Article
Mathematics
Ladji Kane, Daouda Diawara, Lassina Diabate, Moussa Konate, Souleymane Kane, Hawa Bado
Summary: In this study, linear programming problems involving trapezoidal fuzzy numbers are defined as the way of linear programming problems involving interval numbers. The solution concepts of primal and dual linear programming problems involving trapezoidal fuzzy numbers are discussed by converting them into two linear programming problems involving interval numbers. It is shown that both primal and dual problems have optimal solutions, with the two optimal values being equal. Additionally, both optimal solutions obey the strong duality theorem and complementary slackness theorem, demonstrating the correctness and usefulness of the proposed method through numerical examples. The proposed algorithm is flexible, easy, and reasonable.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Muhammad Akraml, Inayat Ullah, Tofigh Allahviranloo
Summary: In this study, we identified the inadequacy of existing arithmetic operations for trapezoidal fuzzy numbers and proposed new operations. We also found drawbacks in the existing Simplex method for solving fully fuzzy linear programming problems and developed a new strategy. Our results were compared with existing methods.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
M. Ranjbar, S. Effati, S. M. Miri
Summary: This paper introduces a new approach to solve fully hesitant fuzzy linear programming problems with hesitant fuzzy numbers as parameters. By converting the problem into interval linear programming problems and using statistical regression analysis, approximate solutions are obtained. The method is validated through an example, showing that the solutions for decision variables and objective function are reasonable.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2022)
Article
Computer Science, Artificial Intelligence
Ali Ebrahimnejad, Madjid Tavana, Vincent Charles
Summary: This paper introduces a new method for solving fuzzy variable linear programming problems, which greatly reduces the workload in fuzzy computations by converting the fuzzy problem into a crisp one and using the standard simplex algorithm. The proposed method only requires arithmetic operations of real numbers and the solution to crisp systems of equations, in contrast to existing methods which involve fuzzy arithmetic operations and the solution to fuzzy systems of equations.
Article
Computer Science, Information Systems
Jiuying Dong, Shuping Wan, Shyi-Ming Chen
Summary: This paper introduces a new fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making. Mathematical programming models are constructed to derive optimal fuzzy weights of criteria and four linear programming models are proposed for different types of decision makers. The concept of fuzzy consistency index and ratio are also proposed and validated through application examples.
INFORMATION SCIENCES
(2021)
Article
Computer Science, Information Systems
Shuping Wan, Jiuying Dong, Shyi-Ming Chen
Summary: This paper introduces a GITrF BWM method based on GITrFNs for MCDM, aiming to enhance decision consistency and effectiveness through techniques such as normalized weight vectors and consistency ratios.
INFORMATION SCIENCES
(2021)
Article
Computer Science, Theory & Methods
Lucian Coroianu
Summary: This paper demonstrates that the nearest trapezoidal approximation of fuzzy numbers can be obtained via quadratic programs, and improves the Lipschitz constant of the approximation operator while preserving ambiguity. Analytical expressions or quadratic programs can be used to achieve the same results, providing Lipschitz constants for the approximation operator even when an analytical expression is not available for similar problems.
FUZZY SETS AND SYSTEMS
(2021)
Article
Computer Science, Artificial Intelligence
Suresh Mohan, Arun Prakash Kannusamy, Sukhpreet Kaur Sidhu
Summary: Sensitivity analysis is a crucial method to study the impact of changes in model parameters on the optimal solution, enabling researchers to analyze the behavior of the optimal solution. By using numerical examples and ranking methods, the range within which parameters can vary without affecting the optimality of the solution can be determined.
COMPUTATIONAL INTELLIGENCE
(2021)
Article
Multidisciplinary Sciences
Anna Lyczkowska-Hanckowiak
Summary: This paper utilizes oriented fuzzy numbers for portfolio analysis, estimating the present value of portfolio elements using discount factors. By considering positively and negatively oriented elements, a portfolio discount factor is obtained through weighted sums, while the imprecision risk of the portfolio is estimated using measures of energy and entropy.
