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Intuitionistic fuzzy solid assignment problems: a software-based approach

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• Published: 23 May 2019
• Volume 10 , pages 661–675, ( 2019 )

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• P. Senthil Kumar   ORCID: orcid.org/0000-0003-4317-1021 1  

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This paper sustains a sound mathematical and computing background. In this paper, the software-based approach for solving intuitionistic fuzzy solid assignment problem (IFSAP) is presented. The IFSAP is formulated and it is solved by using Lingo 17.0 software tool. Theorems related to IFSAP is proved. The IFSAP and its crisp solid assignment problem both are solved at a time and their optimal solution is obtained. In addition, the optimal objective values of both the IFSAP and its crisp solid assignment problem (SAP) are estimated with the help of substituting the optimal solution(s) to their respective decision variables in the objective functions. Some new and important results are proposed. To illustrate the efficiency of the proposed method the numerical example is presented. The reliability of the proposed results are verified by using the numerical example. Strengths and weakness of the paper is mentioned. The novelty of the analysis is given into a coherent, concise, and meaningful manner of analysis. Social issue (real-life problem) is converted into a mathematical model and it is solved by the proposed method. At the end, the advantages of the proposed algorithm is explained.

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Acknowledgements

The author is grateful to anonymous referees for their constructive as well as helpful suggestions and comments to revise the paper in the present form.

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Kumar, P.S. Intuitionistic fuzzy solid assignment problems: a software-based approach. Int J Syst Assur Eng Manag 10 , 661–675 (2019). https://doi.org/10.1007/s13198-019-00794-w

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Received : 24 February 2018

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A Method for Solving Balanced Intuitionistic Fuzzy Assignment Problem

• P. Senthil Kumar , R. J. Hussain
• Published 2014
• Mathematics, Computer Science

19 Citations

New algorithm for solving mixed intuitionistic fuzzy assignment problem, an algorithm for solving unbalanced intuitionistic fuzzy assignment problem using triangular intuitionistic fuzzy number, a simple method for solving fully intuitionistic fuzzy real life assignment problem, optimization of fuzzy k-objective fractional assignment problem using fuzzy programming model, the psk method for solving fully intuitionistic fuzzy assignment problems with some software tools, intuitionistic fuzzy solid assignment problems: a software-based approach, algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set, psk method for solving intuitionistic fuzzy solid transportation problems, a simple and efficient algorithm for solving type-1 intuitionistic fuzzy solid transportation problems, an integer solution in intuitionistic transportation problem with application in agriculture, 21 references, a general approach for solving assignment problems involving with fuzzy cost coefficients, fuzzy assignment problem with generalized fuzzy numbers, a labeling algorithm for the fuzzy assignment problem, an optimal more-for-less solution of mixed constraints intuitionistic fuzzy transportation problems, assignment and travelling salesman problems with coefficients as lr fuzzy parameters.

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Aggregators used in fuzzy control—a review.

1. Introduction

• Provide an accurate and detailed summary of the current state of re-examination of aggregation functions;
• Cover theoretical advances, practical applications, and empirical research in one comprehensive document;
• Highlight the importance of this research and its results for a better understanding and application of aggregation functions;
• Synthesise findings from different studies to identify common themes, patterns, and trends;
• Integrate insights from different research areas to provide a broad perspective and holistic view of the field.
• Section 2 (Preliminaries)—basic assumptions and definitions to remind and facilitate the concept of aggregation and others related to this paper;
• Section 3 (Materials and Methods)—an approach to article search and selection;
• Section 4 (Results)—a synthetic summary of the selected publications and their collation;
• Section 5 (Discussion)—analysis and review of the results;
• Section 6 (Conclusions)—presents conclusions and a summary of the scope of the selected articles.

2. Preliminaries

2.1. basic definitions.

• f(a, a, a, …, a) = a and f(b, b, b, …, b) = b;-*
• for x, y argument values x ≤ y implies f (x) ≤ f (y) for all x, y ∈ I n .

2.2. Classification and General Properties

2.2.1. main classes.

• Conjunctive;
• Disjunctive;

2.2.2. Main Properties

2.2.3. comparability, 2.2.4. continuity and stability, 2.3. main families, 2.3.1. min and max, 2.3.2. means, 2.3.3. medians, 2.3.4. choquet and sugeno integrals, 2.4. selection of aggregation function.

