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Journal articles on the topic 'Triangular intuitionistic fuzzy number'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Liang, Changyong, Shuping Zhao, and Junling Zhang. "Aggregation Operators on Triangular Intuitionistic Fuzzy Numbers and its Application to Multi-Criteria Decision Making Problems." Foundations of Computing and Decision Sciences 39, no. 3 (2014): 189–208. http://dx.doi.org/10.2478/fcds-2014-0011.

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Abstract The aim of this work is to present some aggregation operators with triangular intuitionistic fuzzy numbers and study their desirable properties. Firstly, the score function and the accuracy function of triangular intuitionistic fuzzy number are given, the method for ranking triangular intuitionistic fuzzy numbers are developed. Then, some geometric aggregation operators for aggregating triangular intuitionistic fuzzy numbers are developed, such as triangular intuitionistic fuzzy weighted geometric (TIFWG) operator, the triangular intuitionistic fuzzy ordered weighted geometric (TIFOWG

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John Robinson P. "Multiple Attribute Group Decision Analysis for Intuitionistic Triangular and Trapezoidal Fuzzy Numbers." International Journal of Fuzzy System Applications 5, no. 3 (2016): 42–76. http://dx.doi.org/10.4018/ijfsa.2016070104.

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Solving Multiple Attribute Group Decision Making (MAGDM) problems has become one of the most important researches in recent days. In situations where the information or the data is of the form of an Intuitionistic Triangular Fuzzy Number (ITrFN) or Intuitionistic Trapezoidal Fuzzy Number (ITzFN), a new distance function is defined for ranking the alternatives in the decision making process. After processing the decision information through a sequence of arithmetic aggregation operators, namely, the Intuitionistic Triangular Fuzzy Weighted Arithmetic Averaging (ITrFWAA), Intuitionistic Triangul

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Mondal, Sankar Prasad, Adrijit Goswami, and Sujit Kumar De. "Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral Equation." Advances in Fuzzy Systems 2019 (March 3, 2019): 1–14. http://dx.doi.org/10.1155/2019/4142382.

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In this paper we introduce the different arithmetic operations on nonlinear intuitionistic fuzzy number (NIFN). All the arithmetic operations are done by max-min principle method which is nothing but the application of interval analysis. We also define the nonlinear intuitionistic fuzzy function which is used for finding the values, ambiguities, and ranking of nonlinear intuitionistic fuzzy number. The de-i-fuzzification of the corresponding intuitionistic fuzzy solution is done by average of (α,β)-cut method. Finally we solve integral equation with NIFN by the help of intuitionistic fuzzy Lap

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G. Sudha, R. Sophia Porchelvi, and K. Gnanaselvi. "Solving Critical Path Problem using Triangular Intuitionistic Fuzzy Number." International Journal of Fuzzy Mathematical Archive 14, no. 01 (2017): 01–08. http://dx.doi.org/10.22457/ijfma.v14n1a1.

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This paper presents a method for finding critical path with Intuitionistic fuzzy project network. Triangular Intuitionistic fuzzy numbers are used to represent activity times in the project network and we propose an algorithm for finding critical path. A solution is also given to demonstrate our proposed approach.

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R. Irene Hepzibah and R.Vidhya. "Modified new operations for triangular intuitionistic fuzzy numbers." Malaya Journal of Matematik 2, no. 03 (2014): 301–7. http://dx.doi.org/10.26637/mjm203/017.

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Intuitionistic fuzzy sets (IFS) are a generalization of the concept of fuzzy set. In standard intuitionistic fuzzy arithmetic operations, we have some grievances in subtraction and division operations. In this paper, modified new operations for subtraction and division on triangular intuitionistic fuzzy numbers (TIFNS) are defined. Finally an illustrative example for solving Intuitionistic fuzzy multi-objective linear programming problem (IFMOLPP) using these modified operators is provided.

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Zhang, Xin, and Peide Liu. "METHOD FOR AGGREGATING TRIANGULAR FUZZY INTUITIONISTIC FUZZY INFORMATION AND ITS APPLICATION TO DECISION MAKING / NUMANOMŲ NEAPIBRĖŽTŲJŲ AIBIŲ TEORIJA IR JOS TAIKYMAS PRIIMANT SPRENDIMUS." Technological and Economic Development of Economy 16, no. 2 (2010): 280–90. http://dx.doi.org/10.3846/tede.2010.18.

