Description and Optimum Design of Fuzzy Mechanical Systems

1987 ◽  
Vol 109 (1) ◽  
pp. 126-132 ◽  
Author(s):  
S. S. Rao
Keyword(s):  
Optimum Design ◽  
Fuzzy Set ◽  
Mechanical Systems ◽  
Fuzzy Optimization ◽  
Optimization Techniques ◽  
Fuzzy Constraints ◽  
Constraint Set ◽  
Fuzzy Constraint ◽  
Optimum Solution ◽  
Set Of Points

Much of the decision-making in the real world takes place in an environment in which the goals, the constraints and the consequences of possible actions are not known precisely. To deal quantitatively with imprecision, the tools of fuzzy set theory can be used. This paper deals with the description and optimization of mechanical systems containing fuzzy information. The fuzzy constraints define a fuzzy feasible domain in the design space and hence the fuzzy optimum solution will be defined by a fuzzy set of points. In this work, two methods are presented for solving a fuzzy optimization problem using ordinary optimization techniques. The optimum design of a four-bar function generating mechanism with fuzzy objective function and fuzzy constraint set is considered to illustrate the procedures.

The Fuzzy Reliability Optimum Design of Offshore Jacket Platforms

2002 ◽  
Author(s):  
Gangjun Zhai ◽  
Haigui Kang ◽  
Facong Xu
Keyword(s):  
Optimum Design ◽  
Structural Reliability ◽  
Fuzzy Optimization ◽  
Optimization Method ◽  
Optimum Level ◽  
Design Variables ◽  
Fuzzy Constraint ◽  
Cut Set ◽  
Optimum Model ◽  
Optimum Solution

In consideration of the fuzzy constraint boundary and through analysis of structural reliability, a model of structural fuzzy optimum design is established based on reliability for offshore jacket platforms. According to the characteristics of offshore jacket platforms, the tolerance coefficient of the constraint boundary is determined with the fuzzy optimization method. The optimum level cut set λ*, which is the intersection of the fuzzy constraint set and fuzzy objective set, is determined with the bound search method, and then the fuzzy optimum solution of fuzzy optimization problem is obtained. The center offshore platform SZ36-1 is designed with the fuzzy optimum model based on reliability above; the results are compared with those from deterministic optimum design and fuzzy optimum design. The tendency of design variables and its reasons in the above three methods are analyzed. The results of an example show that the fuzzy optimum design based on reliability is stable and reliable.

scholarly journals Combination of anti-optimization and fuzzy-set-based analysis for structural optimization under uncertainty

1998 ◽  
Vol 4 (3) ◽  
pp. 187-200 ◽  
Author(s):  
J. Fang ◽  
S. M. Smith ◽  
I. Elishakoff
Keyword(s):  
Structural Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Fuzzy Set ◽  
Optimization Problem ◽  
Fuzzy Optimization ◽  
Optimization Methods ◽  
Optimization Under Uncertainty ◽  
Optimization Process ◽  
Membership Functions

An approach to the optimum design of structures, in which uncertainties with a fuzzy nature in the magnitude of the loads are considered, is proposed in this study. The optimization process under fuzzy loads is transformed into a fuzzy optimization problem based on the notion of Werners' maximizing set by defining membership functions of the objective function and constraints. In this paper, Werner's maximizing set is defined using the results obtained by first conducting an optimization through anti-optimization modeling of the uncertain loads. An example of a ten-bar truss is used to illustrate the present optimization process. The results are compared with those yielded by other optimization methods.