Article
Mathematics
Sophia Voulgaropoulou, Nikolaos Samaras, Nikolaos Ploskas
Summary: The selection of the most efficient algorithm for linear programming problems is a significant and challenging process. Previous work used artificial neural networks to formulate a regression model for predicting the execution time of the interior point method. Extension of this work involves examining a prediction model for the performance of CPLEX's primal and dual simplex algorithms using artificial neural networks. The study found that accurate regression models could not be formed, leading to a focus on classification instead.
Article
Management
Giacomo Nannicini
Summary: This paper proposes quantum subroutines for the simplex method, which eliminate the classical computation of the basis inverse. The author shows how to quantize all steps of the simplex algorithm, achieving polynomial speedup in problem dimension but with worse dependence on other numerical parameters. The quantum subroutines have advantages in scalability for well-conditioned sparse problems.
OPERATIONS RESEARCH
(2022)
Article
Mathematics, Applied
Serkan Akbas, Turkan Erbay Dalkilic
Summary: With the development of technology, investors are increasingly relying on computer software to guide their investments. This study proposes a two-stage portfolio selection model that considers investment data and expert opinions to address the issue of investors achieving the same expected return and risk level. By developing mathematical models suitable for trapezoidal fuzzy numbers, a new hybrid portfolio selection algorithm is introduced. The algorithm is tested using stock data from the Dow Jones Index, comparing total return amounts obtained by different methods for investment in January 2021.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Sergei Chubanov
Summary: This paper discusses a linear problem over a finite set of integer vectors and proposes an algorithm to find the optimal solution. The algorithm constructs a path from the initial solution to the optimal solution in the 1-skeleton of the convex hull of feasible solutions, with the length of the path bounded by the sum of distinct component values minus the problem dimension. In the case of binary vectors, the path length is bounded by the number of variables, regardless of the objective function.
SIAM JOURNAL ON OPTIMIZATION
(2021)
Article
Mathematics
Saeid Jafarzadeh Ghoushchi, Elnaz Osgooei, Gholamreza Haseli, Hana Tomaskova
Summary: New methods for solving fully fuzzy linear programming (FFLP) problems have been recommended recently. This study proposes a new approach utilizing triangular fuzzy numbers for fuzzy decision parameters and variables to tackle FFLP problems. By incorporating alpha-cut theory and modified triangular fuzzy numbers, the strategy aims to optimize decision variables and the objective function to obtain the optimal fully fuzzy solution for real-world problems. Multiple numerical examples are solved to demonstrate the effectiveness of this method.
Article
Management
Stewart Curry, Ilbin Lee, Simin Ma, Nicoleta Serban
Summary: This paper explores the variations of optimal value and solutions in optimization modeling with uncertain input parameters through sensitivity analysis and multiparametric programming. By introducing a tolerance approach based on principal component analysis and studying the geometric properties of critical regions, the research provides a theoretical foundation for cases where RIM parameters vary jointly. The proposed framework is evaluated through experiments for sensitivity analysis, model predictive control, and large optimization problems.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2022)
Article
Computer Science, Artificial Intelligence
Marina Torres, David A. Pelta, Jose L. Verdegay, Carlos Cruz
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS
(2019)
Article
Green & Sustainable Science & Technology
Gurupada Maity, Sankar Kumar Roy, Jose Luis Verdegay
Article
Computer Science, Artificial Intelligence
Bapi Dutta, Tanima Singha, Mark Goh, Maria Teresa Lamata, Jose-Luis Verdegay
EXPERT SYSTEMS WITH APPLICATIONS
(2019)
Article
Mathematics, Applied
B. Kheirfam, M. Mohamadi Sangachin
Summary: This paper introduces a new predictor-corrector interior-point algorithm for semidefinite optimization, demonstrating that both predictor and corrector steps contribute to decreasing the duality gap. The proposed algorithm's iteration complexity aligns with the best iteration bound for small neighbourhood algorithms using the Nesterov-Todd direction, and numerical results are provided as well.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2021)
Review
Mathematics
Boris Perez-Canedo, Jose Luis Verdegay, Eduardo Rene Concepcion-Morales, Alejandro Rosete
Article
Mathematics, Applied
B. Kheirfam, A. Nasrollahi, M. Mohammadi
Summary: This paper introduces a new infeasible interior-point algorithm for semidefinite optimization in a large neighborhood of the central path, which utilizes a novel corrective strategy to improve iteration efficiency.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Artificial Intelligence
Ali Abbaszadeh Sori, Ali Ebrahimnejad, Homayun Motameni, Jose Luis Verdegay
Summary: The important issue of improving transportation in connection with traffic is discussed, focusing on the constrained shortest path (CSP) problem and an efficient algorithm designed to find the optimal path.
