scholarly journals Privacy-Preserving Two-Party Computation of Parameters of a Fuzzy Linear Regression

2021 ◽  
pp. 11-19
Author(s):  
Elena Volkova ◽  
◽  
Vladimir Gisin ◽  
Keyword(s):  
Linear Programming ◽  
Linear Regression ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Observation Data ◽  
Fuzzy Linear Regression ◽  
Explanatory Variables ◽  
Common Criterion

Purpose: describe two-party computation of fuzzy linear regression with horizontal partitioning of data, while maintaining data confidentiality. Methods: the computation is designed using a transformational approach. The optimization problems of each of the two participants are transformed and combined into a common problem. The solution to this problem can be found by one of the participants. Results: A protocol is proposed that allows two users to obtain a fuzzy linear regression model based on the combined data. Each of the users has a set of data about the results of observations, containing the values of the explanatory variables and the values of the response variable. The data structure is shared: both users use the same set of explanatory variables and a common criterion. Regression coefficients are searched for as symmetric triangular fuzzy numbers by solving the corresponding linear programming problem. It is assumed that both users are semihonest (honest but curious, or passive and curious), i.e. they execute the protocol, but can try to extract information about the source data of the partner by applying arbitrary processing methods to the received data that are not provided for by the protocol. The protocol describes the transformed linear programming problem. The solution of this problem can be found by one of the users. The number of observations of each user is known to both users. The observation data remains confidential. The correctness of the protocol is proved and its security is justified. Keywords: fuzzy numbers, collaborative solution of a linear programming problem, two-way computation, transformational approach, cloud computing, federated machine learning.

scholarly journals A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE

2007 ◽  
Vol 24 (04) ◽  
pp. 557-573 ◽  
Author(s):  
M. ZANGIABADI ◽  
H. R. MALEKI
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Multiobjective Linear Programming ◽  
Programming Technique ◽  
Linear Programming Problems ◽  
Linear Programming Technique ◽  
Fuzzy Parameters

In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, we propose several theorems which are used to obtain optimal solutions of linear programming problems with fuzzy parameters. Finally some examples are given for illustrating the proposed method of solving linear programming problem with fuzzy parameters.

scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers

2016 ◽  
Vol 33 (06) ◽  
pp. 1650047 ◽  
Author(s):  
Sanjiv Kumar ◽  
Ritika Chopra ◽  
Ratnesh R. Saxena
Keyword(s):  
Linear Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Linear Programming ◽  
Matrix Game ◽  
Matrix Games ◽  
Trapezoidal Fuzzy Numbers ◽  
Fast Approach ◽  
The Matrix

The aim of this paper is to develop an effective method for solving matrix game with payoffs of trapezoidal fuzzy numbers (TrFNs). The method always assures that players’ gain-floor and loss-ceiling have a common TrFN-type fuzzy value and hereby any matrix game with payoffs of TrFNs has a TrFN-type fuzzy value. The matrix game is first converted to a fuzzy linear programming problem, which is converted to three different optimization problems, which are then solved to get the optimum value of the game. The proposed method has an edge over other method as this focuses only on matrix games with payoff element as symmetric trapezoidal fuzzy number, which might not always be the case. A numerical example is given to illustrate the method.

scholarly journals Ranking Function Application for Optimal Solution of Fractional programming problem

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Rasha Jalal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Ranking Function ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Linear Programming Problems

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

scholarly journals Calculating Fuzzy Inverse Matrix Using Linear Programming Problem: An Improved Approach

2021 ◽  
pp. 983-996
Author(s):  
Fatemeh Babakordi ◽  
Nemat Allah Taghi-Nezhad
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Equation System ◽  
Matrix Inverse ◽  
Fuzzy Matrix ◽  
Linear Equation System ◽  
The Matrix ◽  
Left And Right

Calculating the matrix inverse is a key point in solving linear equation system, which involves complex calculations, particularly  when the matrix elements are  (Left and Right) fuzzy numbers. In this paper, first, the method of Kaur and Kumar for calculating the matrix inverse is reviewed, and its disadvantages are discussed. Then, a new method is proposed to determine the inverse of  fuzzy matrix based on linear programming problem. It is demonstrated that the proposed method is capable of overcoming the shortcomings of the previous matrix inverse. Numerical examples are utilized to verify the performance and applicability of the proposed method.

A new approach to solve fully intuitionistic fuzzy linear programming problem with unrestricted decision variables

2021 ◽  
pp. 1-14
Author(s):  
Manisha Malik ◽  
S. K. Gupta ◽  
I. Ahmad
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fuzzy Set ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Planning Problem ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Decision Variables

In many real-world problems, one may encounter uncertainty in the input data. The fuzzy set theory fits well to handle such situations. However, it is not always possible to determine with full satisfaction the membership and non-membership degrees associated with an element of the fuzzy set. The intuitionistic fuzzy sets play a key role in dealing with the hesitation factor along-with the uncertainity involved in the problem and hence, provides more flexibility in the decision-making process. In this article, we introduce a new ordering on the set of intuitionistic fuzzy numbers and propose a simple approach for solving the fully intuitionistic fuzzy linear programming problems with mixed constraints and unrestricted variables where the parameters and decision variables of the problem are represented by intuitionistic fuzzy numbers. The proposed method converts the problem into a crisp non-linear programming problem and further finds the intuitionistic fuzzy optimal solution to the problem. Some of the key significance of the proposed study are also pointed out along-with the limitations of the existing studies. The approach is illustrated step-by-step with the help of a numerical example and further, a production planning problem is also demonstrated to show the applicability of the study in practical situations. Finally, the efficiency of the proposed algorithm is analyzed with the existing studies based on various computational parameters.

scholarly journals Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Haifang Cheng ◽  
Weilai Huang ◽  
Jianhu Cai
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Equality Constraints ◽  
Compromise Programming ◽  
Fuzzy Linear Programming ◽  
Programming Approach ◽  
Optimal Value ◽  
Fuzzy Equality

In the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a method for solving this FFLP problem is also proposed. We first transform the fuzzy equality constraints into the crisp inequality ones using the measure of the similarity, which is interpreted as the feasibility degree of constrains, and then transform the fuzzy objective into two crisp objectives by considering expected value and uncertainty of fuzzy objective. Since the feasibility degree of constrains is in conflict with the optimal value of objective function, we finally construct an auxiliary three-objective linear programming problem, which is solved through a compromise programming approach, to solve the initial FFLP problem. To illustrate the proposed method, two numerical examples are solved.

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