A Study on Optimum Design Using Fuzzy Numbers As Design Variables

1995 ◽  
Author(s):  
Masao Arakawa ◽  
Hiroshi Yamakawa
Keyword(s):  
Fuzzy Sets ◽  
Optimum Design ◽  
Fuzzy Numbers ◽  
Fuzzy Optimization ◽  
Design Parameters ◽  
Numerical Examples ◽  
Design Variables ◽  
Conventional Methods

Abstract In this study, we summerize the method of fuzzy optimization using fuzzy numbers as design variables. In order to detect flaw in fuzzy calculation, we use LR-fuzzy numbers, which is known as its simplicity in calculation. We also use simple fuzzy numbers’ operations, which was proposed in the previous papers. The proposed method has unique characteristics that we can obtain fuzzy sets in design variables (results of the design) directly from single numerical optimizing process. Which takes a large number of numerical optimizing processes when we try to obtain similar results in the conventional methods. In the numerical examples, we compare the proposed method with several other methods taking imprecision in design parameters into account, and demonstrate the effectiveness of the proposed method.

On Considering Constraints of Different Importance in Fuzzy Constraint Satisfaction Problems

1998 ◽  
Vol 06 (05) ◽  
pp. 489-501 ◽  
Author(s):  
Vicenç Torra I Reventós
Keyword(s):  
Constraint Satisfaction ◽  
Real World ◽  
Constraint Satisfaction Problems ◽  
Human Reasoning ◽  
Fuzzy Constraints ◽  
A Value ◽  
Equal Importance ◽  
Real World Applications ◽  
Fuzzy Constraint ◽  
Fuzzy Constraint Satisfaction

Several real-world applications (e.g., scheduling, configuration, …) can be formulated as Constraint Satisfaction Problems (CSP). In these cases, a set of variables have to be settled to a value with the requirement that they satisfy a set of constraints. Classical CSPs are defined only by means of crisp (Boolean) constraints. However, as sometimes Boolean constraints are too strict in relation to human reasoning, fuzzy constraints were introduced. When fuzzy constraints are considered, human reasoning usually performs some compensation between alternatives. Thus other operators than t-norms are advisable. Besides of that, not all constraints can be considered with equal importance. In this paper we show that the WOWA operator can consider both aspects: compensation between constraints and constraints of different importance.

scholarly journals Convexity of hesitant fuzzy sets based on aggregation functions

2020 ◽  
pp. 45-45
Author(s):  
Pedro Huidobro ◽  
Pedro Alonso ◽  
Vladimír Janis ◽  
Susana Montes
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Optimization ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
Geometric Properties ◽  
Aggregation Functions ◽  
Definition Of

Convexity is one of the most important geometric properties of sets and a useful concept in many fields of mathematics, like optimization. As there are also important applications making use of fuzzy optimization, it is obvious that the studies of convexity are also frequent. In this paper we have extended the notion of convexity for hesitant fuzzy sets in order to fulfill some necessary properties. Namely, we have found an appropriate definition of convexity for hesitant fuzzy sets on any ordered universe based on aggregation functions such that it is compatible with the intersection, that is, the intersection of two convex hesitant fuzzy sets is a convex hesitant fuzzy set and it fulfills the cut worthy property.

Application of Fuzzy Logic and Fuzzy Optimization Techniques in Medical Image Processing

Biometrics ◽  
2017 ◽  
pp. 907-932 ◽  
Author(s):  
Niladri Sekhar Datta ◽  
Himadri Sekhar Dutta ◽  
Koushik Majumder
Keyword(s):  
Mathematical Model ◽  
Fuzzy Logic ◽  
Optimization Technique ◽  
Fuzzy Optimization ◽  
Fuzzy Model ◽  
Optimization Method ◽  
Fuzzy Modeling ◽  
Optimization Techniques ◽  
Fuzzy Variables ◽  
Truth Value

Fuzzy logic deals with approximate rather than fixed and exact reasoning. Fuzzy variables may have a truth value that ranges in degree between 0 and 1; extended to handle the concept of partial truth where the truth value may range between completely true or completely false. This computational logic uses truth degrees as a mathematical model of the vagueness phenomenon while probability is a mathematical model of ignorance. A huge number of complex problems may be solve using Fuzzy logic specifically Fuzzy modeling and optimization method. Fuzzy modeling is the understanding of the problem and analysis of the Fuzzy information where the Fuzzy optimization solves Fuzzy model optimally using optimization techniques via membership functions. In this research article authors describe the Fuzzy rules and its application and the different types of well known problems solved by the Fuzzy optimization technique.