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On the foundation of the theory of the intuitionistic fuzzy set, this paper uses the triangular fuzzy number to denote the membership degree and the non‐membership degree and proposes the triangular intuitionistic fuzzy number. Then the operation rules of triangular intuitionistic fuzzy numbers are defined. The weighted arithmetic averaging operator and the weighted geometric average operator are presented and used to the decision making area after defined the score function and the accuracy function. An effective solution is offered for multi‐attitude decision‐making problem and an active try

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Xu, Jun, Jiu-Ying Dong, Shu-Ping Wan, De-Yan Yang, and Yi-Feng Zeng. "A Heterogeneous Multiattribute Group Decision-Making Method Based on Intuitionistic Triangular Fuzzy Information." Complexity 2019 (August 7, 2019): 1–18. http://dx.doi.org/10.1155/2019/9846582.

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How to aggregate decision information in heterogeneous multiattribute group decision making (HMAGDM) is vital. The aim of this paper is to develop an approach to aggregating decision data into intuitionistic triangular fuzzy numbers (ITFNs) for heterogeneous MAGDM problems with real numbers (RNs), interval numbers (INs), triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), and triangular intuitionistic fuzzy number (TIFNs). Using the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS) and geometry entropy method, we first present a gener

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Radhakrishnan S and Saikeerthana D. "Triangular intuitionistic fuzzy sequencing problem." Kongunadu Research Journal 8, no. 2 (2021): 61–68. http://dx.doi.org/10.26524/krj.2021.20.

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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.

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Kumar, Mohit. "Intuitionistic Fuzzy Measures of Correlation Coefficient of Intuitionistic Fuzzy Numbers Under Weakest Triangular Norm." International Journal of Fuzzy System Applications 8, no. 1 (2019): 48–64. http://dx.doi.org/10.4018/ijfsa.2019010103.

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The correlation coefficient of variables has wide applications in statistics and is often calculated in crisp or fuzzy environment. This article extends the application of correlation coefficient to intuitionistic fuzzy environment. In this article, a new method is proposed to measure the correlation coefficient of intuitionistic fuzzy numbers using weakest triangular norm based intuitionistic fuzzy arithmetic operations. Different from previous studies, the correlation coefficient computed in this article is an intuitionistic fuzzy number rather than a crisp or fuzzy number. It is well known

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Kumar, Gaurav, and Rakesh Kumar Bajaj. "Intuitionistic Fuzzy Weighted Linear Regression Model with Fuzzy Entropy under Linear Restrictions." International Scholarly Research Notices 2014 (October 30, 2014): 1–10. http://dx.doi.org/10.1155/2014/358439.

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In fuzzy set theory, it is well known that a triangular fuzzy number can be uniquely determined through its position and entropies. In the present communication, we extend this concept on triangular intuitionistic fuzzy number for its one-to-one correspondence with its position and entropies. Using the concept of fuzzy entropy the estimators of the intuitionistic fuzzy regression coefficients have been estimated in the unrestricted regression model. An intuitionistic fuzzy weighted linear regression (IFWLR) model with some restrictions in the form of prior information has been considered. Furt

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Shams, Mudassir, Nasreen Kausar, Naveed Khan, and Mohd Asif Shah. "Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations." Advances in Mechanical Engineering 15, no. 3 (2023): 168781322311595. http://dx.doi.org/10.1177/16878132231159519.

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Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets. These theories, however, have their own restrictions in terms of membership and non-membership levels. Because it utilizes benchmark or control parameters relating to membership and non-membership levels, this theory is particularly valuable for modeling uncertainty in real-world problems. We propose the unique concept of linear Diophantine fuzzy set with benchmark parameters to overcome these restrictions. Different numerical,

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P., John Robinson, and Henry AmirtharajE C. "Extended TOPSIS with Correlation Coefficient of Triangular Intuitionistic Fuzzy Sets for Multiple Attribute Group Decision Making." International Journal of Decision Support System Technology 3, no. 3 (2011): 15–41. http://dx.doi.org/10.4018/jdsst.2011070102.

