuzzy Sets

Skin Cancer Segmentation Based on Triangular Intuitionistic Fuzzy Sets

Skin Cancer Segmentation Based on Triangular Intuitionistic Fuzzy Sets

A Multi-Criteria Framework for Sustainability Evaluation of Hydrogen-Based Multi-Microgrid Systems under Triangular Intuitionistic Fuzzy Environment

Developing hydrogen-based multi-microgrid systems (HBMMSs) is vital to the low-carbon energy transition, which can promote the utilization of renewable energy and reduce carbon emissions. However, there have been no studies presenting a sustainability evaluation of HBMSSs. Multi-attribute decision-making (MADM) methods are widely used to perform a sustainability evaluation. This paper develops a triangular intuitionistic fuzzy framework to make a comprehensive evaluation of HBMMSs from the perspective of sustainability. Firstly, a sustainability evaluation criteria system including economic, social, environmental, technical, and coordination criteria is established. Secondly, the paper proposes a hybrid fuzzy decision-making method. A triangular intuitionistic fuzzy decision-making trial and evaluation laboratory technique is used to analyze the correlation between criteria and sub-criteria and provides a basis for determining their fuzzy densities. A ranking method combining the triangular intuitionistic fuzzy number, fuzzy measure, and Choquet integral is used to rank the alternatives and choose an optimal one. Moreover, a case study is performed to validate the practicability of the developed framework. Finally, sensitivity analysis, scenario analysis, and comparative analysis are conducted to verify the robustness and effectiveness of the framework. As such, this study provides a guide for evaluating the sustainability of HBMMSs.

Some Novel Theories of Triangular Intuitionistic Fuzzy Numbers and Its Application in Two-Sided Matching

Some Novel Theories of Triangular Intuitionistic Fuzzy Numbers and Its Application in Two-Sided Matching

Operation mode selection of public-funded private-run elderly care agencies based on triangular intuitionistic fuzzy preference relations group decision-making

Operation mode selection of public-funded private-run elderly care agencies based on triangular intuitionistic fuzzy preference relations group decision-making

Triangular Intuitionistic Fuzzy Aggregating and Ranking Function Approach for the Rating of Battery ‘End-of-Life’ Handling Alternatives

The increased adoption of intermittent renewable sources in the energy sector has also increased the use of battery storage systems. However, the negative impact which the improper disposal of batteries has on the environment has stirred debates on its sustainability. To ensure the proper disposal of battery waste, there is a need to identify and rank the most preferred battery ‘end-of-life’ handling alternatives. This paper focuses on identifying the most preferred ‘end-of-life’ handling alternatives for batteries using a modified triangular intuitionistic fuzzy aggregating and ranking function (TIFARF) model. To test the proposed modified TIFARF model, opinions from experts in the Nigerian renewable energy sector were collected, and the results show that the most preferred alternative is incineration, with a closeness coefficient of 0.130, while the least preferred alternative is recycling, whose closeness coefficient is 0.112. The results are an indication of a lack of facilities needed for the proper recycling of battery remains after their lifetime; if adequate facilities are available, the opinion of experts may be biased towards other alternatives. Future studies should focus on more battery ‘end-of-life’ handling alternatives and on countries with adequate facilities that can be used to manage batteries at the end of their lifespan.

Triangular intuitionistic fuzzy sequencing problem

In this paper, we discuss different types of fuzzy sequencing problem with Triangular Intuitionistic Fuzzy Number. Algorithm is given for different types of fuzzy sequencing problem to obtain an optimal sequence, minimum total elapsed time and idle time for machines. To illustrate this, numerical examples are provided.

Novel Heuristic for Intuitionistic Triangular Fuzzy Travelling Salesman Problem

The travelling salesman problem (TSP) is a well-known combinatorial problem frequently used in real-world industries to find the minimum cost cycle between all cities. In this paper, the authors consider the distance matrix between all cities in a vagueness environment, where each element in the distance matrix is presented as an intuitionistic triangular fuzzy set. To solve this problem, the novel heuristic Dhouib-Matrix-TSP1 (DM-TSP1) is enhanced with the centroid ranking function for defuzzification and the range statistical metric for cities selection. In fact, this paper presents the first adaptation of DM-TSP1 to solve TSP under intuitionistic environment. DM-TSP1 can easily generate a good initial basic feasible solution just after just n iterations (where n represents the number of cities). The performance of DM-TSP1 is demonstrated by suitable numerical examples.

