Fuzzy Relation Bilevel Optimization Model in the Wireless Communication Station System

Jianjun Qiu,Huanbin Xue,Guanrong Li,Xiaopeng Yang

doi:10.1109/access.2020.2984095

Abstract

Fuzzy Relation Bilevel Optimization Model in the Wireless Communication Station System

Highlights

MINIMUM MAX-NORM SOLUTION MATRIX AND THE COMPLETE OPTIMAL SOLUTION SET OF PROBLEM (3) we propose the concept of minimum max-norm solution matrix and construct the set of all minimum max-norm matrix solutions (denoted by Xmmns(A, b) later), based on which the complete optimal solution set of Problem (3) (denoted by X1(A, b)) will be further described
For reducing the intensity of electromagnetic radiation as well as the operation cost of base stations on the management of the wireless communication station system, we investigate a bilevel programming problem subject to max-product fuzzy relation inequalities
In this paper, in order to find a better managerial optimal solutions on the management model of the wireless communication station system, we investigate bilevel programming problems constrained by max-product fuzzy relation inequalities

Summary

INTRODUCTION

Motivated by the works of Guu et al [33], [34], we aim to investigate the bilevel optimization problem subject to max-product fuzzy relation inequalities, with application in the wireless communication station system. MINIMAL SOLUTION MATRIX AND YANG’S METHOD FOR THE FIRST LEVEL PROBLEM (3) we review some results on the optimal solution of Problem (3), which could be found in [16]. A. YANG’S METHOD FOR SOLVING PROBLEM (3) BASED ON THE MINIMAL SOLUTION MATRIX For any x = (x1, x2, · · · , xn) ∈ [0, 1]n, we always denote x ∞= max {xj} = x1 ∨ x2 ∨ · · · ∨ xn, 1≤j≤n in this paper, where x ∞ is the max-norm. MINIMUM MAX-NORM SOLUTION MATRIX AND THE COMPLETE OPTIMAL SOLUTION SET OF PROBLEM (3) we propose the concept of minimum max-norm solution matrix and construct the set of all minimum max-norm matrix solutions (denoted by Xmmns(A, b) later), based on which the complete optimal solution set of Problem (3) (denoted by X1(A, b)) will be further described

MINIMUM MAX-NORM SOLUTION MATRIX Theorem 4

NUMERICAL EXAMPLE

CONCLUSION