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This paper extends the technique for order preference by similarity to ideal solution (TOPSIS) for solving multi-attribute group decision making (MAGDM) problems under triangular intuitionistic fuzzy sets by using its correlation coefficient. In situations where the information or the data is of the form of triangular intuitionistic fuzzy numbers (TIFNs), some arithmetic aggregation operators have to be defined, namely the triangular intuitionistic fuzzy ordered weighted averaging (TIFOWA) operator and the triangular intuitionistic fuzzy hybrid aggregation (TIFHA) operator. An extended TOPSIS

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Kannagi, P., and G. Uthra. "Group Replacement Strategy under Fuzzy Methods." International Journal of Engineering and Advanced Technology 9, no. 1s5 (2019): 250–54. http://dx.doi.org/10.35940/ijeat.a1060.1291s519.

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Intuitionistic Fuzzy Numbers play an active role in finding an optimal solution for replacement problems under vague and uncertain situations. This paper gives a group replacement policy under fuzzy environment. Here all the costs and the number of units are taken as Triangular Intuitionistic Fuzzy Numbers (TIFNs). An example is used for illustration of the policy.

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Xu, Bin. "Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators." Journal of Intelligent & Fuzzy Systems 39, no. 3 (2020): 4427–41. http://dx.doi.org/10.3233/jifs-200414.

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The concept of fuzzy number intuitionistic fuzzy sets (FNIFSs) is designed to effectively depict uncertain information in decision making problems which fundamental characteristic of the FNIFS is that the values of its membership function and non-membership function are depicted with triangular fuzzy numbers (TFNs). The dual Hamy mean (DHM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this paper, we used the dual Hamy mean (DHM) operator and dual weighted Hamy mean (WDHM) operator wit

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Atalik, Gultekin, and Sevil Senturk. "A noval ranking approach based on incircle of triangular intuitionistic fuzzy numbers." Journal of Intelligent & Fuzzy Systems 39, no. 5 (2020): 6271–78. http://dx.doi.org/10.3233/jifs-189095.

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Since proposed by Zadeh in 1965, ordinary fuzzy sets help us to model uncertainty and developed many types such as type 2 fuzzy, intuitionistic fuzzy, hesitant fuzzy etc. Intuitionistic fuzzy sets include both membership and non-membership functions for their each element. Ranking of a number is to identify a relationship of scalar quantity between these numbers. Ranking of fuzzy numbers play an important role in modeling problems such as fuzzy decision making, fuzzy linear programming problems. In this study, a new ranking method for triangular intuitionistic fuzzy numbers is proposed. The me

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G. Sudha, R. Sophia Porchelvi, and S. Vishnupriya. "A Novel Approach for Finding Shortest Path in Intuitionistic Fuzzy Network." International Journal of Fuzzy Mathematical Archive 14, no. 01 (2017): 139–46. http://dx.doi.org/10.22457/ijfma.v14n1a17.

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This paper deals with finding the shortest path problem of a network with triangular intuitionistic fuzzy number (TIFN). It proposes a modified algorithm to find the shortest path with intuitionistic fuzzy arc lengths.

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Kumar, P. Senthil. "PSK Method for Solving Mixed and Type-4 Intuitionistic Fuzzy Solid Transportation Problems." International Journal of Operations Research and Information Systems 10, no. 2 (2019): 20–53. http://dx.doi.org/10.4018/ijoris.2019040102.

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In this article, the author categorises the solid transportation problem (STP) under uncertain environments. He formulates the mixed and fully intuitionistic fuzzy solid transportation problems (FIFSTPs) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P. Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the mixed and type-4 IFSTP and the optimal objective value of mixed and type-4 IFSTP is obtained in terms of triangular in

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Pathade, Priyanka A., and Kirtiwant P. Ghadle. "Transportation Problem with Triangular Mixed Intutionistic Fuzzy Numbers Solved By BCM." International Journal of Fuzzy Mathematical Archive 15, no. 01 (2018): 55–61. http://dx.doi.org/10.22457/ijfma.v15n1a5.

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In this paper, we formulate a transportation problem in which sources, destinations and costs are different types of fuzzy numbers. We used real, fuzzy and intuitionistic fuzzy numbers are employed to get the optimal solution. Mixed intuitionistic fuzzy BCM is used to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. The method is illustrated by a numerical examples.