Least-looping stepping-stone-based ASM approach for transportation and triangular intuitionistic fuzzy transportation problems

Transportation problem (TP) is a popular branch of Linear Programming Problem in the field of Transportation engineering. Over the years, attempts have been made in finding improved approaches to solve the TPs. Recently, in Quddoos et al. (Int J Comput Sci Eng (IJCSE) 4(7): 1271–1274, 2012), an efficient approach, namely ASM, is proposed for solving crisp TPs. However, it is found that ASM fails to provide better optimal solution in some cases. Therefore, a new and efficient ASM appoach is proposed in this paper to enhance the inherent mechanism of the existing ASM method to solve both crisp TPs and Triangular Intuitionistic Fuzzy Transportation Problems (TIFTPs). A least-looping stepping-stone method has been employed as one of the key factors to improve the solution quality, which is an improved version of the existing stepping-stone method (Roy and Hossain in, Operation research Titus Publication, 2015). Unlike stepping stone method, least-looping stepping-stone method only deals with few selected non-basic cells under some prescribed conditions and hence minimizes the computational burden. Therefore, the framework of the proposed method (namely LS-ASM) is a combination of ASM (Quddoos et al. 2012) and least-looping stepping-stone approach. To validate the performance of LS-ASM, a set of six case studies and a real-world problem (those include both crisp TPs and TIFTPs) have been solved. The statistical results obtained by LS-ASM have been well compared with the existing popular modified distribution (MODI) method and the original ASM method, as well. The statistical results confirm the superiority of the LS-ASM over other compared algorithms with a less computationl effort.

Sustainability Indicator Selection by a Novel Triangular Intuitionistic Fuzzy Decision-Making Approach in Highway Construction Projects

The construction industry has been criticized as being a non-sustainable industry that requires effective tools to monitor and improve its sustainability performance. The multiplicity of indicators of the three pillars of sustainability—economic, social, and environmental—complicates construction sustainability assessments for project managers. Therefore, prioritizing and selecting appropriate sustainability indicators (SIs) is essential prior to conducting a construction sustainability assessment. The main purpose of this research is to select the most appropriate set of SIs to address all three pillars of highway sustainability by a new group decision-making approach. The proposed approach accounts for risk attitudes of experts and entropy measures under a triangular intuitionistic fuzzy (TIF) environment, to handle the inherent uncertainty and vagueness that is present throughout the evaluation process. Furthermore, new separation measures and ranking scores are introduced to distinguish the preference order of SIs. Eventually, the approach is implemented in a case study of highway construction projects and the applicability of the approach is examined. To investigate the stability and validity of computational results, a sensitivity analysis is carried out and a comparison is made between the obtained ranking outcomes and the traditional decision-making methods.

基于TODIM法的三角直觉模糊多属性决策算法及应用

基于TODIM法的三角直觉模糊多属性决策算法及应用

Development of a fixable model for the reliability and safety evaluation of the components of a commercial lithium-ion battery

Abstract In recent years, efforts and attention are gradually been shifted to the pollution-free renewable energy (fuel cell and lithium-ion battery), for propelling vehicles and for rural and urban electrification. With the advancement of these renewable energies, it is only necessary to continuously explore their behaviour, reliability, and safety. In this paper, the study will be focused on the reliability and safety of the components of the lithium-ion battery, by proposing a fixable model for the evaluation of their reliability and safety. The model proposed (Triangular Intuitionistic Fuzzy Aggregating and Ranking Function (TIFARF) model), is one that has been coined from the reliability-centered maintenance concept, which is aimed at probing into the reliability and safety of the components of the battery. It is proactive reliability and safety management approach and it is intended to determine what could happen when it is used in electric vehicles or aircraft. The results from the evaluation show that the electrolyte (ES3), has the least reliability and the highest safety concerns according to the analysis and opinion represented by the invited experts. Hence the electrolyte (ES3), should be given the most or top reliability and safety priority. The model has the advantage of been able to model imprecise information in the evaluation of the reliability and safety concerns associated with the lithium-ion battery.

Intuitionistic Fuzzy Sets in Multi-Criteria Group Decision Making Problems Using the Characteristic Objects Method

Over the past few decades, several researchers and professionals have focused on the development and application of multi-criteria group decision making (MCGDM) methods under a fuzzy environment in different areas and disciplines. This complex research area has become one of the more popular topics, and it seems that this trend will be increasing. In this paper, we propose a new MCGDM approach combining intuitionistic fuzzy sets (IFSs) and the Characteristic Object Method (COMET) for solving the group decision making (GDM) problems. The COMET method is resistant to the rank reversal phenomenon, and at the same time it remains relatively simple and intuitive in practical problems. This method can be used for both symmetric and asymmetric information. The Triangular Intuitionistic Fuzzy Numbers (TIFNs) have been used to handle uncertain data. This concept can ensure the preference information about an alternative under specific criteria more comprehensively and allows for easy modelling of symmetrical or asymmetrical linguistic values. Each expert provides the membership and non-membership degree values of intuitionistic fuzzy numbers (IFNs). So this approach deals with a different kind of uncertainty than with hesitant fuzzy sets (HFSs). The proposed combination of COMET and IFSs required an adaptation of the matrix of expert judgment (MEJ) and allowed to capture the behaviour aspects of the decision makers (DMs). Therefore, we get more reliable solutions while solving MCGDM problems. Finally, the proposed method is presented in a simple academic example.