• Select an aggregation function that must match the semantics of the aggregation procedure;
• Choose the right member of the class/family that does what it is supposed to do—produce the right output for the input.
• the least-squares norm ( p = 2)
• the latest absolute deviation norm ( p = 1):
• the Chebyshev norm ( p = ∞):
• or their weighted analogues, like:

3. Materials and Methods

3.1. dataset and devices, 3.2. methods, 4.1. scope of topics in the publications, 4.2. early attempts, 4.3. late attempts.

• In the first stage, the optimal charging of each PEV is calculated using the Bee algorithm as the aggregator optimizer;
• In the second stage, the aggregated power is distributed among electric vehicles using a fuzzy controller.

5. Discussion

5.1. limitations of current approaches to aggregators.

• Selection of aggregator functions: its subjectivity and lack of standardization—there is no universally accepted standard for the selection of aggregation operators, which may lead to inconsistencies between different systems and applications;
• Computational complexity that limits performance and scalability, especially in real-time fuzzy control applications where fast response times are important, and as the number of input data increases, the computational burden of some aggregation methods may become too high;
• Potential loss of information: oversimplification, especially when using simple aggregation methods such as minimum or maximum operators, which may result in less accurate or less diverse resulting control;
• Nonlinearity and uncertainty: some aggregation methods may introduce nonlinearity into the system, making the behavior of a fuzzy control system more difficult to predict and analyze, as well as suboptimal performance in uncertain environments;
• Context dependence: lack of adaptability in dynamic environments where the relationships between inputs and outputs may change over time;
• Input interdependence: ignoring the interconnectedness of inputs can lead to incorrect control decisions;
• The complexity of designing and tuning aggregation operators can be high and time-consuming, especially when tuning for a specific application domain;
• Integration with other systems: aggregation methods in fuzzy control systems may not be easily integrated with other control or decision-making systems;
• Objectively assessing the performance of different aggregation operators can be difficult, placing high demands on comparison and selection of the most appropriate one for a particular application.

5.2. Directions of Further Studies on Aggregators

• Adaptive aggregation methods: developing aggregation operators that adapt to changing contexts or operating conditions in real time based on the current or predicted state of the system;
• Learning-based aggregation: implementing machine-learning techniques (neural networks, reinforcement learning) to learn optimal aggregation strategies from data to improve the adaptability and performance of fuzzy control systems;
• Complexity reduction: designing more computationally efficient aggregation algorithms that reduce the computational load, especially for real-time applications and systems with a large number of inputs, but also developing simplified aggregation models as a trade-off between computational efficiency and the accuracy of the aggregated result (sufficient aggregator instead of optimal aggregator);
• Creating aggregation operators resistant to uncertainty (e.g., based on the integration of concepts from the probabilistic and interval approaches);
• Development of nonlinear aggregation techniques that can better capture the complex relationships between inputs while maintaining computational feasibility;
• Correlation-aware aggregation: create multidimensional aggregation operators that consider common distributions of input data, providing a more accurate representation of their common behavior;
• Multi-criteria and multi-objective aggregation: development of multi-criteria decision-making (MCDM) techniques with fuzzy aggregation to handle scenarios with many conflicting goals or criteria—Pareto-optimal aggregation also applies here;
• Hybrid control systems: combining fuzzy aggregation methods with other control strategies;
• Development of aggregator performance metrics and benchmarking frameworks to objectively evaluate and compare different aggregation operators in terms of accuracy, robustness, computational efficiency, and adaptability in various practical applications.

6. Conclusions

Author contributions, data availability statement, conflicts of interest.

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Kozielski, M.; Prokopowicz, P.; Mikołajewski, D. Aggregators Used in Fuzzy Control—A Review. Electronics 2024 , 13 , 3251. https://doi.org/10.3390/electronics13163251

Kozielski M, Prokopowicz P, Mikołajewski D. Aggregators Used in Fuzzy Control—A Review. Electronics . 2024; 13(16):3251. https://doi.org/10.3390/electronics13163251

Kozielski, Mirosław, Piotr Prokopowicz, and Dariusz Mikołajewski. 2024. "Aggregators Used in Fuzzy Control—A Review" Electronics 13, no. 16: 3251. https://doi.org/10.3390/electronics13163251

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• Fuzzy Ranking Method to Assignment Problem with Fuzzy Costs

2012, International Journal of Mathematical Archive ( …

This paper presents solution methodology for assignment problem with fuzzy cost. The fuzzy costs are considered as trapezoidal fuzzy numbers. Ranking method (introduced by S. Abbasbandy and T. Hajjary, 2009) has been used for ranking the trapezoidal fuzzy ...

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