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Seikh, Mijanur Rahaman, Prasun Kumar Nayak, and Madhumangal Pal. "Notes on triangular intuitionistic fuzzy numbers." International Journal of Mathematics in Operational Research 5, no. 4 (2013): 446. http://dx.doi.org/10.1504/ijmor.2013.054730.

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Elizabeth, S., and L. Sujatha. "Project scheduling method using triangular intuitionistic fuzzy numbers and triangular fuzzy numbers." Applied Mathematical Sciences 9 (2015): 185–98. http://dx.doi.org/10.12988/ams.2015.410852.

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Hasan, Mohammad Kamrul. "ARITHMETIC OPERATIONS OF GENERALIZED PICTURE FUZZY NUMBERS BY (α, γ, β) – CUT METHOD". Journal of Dynamics and Control 9, № 5 (2025): 147–81. https://doi.org/10.71058/jodac.v9i5014.

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Picture fuzzy set is an extension of intuitionistic fuzzy set and fuzzy set and it is capable to analyze the uncertain and vague information more effectively. It is applicable in situations where human decisions claim more variety of responses like yes, no, abstain and refusal which cannot be addressed in the traditional fuzzy set and intuitionistic fuzzy set. In this article, the arithmetic operations such as scalar multiplication of a generalized trapezoidal and triangular picture fuzzy numbers and the division and multiplication of two generalized trapezoidal and triangular picture fuzzy nu

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Singh, Surendra, and Tanuj Kumar. "An intuitionistic fuzzy inventory model with waste disposal using the triangular intuitionistic fuzzy numbers." Journal of Physics: Conference Series 2223, no. 1 (2022): 012004. http://dx.doi.org/10.1088/1742-6596/2223/1/012004.

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Abstract In the present study, we formulate an inventory model with waste disposal cost under the intuitionistic fuzzy environment. To optimize the best inventory policy under the intuitionistic fuzzy environment, the alpha-cut approach is used for the defuzzification of all intuitionistic fuzzy decision variables. This study aims to reduce the total inventory cost and adjust the waste outcomes during the production processes to keep a clean and green climate, which will be cost-effective for any organization, both environmentally and economically. A numerical example is presented regarding th

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Kaur, Prabjot. "Selection of Vendor Based on Intuitionistic Fuzzy Analytical Hierarchy Process." Advances in Operations Research 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/987690.

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Business environment is characterized by greater domestic and international competitive position in the global market. Vendors play a key role in achieving the so-called corporate competition. It is not easy however to identify good vendors because evaluation is based on multiple criteria. In practice, for VSP most of the input information about the criteria is not known precisely. Intuitionistic fuzzy set is an extension of the classical fuzzy set theory (FST), which is a suitable way to deal with impreciseness. In other words, the application of intuitionistic fuzzy sets instead of fuzzy set

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Alolaiyan, Hanan, Laila Latif, Umer Shuaib, Abdul Razaq, and Qin Xin. "A novel development to encrypt data communication under t-intuitionistic fuzzy environment." PLOS ONE 19, no. 9 (2024): e0308140. http://dx.doi.org/10.1371/journal.pone.0308140.

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The field of cryptography has grown significantly with the advent of information and communication technologies due to the increasing complexity of cyber threats and rising security requirements. This evolution has come with the creation of new cryptosystems and improvements to current ones. This study is the first to explore the RSA approach in the framework of t-intuitionistic fuzzy subgroups. This technique makes group-based cryptographic operations safer when there are unclear relationships and hesitations. This supports the complex and uncertain nature of subgroup membership, allowing for

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Dr., M. Mary Jansi Rani, and Jamshida K. "NUMERICAL SOLUTION OF INTUITIONISTIC FUZZY DIFFERENTIAL EQUATION USING RUNGE-KUTTA METHOD." International Journal of Scientific Research and Modern Education (IJSRME) 5, no. 2 (2020): 1–10. https://doi.org/10.5281/zenodo.4431131.