A new approach to rank the decision making units in presence of infeasibility in intuitionistic fuzzy environment

Data envelopment analysis (DEA) is a linear programming based methodology to determine the relative performance efficiencies of homogeneous decision making units (DMUs). In real world applications, some input and output datas do not possess crisp/fuzzy essence but they possess intuitionistic fuzzy (IF) essence. So, in this study, we develop an IF BCC (IFBCC) and an IF super efficiency BCC (IFSEBCC) model with triangular IF numbers (TIFNs) input/output data. Firstly, the efficiencies of DMUs are determined using IFBCC model. If DMUs are efficient then the super efficiencies of DMUs are determined using IFSEBCC model. If DMUs do not have feasible (finite) efficiencies/super efficiencies in intuitionistic fuzzy environment, then we can not rank the DMUs. Therefore, we develop IF models to determine the efficiencies of DMUs and ranking the DMUs in the presence of infeasibility in intuitionistic fuzzy environment. Two illustrative examples and one real life application are provided to illustrate the applications of the proposed IF models. Finally, comparison has been performed with the existing crisp models.

Interval-Valued Intuitionistic Fuzzy Linear Programming Problem

In many existing methods of linear programming problem (LPP), precise values of parameters have been used but parameters of LPP are imprecise and ambiguous due to incomplete information. Several approaches and theories have been developed for dealing LPP based on fuzzy set (FS), intuitionistic fuzzy set (IFS) which are characterized by membership degree, membership and non-membership degrees, respectively. It’s interesting to note that single membership and non-membership degrees do not deal properly the state of uncertainty and hesitation. Further, we face a kind of uncertainty occurs a kind of uncertainty. Interval-valued intuitionistic fuzzy sets (IV-IFS) is a perfect key for handling uncertainty and hesitation than FS and IFS. In this paper, we define an interval-valued intuitionistic fuzzy number (IV-IFN) and its expected interval and expected values. We also introduce the concept of interval-valued intuitionistic fuzzy linear programming problem (IV-IFLPP). Further, we find the solutions of IV-IFLPP and compare the obtained optimal solutions with existing methods [D. Dubey and A. Mehra, Linear programming with Triangular Intuitionistic Fuzzy Numbers, in Proc. of the 7th Conf. and of the European Society for Fuzzy Logic and Technology (EUSFLAT-LFA 2011), R. Parvathi and C. Malathi, Intuitionistic fuzzy linear optimization, Notes on Intuitionistic Fuzzy Sets 18 (2012) 48–56]. Proposed technique may be used successfully in various areas in the formulation of our country’s five year plans, these include transportation, food-grain storage, urban development, national, state and district level plans, etc., The Indian Railways may use IV-IFLPP technique for linking different railway zones in more realistic way. Agricultural research institutes may use proposed technique for crop rotation mix of cash crops, food crops and fertilizer mix. Airlines can apply IV-IFLPP in the selection of routes and allocation of aircrafts to different routes. Private and public sector oil refineries may use IV-IFLPP for blending of oil ingredients to produce finished petroleum products.

T1 Weighted MR Brain Image Segmentation with Triangular Intuitionistic Fuzzy Set

Segmentation of medical image is a very important step in processing of image to help examination of diseases. The early detection of ailments from the normal diseases is essential for the physicist to stop and provide treatment. Increasing Cerebrospinal fluid in brain causes dementia which is an increasing mostly prevalent now days. Segmentation of brain images is a challenge due to the existence of noise and intensity in-homogeneity that creates hesitation in segmenting the tissues. This paper is about a fresh segmentation method that uses triangular membership function to distinguish the early regions of brain tissue with intuitionistic fuzzy set. The triangular membership function helps in identifying the initial clusters and regions and facilitates in the decline of the number of iterations needed for segmentation. The proposed method successfully determines the brain tissues avoiding local minima and need of initial clusters. Hence, outperforms the existing method with increased accuracy and reduced computation time

Study on performance evaluation of the production process - fuzzy MCDM approach

Improvement of the production process presents a very important management task for both researchers and practitioners and enables a better market position of the enterprise. Key Performance Indicators (KPIs) of the production process can provide useful information on the current state of the ongoing process. In this paper, the relative importance of KPIs and their values at the enterprise level were assessed by the experts and decision-makers. Their estimates are described by the linguistic variables which were modeled by intuitionistic fuzzy numbers. The weights vector of KPIs at the level of the considered enterprise is given by the Fuzzy Analytic Hierarchical Process (FAHP) with Triangular Intuitionistic Fuzzy Numbers (TIFNs). The rank of enterprises with respect to KPIs’ values and their weights was calculated using the modified TOPSIS with TIFNs. The developed model was tested on 30 enterprises from Serbia, belonging to the sector of small and medium-sized (SME) production enterprises. The improvement strategies of KPIs should be proposed at the level of each enterprise, separately, respecting the KPIs’ values of the first-ranked enterprise.