Fuzzy relation inequality-based consistency of the wireless communication basic-station system considering the non-working state stations

• Published in: Soft computing (Berlin, Germany) Vol. 26; no. 11; pp. 5131 - 5142
• Main Authors: Yang, Xiaopeng, Li, Jianzhong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2022
• Subjects: Artificial Intelligence; Computational Intelligence; Control; Engineering; Fuzzy Systems and Their Mathematics; Mathematical Logic and Foundations; Mechatronics; Robotics; Wireless communication basic-station system; Fuzzy relation equation; System consistency; Fuzzy relation inequality; Max-product composition
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-022-07076-x

Requirements of the electromagnetic intensities of radio waves in a wireless communication basic-station (WCBS) system could be reduced into a system of fuzzy relation inequalities with max-product composition. In order to check the consistency of a WCBS system with some non-working basic stations, we first introduce the consistency checking method for a WCBS system without any non-working basic station. An index set approach is designed for the consistency checking, with some numerical examples illustrating the effectiveness of our proposed approach. Moreover, in order to reduce the maintenance cost of the basic stations, we further discuss the minimum number of working stations, ensuring that the WCBS system is consistent. The corresponding minimization problem is equivalently converted into a 0-1 integer programming problem, which could be directly solved by some common softwares. The major contribution of this work is to develop an effective approach for obtaining the minimum number of working stations for a given WCBS system. Our obtained results have been formally proved in theory and illustrated by some numerical examples.