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The aim of this paper is to propose Runge-Kutta (ERK) methods of order 3 and 4 for solving intuitionistic fuzzy differential equations (IFDEs). Convergence analysis of RK methods has been carried out. The applicability of RK methods is illustrated by solving intuitionistic fuzzy differential equations with triangular intuitionistic fuzzy numbers. Comparison of the numerical solution with exact solution shows good accuracy.

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Dhouib, Souhail. "Unravelling the assignment problem under intuitionistic triangular fuzzy environment by the novel heuristic Dhouib-Matrix-AP1." Yugoslav Journal of Operations Research, no. 00 (2023): 5. http://dx.doi.org/10.2298/yjor220915005d.

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The Assignment Problem (AP) can be stated as n activities to be assigned to n resources in such a way that the overall cost of assignment is minimized and each activity is assigned to one and only one resource. In real-life, the parameters of the AP are presented as uncertain numbers due to the lack of knowledge, experiences or any other (internal or external) factor. In this paper, the AP is considered under intuitionistic triangular fuzzy number and solved by the novel constructive heuristic Dhouib-Matrix-AP1 (DM-AP1) with a time complexity of O(n). Actually, this paper presents the first en

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Yu, Chun-Min, Kuo-Ping Lin, Gia-Shie Liu, and Chia-Hao Chang. "A Parameterized Intuitionistic Type-2 Fuzzy Inference System with Particle Swarm Optimization." Symmetry 12, no. 4 (2020): 562. http://dx.doi.org/10.3390/sym12040562.

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The aim of this study was to develop a novel intuitionistic Type-2 fuzzy inference system (IT-2 FIS) which adopts a parameterized Yager-generating function and particle swarm optimization (PSO). In IT-2 FIS, the intuitionistic Type-2 is set as a fuzzy symmetrical triangular number in which the hesitation degree adopts the Yager-generating function, and the parameters of the proposed IT-2 FIS adopting the PSO are tuned. The intuitionistic and Type-2 fuzzy sets have been proven to be the most effective for handling more uncertainty. Therefore, this study proposes an intuitionistic Type-2 set wit

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Saranya, Vijaya Kumar, and Shanmuga Sundari Murugan. "A comparative analysis of the fuzzy and intuitionistic fuzzy environment for group and individual equipment replacement Models in order to achieve the optimized results." International Journal for Simulation and Multidisciplinary Design Optimization 14 (2023): 7. http://dx.doi.org/10.1051/smdo/2023006.

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The main goal of this research is to compare group and individual replacement models based on fuzzy replacement theory and intuitionistic fuzzy replacement theory. The capital costs are assumed to be triangular fuzzy numbers, triangular intuitionistic fuzzy numbers, and trapezoidal intuitionistic fuzzy numbers, respectively. As a result, interpreting the direct relationship between volatility and ambiguity is critical. It is difficult to predict when specific equipment will unexpectedly fail. This problem can be solved by calculating the probability of failure distribution. Furthermore, the fa

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Chaudhary, Priti, and Tanuj Kumar. "Intuitionistic fuzzy inventory model with quadratic demand rate, time-dependent holding cost and shortages." Journal of Physics: Conference Series 2223, no. 1 (2022): 012003. http://dx.doi.org/10.1088/1742-6596/2223/1/012003.

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Abstract In the present work, we studied an inventory model under quadratic demand rate, linearly time-dependent holding cost, constant deterioration rate and allowed shortages. Intuitionistic fuzzy set (IFS) theory is an efficient tool to reduce the uncertainty that occurs due to hesitation, so we studied the considered model under intuitionistic fuzzy set theory. Further, the model is transformed into an intuitionistic fuzzy inventory model by taking the decision variables as triangular intuitionistic fuzzy numbers. To optimize the best inventory policy under the intuitionistic fuzzy environ

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Lu, Zhiming, and Youting Li. "A Multi-Criteria Framework for Sustainability Evaluation of Hydrogen-Based Multi-Microgrid Systems under Triangular Intuitionistic Fuzzy Environment." Sustainability 15, no. 4 (2023): 3708. http://dx.doi.org/10.3390/su15043708.

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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, s

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Rameshan, N., and D. S. Dinagar. "A METHOD FOR FINDING CRITICAL PATH WITH SYMMETRIC OCTAGONAL INTUITIONISTIC FUZZY NUMBERS." Advances in Mathematics: Scientific Journal 9, no. 11 (2020): 9273–86. http://dx.doi.org/10.37418/amsj.9.11.32.