Towards a Dynamic Font Respecting the Arabic Calligraphy

2011 ◽  
pp. 359-388
Author(s):  
Abdelouahad Bayar ◽  
Khalid Sami
Keyword(s):  
Mathematical Model ◽  
Optimization Techniques ◽  
Plane Curves ◽  
Time Processing ◽  
Cpu Time ◽  
Dynamic Character ◽  
Context Dependent ◽  
Set Of Points ◽  
Arabic Calligraphy

To justify texts, Arabic calligraphers use to stretch some letters with small flowing curves; the kashida instead of inserting blanks among words. Of course, such stretchings are context dependent. An adequate tool to support such writing may be based on a continuous mathematical model. The model has to take into account the motion of the qalam. The characters may be represented as outlines. Among the curves composing the characters outlines, some intersections are to be determined dynamically. In the Naskh style, the qalam‘s head behaves as a rigid rectangle in motion with a constant inclination. To determine the curves delimiting the set of points to shade when writing, we have to find out a mathematical way to compare plane curves. Moreover, as the PostScript procedure to produce a dynamic character, should be repeated whenever the letter is to draw, the development of a font supporting a continuous stretching model, allowing stretchable letters with no overlapping outlines, without optimization would be of a high cost in CPU time. In this chapter, some stretching models are given and discussed. A method to compare curves is presented. It allows the determination of the character encoding with eventually overlapping outlines. Then a way to approximate the curves intersection coefficients is given. This is enough to remove overlapping outlines. Some evaluations in time processing to confirm the adopted optimization techniques are also exposed.

Fuzzy Optimization Design on Stranded Wire Helical Spring of High-Frequency Vibration Sieve

2010 ◽  
Vol 97-101 ◽  
pp. 4066-4070 ◽  
Author(s):  
Xiao Xin Gong ◽  
Yan Nian Rui ◽  
Ying Ping He
Keyword(s):  
High Frequency ◽  
Optimization Design ◽  
Fuzzy Theory ◽  
Fuzzy Optimization ◽  
Helical Spring ◽  
High Frequency Vibration ◽  
Vibration Resistance ◽  
Design Variables ◽  
The Common ◽  
Optimum Solution

When the common cylindrical helical spring is used in high-frequency vibration sieve for slime dewatering, there are many problems such as poor vibration resistance, easy happening fatigue fracture, etc. In order to solve these problems, this paper uses the stranded wire helical spring as a support instead, and applies fuzzy theory method to get the optimization design. By selecting the design variables correlated with spring and determining the objective function together with the constraint conditions, the fuzzy optimization mathematical model is built and the optimum solution is obtained so as to achieve the perfect results of optimization.

Three-dimensional optimum design of the cooling lines of injection moulds based on boundary element design sensitivity analysis

2002 ◽  
Vol 216 (7) ◽  
pp. 1067-1071 ◽  
Author(s):  
H Zhou ◽  
D Li ◽  
S Cui
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Boundary Element ◽  
Optimum Design ◽  
Three Dimensional ◽  
Design Sensitivity ◽  
Boundary Integral ◽  
Optimization Techniques ◽  
Design Sensitivity Analysis ◽  
Design Variables

A three-dimensional numerical simulation using the boundary element method is proposed, which can predict the cavity temperature distributions in the cooling stage of injection moulding. Then, choosing the radii and positions of cooling lines as design variables, the boundary integral sensitivity formulations are deduced. For the optimum design of cooling lines, the squared difference between the objective temperature and the temperature of the cavity is taken as the objective function. Based on the optimization techniques with design sensitivity analysis, an iterative algorithm to reach the minimum value of the objective function is introduced, which leads to the optimum design of cooling lines at the same time.

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