A Fuzzy Dynamic Programming Approach for Mixed-Discrete Multistage Decision Processes

2004 ◽  
Author(s):  
Ying Xiong ◽  
Singiresu S. Rao
Keyword(s):  
Decision Making ◽  
Dynamic Programming ◽  
Design Space ◽  
Optimization Problems ◽  
Real Life ◽  
Optimal Solution ◽  
Dynamic Programming Method ◽  
Programming Approach ◽  
Fuzzy Goal ◽  
Fuzzy State

Many engineering optimization problems can be considered as multistage decision-making problems. If the system involves uncertainty in the form of linguistic parameters and vague data, a fuzzy approach is to be used for its description. The solution of such problems can be accomplished through fuzzy dynamic programming. However, most of the existing fuzzy dynamic programming algorithms can not deal with mixed-discrete design variables in the optimization of mechanical systems containing fuzzy information. They often assumed that a fuzzy goal is imposed only on the final state for simplicity, the values of fuzzy goal and other parameters need to be predefined, and an optimal solution is obtained in the continuous design space only. To better reflect the nature of uncertainties present in real-life optimization problems, a mixed-discrete fuzzy dynamic programming (MDFDP) approach is proposed in this work for solving multistage decision-making problems in mixed-discrete design space with a fuzzy goal and a fuzzy state imposed on each stage. The feasibility and versatility of the proposed method are illustrated by considering the design of a four-bar truss. To the authors’ knowledge, this work represents the first fuzzy dynamic programming method reported in the literature for dealing with mixed-discrete optimization problems.

A Fuzzy Dynamic Programming Approach for the Mixed-Discrete Optimization of Mechanical Systems

2004 ◽  
Vol 127 (6) ◽  
pp. 1088-1099 ◽  
Author(s):  
Ying Xiong ◽  
Singiresu S. Rao
Keyword(s):  
Decision Making ◽  
Dynamic Programming ◽  
Discrete Optimization ◽  
Design Space ◽  
Optimization Problems ◽  
Mechanical Systems ◽  
Real Life ◽  
Programming Approach ◽  
Fuzzy Goal ◽  
Fuzzy State

Many engineering optimization problems can be considered as multistage decision-making problems. If the system involves uncertainty in the form of linguistic parameters and vague data, a fuzzy approach is to be used for its description. The solution of such problems can be accomplished through fuzzy dynamic programming. However, most of the existing fuzzy dynamic programming algorithms cannot deal with mixed-discrete design variables in the optimization of mechanical systems containing fuzzy information. They often assumed that a fuzzy goal is imposed only on the final state for simplicity, the values of fuzzy goal and other parameters need to be predefined, and an optimal solution is obtained in the continuous design space only. To better reflect the nature of uncertainties present in real-life optimization problems, a mixed-discrete fuzzy dynamic programming (MDFDP) approach is proposed in this work for solving multistage decision-making problems in mixed-discrete design space with a fuzzy goal and a fuzzy state imposed on each stage. The method can also be extended to solve general mixed-discrete fuzzy nonlinear programming problems if their corresponding crisp problems can be solved using dynamic programming approaches. The feasibility and versatility of the proposed method are illustrated by considering the design of a four-bar truss and the reliability-based optimization of a gearbox. To the authors’ knowledge, this work represents the first fuzzy dynamic programming method reported in the literature for dealing with mixed-discrete optimization problems.

scholarly journals Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems

2021 ◽  
Author(s):  
Firoz Ahmad
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Practical Implication ◽  
Real Life ◽  
Future Research ◽  
Programming Approach ◽  
Solution Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiobjective Optimization Problems

AbstractThis study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.

scholarly journals ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1456
Author(s):  
Stefka Fidanova ◽  
Krassimir Todorov Atanassov
Keyword(s):  
Decision Making ◽  
Knapsack Problem ◽  
Propositional Logic ◽  
Optimization Problems ◽  
Real Life ◽  
Combinatorial Optimization Problems ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Multiple Constraint

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

An Optimal Power Management Strategy for Hydraulic Hybrid Output Coupled Power-Split Transmission

2009 ◽  
Author(s):  
Rajneesh Kumar ◽  
Monika Ivantysynova
Keyword(s):  
Dynamic Programming ◽  
Power Management ◽  
Control Strategy ◽  
Management Strategy ◽  
Optimal Solution ◽  
Programming Approach ◽  
Power Management Strategy ◽  
Optimal Power ◽  
Power Split ◽  
Instantaneous Optimization

Power-split drive represents a class of Continuously Variable Transmission (CVT) that combines the convenience of CVT with the high overall transmission efficiency. In its hybrid configuration, a high pressure accumulator is used to capture the braking energy that is regenerated to aid the engine power during the next propulsion event. Output coupled power split drives are particularly suited for small and medium duty vehicle applications. In this work, optimal power management strategy has been designed based on Dynamic Programming approach. Although the control strategy obtained by Dynamic Programming is non-causal, it represents the benchmark solution against which other implementable power management schemes can be compared. Another control strategy based on instantaneous optimization is also discussed where a given cost function is minimized at every instant. It results in a sub-optimal solution that is practical and implementable. Finally, Dynamic Programming results are utilized to discuss the possible improvements that can be made to the instantaneous optimization based control strategy.