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The concept of this paper represents finding fuzzy critical path using octagonal fuzzy number. In project scheduling, a new method has been approached to identify the critical path by using Symmetric Octagonal Intuitionistic Fuzzy Number (SYMOCINTFN). For getting a better solution, we use the fuzzy octagonal number rather than other fuzzy numbers. The membership functions of the earliest and latest times of events are by calculating lower and upper bounds of the earliest and latest times considering octagonal fuzzy duration. The resulting conditions omit the negative and infeasible solution. T

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Kousar, Sajida, Afia Zafar, Nasreen Kausar, Dragan Pamucar, and Parameshwari Kattel. "Fruit Production Planning in Semiarid Zones: A Novel Triangular Intuitionistic Fuzzy Linear Programming Approach." Mathematical Problems in Engineering 2022 (February 12, 2022): 1–13. http://dx.doi.org/10.1155/2022/3705244.

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A triangular intuitionistic fuzzy linear programming (TIFLP) model is formulated for the planning of sustainable fruit production system for hyperarid regions while assuming the availability of resources and existing knowledge. A remarkable advancement is achieved through the composition of intuitionistic fuzzy concept with the linear programming by considering all parameters and variables in the form of triangular intuitionistic fuzzy numbers, which provides a planning or strategic tool for handling uncertain situations with more control and in a realistic way. This fuzzy optimization model i

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Kumar, P. Senthil. "PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems." International Journal of Fuzzy System Applications 7, no. 4 (2018): 62–99. http://dx.doi.org/10.4018/ijfsa.2018100104.

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This article proposes a method for solving intuitionistic fuzzy solid transportation problems (IFSTPs) in which only the transportation costs are represented in terms of intuitionistic fuzzy numbers (IFNs). The remaining parameters, namely: supply, demand and conveyance capacity, are all considered into crisp numbers. This type of STP is called a type-2 IFSTP. When solving the real life solid transportation problems (STPs) those tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the in

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Liu, Yujia, Jian Wu, and Changyong Liang. "Attitudinal ranking and correlated aggregating methods for multiple attribute group decision making with triangular intuitionistic fuzzy Choquet integral." Kybernetes 44, no. 10 (2015): 1437–54. http://dx.doi.org/10.1108/k-02-2014-0040.

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Purpose – The purpose of this paper is to propose novel attitudinal prioritization and correlated aggregating methods for multiple attribute group decision making (MAGDM) with triangular intuitionistic fuzzy Choquet integral. Design/methodology/approach – Based on the continuous ordered weighted average (COWA) operator, the triangular fuzzy COWA (TF-COWA) operator is defined, and then a novel attitudinal expected score function for triangular intuitionistic fuzzy numbers (TIFNs) is investigated. The novelty of this function is that it allows the prioritization of TIFNs by taking account of the

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Lone, M. A., S. A. Mir, and M. S. Wani. "An Integer solution in Intuitionistic Transportation Problem with Application in Agriculture." Oriental journal of computer science and technology 10, no. 1 (2017): 18–23. http://dx.doi.org/10.13005/ojcst/10.01.03.

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In this paper, we investigate a Transportation problem which is a special kind of linear programming in which profits; supply and demands are considered as Intuitionistic triangular fuzzy numbers. The crisp values of these Intuitionistic triangular fuzzy numbers are obtained by defuzzifying them and the problem is formulated into linear programming problem. The solution of the formulated problem is obtained through LINGO software. If the obtained solution is non-integer then Branch and Bound method can be used to obtain an integer solution.

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Zhou, Jinming, Tomas Baležentis, and Dalia Streimikiene. "Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots." Symmetry 11, no. 2 (2019): 218. http://dx.doi.org/10.3390/sym11020218.

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In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Wei

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Pérez-Cañedo, Boris, José Luis Verdegay та Eduardo René Concepción-Morales. "An ε-Constraint Method for Multiobjective Linear Programming in Intuitionistic Fuzzy Environment". International Journal of Intelligent Systems 2023 (12 квітня 2023): 1–14. http://dx.doi.org/10.1155/2023/9677396.

