# Fuzzy Logic in Selection of Maritime Search and Rescue Units
## 4 Case Study
### Procedure Description
Small units, such as yachts, fishing boats or small merchant vessels, have a small superstructure, and the lookout's eyes can be at a height of a few metres above the water surface (ca. 10 m). Medium-sized merchant vessels, passenger ships, and specialised vessels have higher superstructures with an observation altitude of 20 to 30 m. Ultra-large vessels, such as the biggest cruise ships, tankers, container ships and car carriers, can have an observation altitude of more than 40 or even 50 m The vessel may be classified into Low, Medium and/or High sets (Figure 3). The vessel's medical equipment determines its ability to provide medical assistance. Civilian vessels may vary greatly in this respect. The equipment of small units is usually very basic and may include means of thermal protection and a first aid kit. Larger units may have a room where survivors can be provided with shelter. Medical equipment includes, inter alia, defibrillators, oxygen bottles and respirators, spineboards, vacuum mattresses, infusion pumps, intubation and thorax drainage equipment, labour kits, etc. Several levels of readiness to provide medical assistance can be distinguished, e.g.,:  
* The vessel has an advanced medical module and a doctor on board
* The vessel has equipment and rooms for providing medical assistance (e.g., an on-board hospital)
* The vessel has standard medical equipment and is able to provide some medical assistance (medicines, oxygen, AED)
* The vessel has thermal protection means and/or a first aid kit
* The vessel is not able to provide any medical assistance  
The author proposes two sets where medical equipment is evaluated numerically on a scale from 0 to 1. The vessel can be classified in the Basic and/or Advanced set (Figure 3). Figure 3: Input linguistic variables and output value. On this basis, the input values for observation altitude (o.a.) and degree of medical equipment (m.e.) of the vessels were determined:  
\[V_{1}=(12,\ 0.5),\ V_{2}=(45,\ 0.65),\ V_{3}=(30,\ 0.5),\ V_{4}=(24,\ 0.5),\ V_{5}=(16,\ 0.8)\]  
Based on experience, the expert has developed the following decision rules:  
* IF the observation altitude is low AND the medical equipment is basic THEN the quality is low. * IF the observation altitude is low AND the medical equipment is advanced THEN the quality is average. * IF the observation altitude is medium AND the medical equipment is basic THEN the quality is average. * IF the observation altitude is medium AND the medical equipment is advanced THEN the quality is high. * IF the observation altitude is high AND the medical equipment is basic THEN the quality is average. * IF the observation altitude is high AND the medical equipment is advanced THEN the quality is high. Based on the above, the criterion 'quality' can be identified. The criterion is minimised. The criterion is very important but less significant than speed (weighting 0.25). Operation of the controller for the Vessel 1 is shown in Figure 4. The input value of the observation altitude criterion is o.a. = 12 metres, the medical equipment is medium (on-board hospital, oxygen, AED, medicines, staff) and evaluated at m.e. = 0.5. On this basis, suitability of the vessel can be evaluated. After rule aggregation, defuzzification was performed. Application of the implication operator allowed the following calculations:  
\[\left\{ \begin{array}{l}H_{quality=low}\ (\text{o.a.}=12,\ \text{m.e.}=0.5)= \text{min}\ \ (\mu_{low}(12),\ \mu_{basic}(0.5))=\text{min}(0.87,\ 0.5)=0.5\\ H_{quality=average}\ (\text{o.a.}=12,\ \text{m.e.}=0.5)=\text{min}\ \ (\mu_{low}(12),\ \mu_{advanced}(0.5))=\text{min}(0.87,\ 0.5)=0.5\\ \end{array} \right.\]  
\[\left\{ \begin{array}{l}H_{quality=average}\ (\text{o.a.}=12,\ \text{m.e.}=0.5)= \text{min}\ \ (\mu_{medium}(12),\ \mu_{basic}(0.5))=\text{min}(0.13,\ 0.5)=0.13\\ \mu_{quality=high}\ (\text{o.a.}=12,\ \text{m.e.}=0.5)=\text{min}\ \ (\mu_{medium}(12),\ \mu_{advanced}(0.5))=\text{min}(0.13,\ 0.5)=0.13\\ \end{array}