*Article* **Optimal Placement of Pressure Sensors Using Fuzzy DEMATEL-Based Sensor Influence**

**Jorge Francés-Chust 1,2, Bruno M. Brentan 2,3, Silvia Carpitella 2,4and Joaquín Izquierdo 2,\* and Idel Montalvo 2,5**


Received: 30 December 2019; Accepted: 6 February 2020; Published: 12 February 2020

**Abstract:** Nowadays, optimal sensor placement (OSP) for leakage detection in water distribution networks is a lively field of research, and a challenge for water utilities in terms of network control, management, and maintenance. How many sensors to install and where to install them are crucial decisions to make for those utilities to reach a trade-off between efficiency and economy. In this paper, we address the where-to-install-them part of the OSP through the following elements: nodes' sensitivity to leakage, uncertainty of information, and redundancy through conditional entropy maximisation. We evaluate relationships among candidate sensors in a network to get a picture of the mutual influence among the nodes. This analysis is performed within a multi-criteria decision-making approach: specifically, a herein proposed variant of DEMATEL, which uses fuzzy logic and builds comparison matrices derived from information obtained through leakage simulations of the network. We apply the proposal first to a toy example to show how the approach works, and then to a real-world case study.

**Keywords:** water distribution network; leakage; optimal sensor placement; sensitivity; uncertainty; entropy; multi-criteria decision-making; DEMATEL