scholarly journals Parking Site Selection for Light Rail Stations in Muaeng District, Khon Kaen, Thailand

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1055
Author(s):  
Narueset Prasertsri ◽  
Satith Sangpradid
Keyword(s):  
Decision Making ◽  
Site Selection ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Fuzzy Topsis ◽  
Geographical Information ◽  
Light Rail ◽  
Analytic Hierarchy ◽  
North East ◽  
Khon Kaen

Khon Kaen District is in the central, north-east part of Thailand and is being developed to handle the country’s growth. Khon Kaen District is undertaking the project of building a light rail as a facility for the people. Consequently, one of the problems is ensuring adequate parking for people using the light rail service. In general, the symmetry concept naturally used in decision making to finding an optimal solution for decision and optimization problems. In this paper, multi-criteria decision analysis (MCDA) and multi-objective decision making (MODM) were used to solve the parking site selection problem, which made the decision easier. This paper proposed an analytic hierarchy process (AHP) technique, combined with the geographical information system (GIS), to evaluate the weight of the criteria used in the analysis and find potential parking solutions. Furthermore, this paper proposed the application of a linguistic technique with fuzzy TOPSIS methods to analyze the appropriateness of parking site selections from potential candidates to support use of the light rail. The results of the MCDA show that the most suitable parking lot location is along the light rail and closest to the business area. The results of the fuzzy TOPSIS method, both positive and negative ideal decisions, can help inform decision makers in selecting which candidate site is optimal for parking.

Fuzzy Linear Programming: A Modern Tool for Decision Making

2012 ◽  
Author(s):  
Pandian M. Vasant ◽  
R. Nagarajan ◽  
Sazali Yaacob
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Production Planning ◽  
Membership Function ◽  
Industrial Production ◽  
Real Life ◽  
Fuzzy Linear Programming ◽  
Programming Approach ◽  
Modern Trend ◽  
Application Problem

The modern trend in industrial application problem deserves modeling of all relevant vague or fuzzy information involved in a real decision making problem. In the first part of the paper, some explanations on tri partite fuzzy linear programming approach and its importance have been given. In the second part, the usefulness of the proposed S-curve membership function is established using a real life industrial production planning of a chocolate manufacturing unit. The unit produces 8 products using 8 raw materials, mixed in various proportions by 9 different processes under 29 constraints. A solution to this problem establishes the usefulness of the suggested membership function for decision making in industrial production planning. Key words: Fuzzy linear programming, Satisfactory solution; Decision maker; Implementer; Analyst; Fuzzy constraint; Vagueness.

WEIGHTED ADDITIVE MODELS FOR SOLVING FUZZY GOAL PROGRAMMING PROBLEMS

2008 ◽  
Vol 25 (05) ◽  
pp. 715-733 ◽  
Author(s):  
M. A. YAGHOOBI ◽  
D. F. JONES ◽  
M. TAMIZ
Keyword(s):  
Decision Making ◽  
Goal Programming ◽  
Real Life ◽  
Additive Model ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Fuzzy Goal Programming ◽  
Additive Models ◽  
New Model ◽  
Fuzzy Goal

Weighted additive models are well known for dealing with multiple criteria decision making problems. Fuzzy goal programming is a branch of multiple criteria decision making which has been applied to solve real life problems. Several weighted additive models are introduced to handle fuzzy goal programming problems. These models are based on two approaches in fuzzy goal programming namely goal programming and fuzzy programming techniques. However, some of these models are not able to solve all kinds of fuzzy goal programming problems and some of them that appear in current literature suffer from a lack of precision in their formulations. This paper focuses on weighed additive models for fuzzy goal programming. It explains the oversights within some of them and proposes the necessary corrections. A new improved weighted additive model for solving fuzzy goal programming problems is introduced. The relationships between the new model and some of the existing models are discussed and proved. A numerical example is given to demonstrate the validity and strengths of the new model.

scholarly journals Fuzzy linear mathematical programming in agriculture

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 72-76
Author(s):  
MA Lone ◽  
MS Puktha ◽  
SA Mir
Keyword(s):  
Decision Making ◽  
Mathematical Programming ◽  
Agricultural Land ◽  
Optimal Allocation ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Programming Approach ◽  
Fuzzy Mathematical Programming ◽  
Mathematical Programming Approach ◽  
Land Cultivation

In this paper we present a Fuzzy linear Mathematical programming approach for optimal allocation of land under cultivation. Fuzzy Mathematical programming approach is more realistic and flexible optimal solution for the agricultural land cultivation problem. In this study we have discussed how to deal with decision making problems that are described by Fuzzy linear programming (Flp) models and formulated with the elements of uncertainty. This form of approximation can be convenient and sufficient for making good decisions. BIBECHANA 13 (2016) 72-76

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