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Effective decision-making requires well-founded optimization models and algorithms tolerant of real-world uncertainties. In the mid-1980s, intuitionistic fuzzy set theory emerged as another mathematical framework to deal with the uncertainty of subjective judgments and allowed to represent hesitancy in a decision-making problem. Nowadays, intuitionistic fuzzy multiobjective linear programming (IFMOLP) problems are a topic of extensive research, for which a considerable number of solution approaches are being developed. Among the available solution approaches, ranking function-based approaches

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Tarmudi, Zamali. "AFuzzy Unifying Format Basedon Triangular Fuzzy Numbers and Intuitionistic Fuzzy Numbers." IOSR Journal of Mathematics 13, no. 02 (2017): 95–104. http://dx.doi.org/10.9790/5728-13020295104.

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Remad, Fedia Daami, and Hela Moalla Frikha. "The multicriteria group decision making FlowSort method under uncertainty." Multiple Criteria Decision Making 16 (2021): 122–39. http://dx.doi.org/10.22367/mcdm.2021.16.07.

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Crisp values are insufficient to model real-life situations and imprecise ideas are frequently represented in multicriteria decision aid analysis. In fact, it is difficult to treat the evaluation criteria precisely and to fix exact preferences rating. The triangular intuitionistic fuzzy numbers succeeded to treat this kind of ambiguity in a great deal of research than other forms of fuzzy representation functions. The field of sorting issues is an active research topic in the multiple criteria decision aid (MCDA). This study extended one of the sorting methods, FLOWSORT, for solving multiple c

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Krylovas, Aleksandras, and Natalja Kosareva. "EXPERT ESTIMATES AVERAGING BY CONSTRUCTING INTUITIONISTIC FUZZY TRIANGLES." Mathematical Modelling and Analysis 20, no. 3 (2015): 409–21. http://dx.doi.org/10.3846/13926292.2015.1049970.

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The problem of ranking (sorting) of m alternatives is considered when experts evaluate each alternative according to k criteria. Functions of arithmetic and geometric averages are constructed for decision making. We present a generalization of this scheme when there are evaluation matrices of several experts and this information is aggregated in the form of triangular intuitionistic fuzzy numbers. Fuzzy triangles were constructed with different uncertainty levels, experts decision matrices and the number of experts varied from 2 to 5. Moreover, method for construction of experts decision proba

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Zhou, Hui, and Haiping Ren. "A novel ranking function-based triangular intuitionistic fuzzy fault tree analysis method." Journal of Intelligent & Fuzzy Systems 39, no. 3 (2020): 2753–61. http://dx.doi.org/10.3233/jifs-191018.

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In reliability field, the probabilities of basic events are often treated as exact values in conventional fault tree analysis. However, for many practical systems, because the concept of events may be ambiguous, the factors affecting the occurrence of events are complex and changeable, so it is difficult to obtain accurate values of the occurrence probability of events. Fuzzy sets can well deal with these situations. Thus this paper will develop a novel fault tree analysis method in the assumption of the values of probability of basic events expressed with triangular intuitionistic fuzzy numbe

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Fu, Yong, Yong Qin, Weizhong Wang, Xinwang Liu, and Limin Jia. "An Extended FMEA Model Based on Cumulative Prospect Theory and Type-2 Intuitionistic Fuzzy VIKOR for the Railway Train Risk Prioritization." Entropy 22, no. 12 (2020): 1418. http://dx.doi.org/10.3390/e22121418.

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This paper aims toward the improvement of the limitations of traditional failure mode and effect analysis (FMEA) and examines the crucial failure modes and components for railway train operation. In order to overcome the drawbacks of current FMEA, this paper proposes a novel risk prioritization method based on cumulative prospect theory and type-2 intuitionistic fuzzy VIKOR approach. Type-2 intuitionistic VIKOR handles the combination of the risk factors with their entropy weight. Triangular fuzzy number intuitionistic fuzzy numbers (TFNIFNs) applied as type-2 intuitionistic fuzzy numbers (Typ

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Jenifer, D. H., and R. Irene Hepzibah. "On Solving Linear Complementarity Problem using Principal Pivoting Method." Indian Journal Of Science And Technology 17, no. 47 (2024): 4993–98. https://doi.org/10.17485/ijst/v17i47.3095.

