scholarly journals A Fuzzy Interactive BI-objective Model for SVM to Identify the Best Compromise Solution for Measuring the Degree of Infection With Corona Virus Disease (Covid-19)

2021 ◽  
Vol 11 (1) ◽  
pp. 13-22
Author(s):  
Mohammed Zakaria Moustafa ◽  
Hassan Mahmoud Elragal ◽  
Mohammed Rizk Mohammed ◽  
Hatem Awad Khater ◽  
Hager Ali Yahia
Keyword(s):  
Quadratic Programming ◽  
Programming Model ◽  
Virus Disease ◽  
Fuzzy Model ◽  
Efficient Solutions ◽  
Support Vector ◽  
Compromise Solution ◽  
Weighting Method ◽  
Quadratic Programming Problems ◽  
Objective Model

A support vector machine (SVM) learns the decision surface from two different classes of the input points. In several applications, some of the input points are misclassified and each is not fully allocated to either of these two groups. In this paper a bi-objective quadratic programming model with fuzzy parameters is utilized and different feature quality measures are optimized simultaneously. An α-cut is defined to transform the fuzzy model to a family of classical bi-objective quadratic programming problems. The weighting method is used to optimize each of these problems. For the proposed fuzzy bi-objective quadratic programming model, a major contribution will be added by obtaining different effective support vectors due to changes in weighting values. The experimental results, show the effectiveness of the α-cut with the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions. The main contribution of this paper includes constructing a utility function for measuring the degree of infection with coronavirus disease (COVID-19).

scholarly journals A Fuzzy BI-Objective Model for SVM with an Interactive Procedure to Identify the Best Compromise Solution

2020 ◽  
Author(s):  
Hager Ali Yahia ◽  
Mohammed Zakaria Moustafa ◽  
Mohammed Rizk Mohammed ◽  
Hatem Awad Khater
Keyword(s):  
Quadratic Programming ◽  
Programming Model ◽  
Fuzzy Model ◽  
Efficient Solutions ◽  
Support Vector ◽  
Compromise Solution ◽  
Weighting Method ◽  
Quadratic Programming Problems ◽  
Objective Model ◽  
Fuzzy Parameters

A support vector machine (SVM) learns the decision surface from two different classes of the input points. In many applications, there are misclassifications in some of the input points and each is not fully assigned to one of these two classes. In this paper a bi-objective quadratic programming model with fuzzy parameters is utilized and different feature quality measures are optimized simultaneously. An α-cut is defined to transform the fuzzy model to a family of classical bi-objective quadratic programming problems. The weighting method is used to optimize each of these problems. An important contribution will be added for the proposed fuzzy bi-objective quadratic programming model by getting different efficient support vectors due to changing the weighting values. The experimental results show the effectiveness of the α-cut with the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions.

A MULTI-CLASS SUPPORT VECTOR MACHINE: THEORY AND MODEL

2013 ◽  
Vol 12 (06) ◽  
pp. 1175-1199 ◽  
Author(s):  
MINGHE SUN
Keyword(s):  
Support Vector Machine ◽  
Quadratic Programming ◽  
Programming Model ◽  
Inner Product ◽  
High Dimensional ◽  
Support Vector ◽  
Test Problems ◽  
Discriminant Functions ◽  
Input Space ◽  
Feature Spaces

A multi-class support vector machine (M-SVM) is developed, its dual is derived, its dual is mapped to high dimensional feature spaces using inner product kernels, and its performance is tested. The M-SVM is formulated as a quadratic programming model. Its dual, also a quadratic programming model, is very elegant and is easier to solve than the primal. The discriminant functions can be directly constructed from the dual solution. By using inner product kernels, the M-SVM can be built and nonlinear discriminant functions can be constructed in high dimensional feature spaces without carrying out the mappings from the input space to the feature spaces. The size of the dual, measured by the number of variables and constraints, is independent of the dimension of the input space and stays the same whether the M-SVM is built in the input space or in a feature space. Compared to other models published in the literature, this M-SVM is equally or more effective. An example is presented to demonstrate the dual formulation and solution in feature spaces. Very good results were obtained on benchmark test problems from the literature.

