# Fuzzy Sets Application to Healthcare Systems

By Lazzari, Luisa L.; Moulia, Patricia I. | Fuzzy Economic Review, November 2012 | Go to article overview

# Fuzzy Sets Application to Healthcare Systems

Lazzari, Luisa L., Moulia, Patricia I., Fuzzy Economic Review

The fuzzy set concept was introduced by LotfiA. Zadeh in 1965 to provide a tool to describe vague predicates or classes with imprecise boundaries and which enable an uncertainty nonadditive calculation, based on softoperators.

Zadeh recognises that conventional quantitative techniques of systems analysis are intrinsically inappropriate to address humanistic systems. The medical field is appropriate to apply the fuzzy set theory, as vague predicates and subjectivity are an important part of it.

In this paper, the fuzzy set concept is used to provide a more flexible definition of certain parameters which state an individual's health condition, and which will allow to formulate a diagnosis model for the risk of suffering a certain disease, and it is characterized as a case of cardiovascular risk. This model is applied to the development of an expansion strategy for a private health insurance company, which considers sustainability of the healthcare system.

Keywords: fuzzy sets, health parameters, healthcare systems

JEL Classification: I19, P46, C65

(ProQuest: ... denotes formulae omitted.)

1. INTRODUCTION

LotfiA. Zadeh (1965) introduced the fuzzy set concept to promote a tool which aim is to describe vague predicates or classes with imprecise boundaries and which enables an uncertainty non-additive calculation, based on softoperators.

A predicate is an adjective that qualifies certain known objects. It linguistically formulates a certain object's property.

A crisp predicate is an accurate property of the elements of a set that may or may not check, for example, an "even number". It allows to classify discourse objects into two crisp sets and it does not accept linguistic modifiers.

A vague predicate is an inaccurate property of a set of elements that admits different degrees of truth. For example, the "high" predicate may be used in different domains, "an item's price is high", "Alice's blood pressure is high", and it allows for linguistic modifiers, as in "a product's performance is very high", "an individual's cholesterol is too high", or "George's weight is quite high". Given that the properties expressed as vague predicates are not only true or false, but admit different degrees of truth, they do not classify discourse objects into two sets (Trillas, 1998).

Zadeh extended the classical sets theory to be able to operate with classes defined by vague predicates, generalizing a set membership concept, for which there were only two possibilities: It belongs or it does not belong. Membership has ceased being dichotomic to become graded. Objects belong to several classes with different membership degrees in each of them.

Zadeh's calculation enables a way of representing and managing reasoning with vague predicates and it has crisp predicate calculations, as a particular case, which defines classical sets. Crispness or accuracy appear as a fuzziness or inaccuracy boundary case (Trillas, 1998).

Zadeh recognises that conventional quantitative techniques of systems analysis are intrinsically inappropriate to address humanistic systems.

Fuzzy models have turned into an appropriate tool to treat uncertainty in different fields. One of them is the medical field, as vague predicates and subjectivity are an important part of it (Mordeson et al., 2000).

An issue posed is assessing the admissible variability range of certain parameters which indicate an individual's health condition. Basic health parameters are simple, accessible and good indicators of the functioning of the body.

Some of them are:

* Weight and volume parameters: BMI (Body Mass Index) and WHP (Waist to Hip Ratio).

* Systolic blood pressure (maximum) and diastolic blood pressure (minimum).

* Heart rate.

* Glucose.

* Total cholesterol, LDL ("bad") cholesterol, HDL ("good") cholesterol and triglycerides.

* Respiratory parameters: VC (Vital Capacity) and FEV1 (Forced Expiratory Volume in 1 second). …

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