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS
(2021)
Article
Mathematics, Applied
B. Kheirfam
Summary: This paper introduces an arc-search infeasible interior-point algorithm for semidefinite optimization, demonstrating its complexity order. Furthermore, through a simplified version of the algorithm, it is proven that the iteration complexity bound of the algorithm is equivalent to the best iteration bound for feasible interior-point algorithms.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Behrouz Kheirfam, Naser Osmanpour
Summary: This paper presents a new predictor-corrector interior-point algorithm based on a wide neighborhood for semidefinite optimization. The algorithm reduces the duality gap at every predictor and corrector steps, with an iteration complexity matching the currently best known iteration bound for wide neighborhood algorithms. Numerical results confirm the reliability and promise of the proposed algorithm.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Computer Science, Information Systems
Cynthia Porras, Boris Perez-Canedo, David A. Pelta, Jose L. Verdegay
Summary: This paper investigates the tourism trip design problem with time-dependent recommendation factors. By solving 27 real-world instances, it is found that including waiting times has little impact on the quality of solutions, and it leads to longer solving times. This highlights the importance of properly evaluating the benefits of making the problem model more complex.
Article
Business
Jose Luis Verdegay, Ma Teresa Lamata, David Pelta, Carlos Cruz
Summary: Computers process information and make decisions, with AI systems achieving levels of decision-making comparable to or exceeding humans. While these Autonomous Decision Systems can enhance efficiency, the potential for replacing humans raises concerns, making avoiding system malfunctions a top priority.
Article
Operations Research & Management Science
Behrouz Kheirfam
Summary: This paper presents a full-Newton step interior-point method for solving monotone Weighted Linear Complementarity Problem, utilizing the technique of algebraic equivalent transformation (AET) and achieving a quadratic rate of convergence to the target point on the central path.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2022)
Article
Computer Science, Artificial Intelligence
Boris Perez-Canedo, Cynthia Porras, David A. Pelta, Jose Luis Verdegay
Summary: Decisions made in various fields such as economics, engineering, industry, and medical sciences rely on finding and interpreting solutions to optimization problems. It is important to consider the decision-making context as a filter, along with the natural constraints of the problem, to avoid obtaining optimal but irrelevant solutions. This article proposes a method of modeling contexts using fuzzy propositions and introduces two approaches (a priori and a posteriori) for solving optimization problems under their influence. The results provide researchers and practitioners with a methodology for more effective optimization and decision making.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Mathematics, Applied
B. Kheirfam
Summary: In this paper, a new corrector-predictor interior-point method for solving semidefinite optimization is proposed. The centering equation of the system is transformed algebraically to define the central path. The algebraic transformation plays a crucial role in calculating the new search directions. The algorithm's iteration complexity is proven to match the best known results for interior-point methods (IPMs). This is the first corrector-predictor interior-point algorithm using search directions obtained from the desired algebraic transformation for semidefinite optimization. Numerical experiments are conducted to demonstrate the efficiency of the new algorithm.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Behrouz Kheirfam, Naser Osmanpour, Mohammad Keyanpour
Summary: The algorithm presented is an arc-search infeasible interior-point algorithm utilizing Nesterov-Todd search directions and based on the negative infinity neighborhood of the central path. It searches for an approximate solution of the problem along the ellipsoidal approximation of the entire central path with iteration complexity bound O(n(3/2) log epsilon(-1)). Numerical results demonstrate the efficiency and promise of the algorithm.
NUMERICAL ALGORITHMS
(2021)