User and Operator Perspectives in Public Transport Timetable Synchronization Design

2017 ◽  
Vol 2667 (1) ◽  
pp. 154-163
Author(s):  
Tao Liu ◽  
Avishai (Avi) Ceder
Keyword(s):  
Public Transport ◽  
Traffic Congestion ◽  
Large Scale ◽  
Systems Approach ◽  
Programming Model ◽  
Efficient Solutions ◽  
Linear Constraints ◽  
Nonlinear Integer Programming ◽  
Modeling Framework ◽  
Objective Model

Increased traffic congestion and the adverse environmental effect of private cars have resulted in an increasingly pressing need for an integrated public transport (PT) system that is more attractive than private car use. The intelligent PT timetable synchronization design is one way to improve the integration and service quality of a PT system with increased connectivity, synchronization, and attractiveness toward far more user-oriented, system-optimal, smart, and sustainable travel. This paper proposes a new multicriteria optimization modeling framework with a systems approach for the PT timetable synchronization design problem. A new bi-objective model is proposed; it takes PT user and operator interests into account. The nature of the overall mathematical formulations of the new model is bi-objective nonlinear integer programming with linear constraints. On the basis of the characteristics of the model, a novel deficit function (DF)–based sequential search method is proposed to solve the problem so as to obtain Pareto-efficient solutions. The visual nature of the proposed DF and the two-dimensional fleet-cost space graphical techniques can facilitate the decision-making process of PT schedulers for finding a desired solution. Numerical results from a small PT network demonstrate that the proposed mathematical programming model and solution method are effective in practice and have the potential to be applied in large-scale and realistic networks.

scholarly journals A mixed quadratic programming model for a robust support vector machine

2021 ◽  
Vol 8 (1) ◽  
pp. 27-36
Author(s):  
Raquel Serna-Diaz ◽  
Raimundo Santos Leite ◽  
Paulo J. S. Silva
Keyword(s):  
Support Vector Machine ◽  
Quadratic Programming ◽  
Programming Model ◽  
Support Vector

Methodology for Solving Multi-Objective Quadratic Programming Problems in a Fuzzy Stochastic Environment

2019 ◽  
pp. 177-217
Keyword(s):  
Quadratic Programming ◽  
Deterministic Model ◽  
Programming Model ◽  
Probability Distributions ◽  
Fuzzy Programming ◽  
Chance Constraints ◽  
Membership Functions ◽  
Quadratic Programming Problems ◽  
Constrained Programming ◽  
Fuzzy Programming Model

This chapter presents two methodologies for solving quadratic programming problems with multiple objectives under fuzzy stochastic environments. The right side parameters of the chance constraints of both the models are chosen as fuzzy random variables (FRVs) following different probability distributions. Like the previous chapters, chance constrained programming (CCP) methodology is employed to the fuzzy chance constraints to develop fuzzy programming model. In the first model, cut of fuzzy sets and fuzzy partial order relations are incorporated to the fuzzy programming model to develop an equivalent deterministic model. For the second model, defuzzification method of fuzzy numbers (FNs), which are presented in Chapter 2, are taken into consideration to generate equivalent quadratic programming model in a crisp environment. As the objective functions are quadratic in nature, it is easy to understand that the membership functions obtained through methodological development process are also quadratic in nature. To linearize the quadratic membership functions, linearization techniques are employed in this chapter. Finally, for achieving the maximum degree of each of the membership goals of the objectives, a fuzzy goal programming (FGP) approach is developed for the linearized membership goals and solved by minimizing under-deviational variables and satisfying modified system constraints in fuzzy stochastic decision-making environments. To illustrate the acceptability of the developed methodology presented in this chapter, some numerical examples are included.

Method Based on the Minimum Deviation for Multi-Attribute Decision-Making and its Application

2014 ◽  
Vol 989-994 ◽  
pp. 2547-2550
Author(s):  
Hong An Zhou
Keyword(s):  
Decision Making ◽  
Quadratic Programming ◽  
Programming Model ◽  
Existence Of Solution ◽  
Weighting Method ◽  
Preference Information ◽  
Minimum Deviation ◽  
Attribute Weights ◽  
Subjective Preference ◽  
Multi Attribute Decision Making

The multi-attribute decision making (MADM) problem is studied, in which the information about attribute weights is unknown and the decision maker (DM) has avail preference information on alternatives. Firstly, a quadratic programming model based on the minimum deviation between the objective decision-making information and the subjective preference information on alternatives is established. Secondly, the existence of solution to the model is proved and the calculated formula of the attribute weights are given, thus the overall values of the alternatives are gained by using the additive weighting method. Based on these values, the selecting the best on alternatives is processed. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

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