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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 terminat

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Kousar, S., M. Batool, N. Kausar, D. Pamucar, E. Ozbilge, and B. Tantay. "Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain network." Advances in Production Engineering & Management 17, no. 3 (2022): 381–93. http://dx.doi.org/10.14743/apem2022.3.443.

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The urge to remanufacture and address environmental concerns in various industrial processes has drawn the attention of academics as well as practitioners towards Closed-loop Supply Chain Networks (CLSC). Although everchanging and complex external factors including social and economic ones, adversely impact the sustainable development of closed-loop supply chain networks. The basic aim of the research is to optimize the functioning of CLSC networks. For the above-said, two objective functions are made. The first objective is to minimize the cost of production and assembly expenses of the forwa

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Dr., R. Sophia Porchelvi, and Umamaheswari M. "A NEW PROPOSED METHOD FOR SOLVING INTUITIONISTIC FUZZY PARAMETRIC LINEAR COMPLIMENTARITY PROBLEMS." International Journal of Current Research and Modern Education, Special Issue (August 14, 2017): 70–74. https://doi.org/10.5281/zenodo.842840.

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In this paper, a new approach for solving the Fuzzy Linear Complimentarity Problem (FLCP) is suggested. Here, the cost coefficients, constrained coefficients and the right hand side coefficients are represented by Intuitionistic triangular fuzzy numbers. Using the KKT conditions and the implementation of the complementary pivot method using the inverse of the basis is proposed to solve the Intuitionistic Fuzzy Linear Complementarity Problems (FLCP). The effectiveness of the proposed method is illustrated by means of an example.

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Dhouib, Souhail. "Novel Heuristic for Intuitionistic Triangular Fuzzy Travelling Salesman Problem." International Journal of Applied Evolutionary Computation 12, no. 4 (2021): 39–55. http://dx.doi.org/10.4018/ijaec.2021100104.

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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 firs

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Padma, G., N. Ravi Shankar, and Kolli Srinivasa Rao. "Optimizing transportation network through IFN ranking : A comprehensive approach." Journal of Statistics and Management Systems 28, no. 4 (2025): 795–808. https://doi.org/10.47974/jsms-1418.

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The model of an Intuitionistic Uncertain Numeral is important used for computing an uncertain number, and ordering IFNs poses a significant contest in transport. This paper objects to present a method for resolving intuitionistic uncertain transport difficulties using IFNs and applying it to triangular intuitionistic fuzzy numbers. This research introduces an innovative approach to optimizing transportation networks by leveraging Intuitionistic Fuzzy Numbers (IFNs). Real-world case studies validate the superiority of the proposed IFN-based system over traditional methods, emphasizing its abili

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T. Nagalakshmi,. "Solution of a Triangular Intuitionistic Fuzzy Optimal Subdivision Problem - A Novel Approach." Advances in Nonlinear Variational Inequalities 28, no. 7s (2025): 419–29. https://doi.org/10.52783/anvi.v28.4542.

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Introduction: Dynamic Programming is the mathematical technique of optimizing a series of connected decisions over a given amount of time. The process of making decisions in many real-world scenarios involves choosing a set of plans from a wide range of possible combinations in unclear circumstances. Objectives: In this article, a novel approach is developed to solve a triangular intuitionistic fuzzy optimal subdivision problem in which a positive quantity which is to be partitioned is taken as triangular intuitionistic fuzzy number. Methods: The mathematical induction technique is applied in

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Nan, Jiang-Xia, Mao-Jun Zhang, and Deng-Feng Li. "A methodology for matrix games with payoffs of triangular intuitionistic fuzzy number." Journal of Intelligent & Fuzzy Systems 26, no. 6 (2014): 2899–912. http://dx.doi.org/10.3233/ifs-130956.

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Yang, Jie, Deng-Feng Li, and Li-Bang Lai. "Parameterized bilinear programming methodology for solving triangular intuitionistic fuzzy number bimatrix games." Journal of Intelligent & Fuzzy Systems 31, no. 1 (2016): 115–25. http://dx.doi.org/10.3233/ifs-162125.

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