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# InrecoLan FuzzyMath: Wikis

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# Encyclopedia

## Overview

InrecoLAN FuzzyMath is a fuzzy logic add-in for OpenOffice.org Calc.

InrecoLAN FuzzyMath allows to use uncertain or approximate values in OpenOffice.org Calc. It means with InrecoLAN FuzzyMath you can perform ordinary arithmetic operations and use ordinary mathematical and financial functions with uncertain values as if they are standard, or crisp, numbers.

## What is Fuzzy Number

Fuzzy numbers are used to represent uncertain or approximate values. For example, you want to create a budget but are uncertain of the number of your customers, NOC. The only thing you are fully confident is that the NOC lies between 50 and 100, and the most possible value of it is 70. In this case you should represent the NOC like the set of pairs: Z=({50;0}, {70;1}, {100;0}),, where 0, 1 and 0 are your beliefs in exact NOC - 50, 70 and 100 correspondingly. As you have done this you got the fuzzy number Z.

We call the minimum possible value of fuzzy number Minimum, the Maximum possible value - Maximum, and most possible value - Best.

Note:

1. Beliefs of Minimum and Maximum have to be equal to 0. Belief of Best usually equals to 1.
2. Belief of any value has to lie between 0 and 1.
3. You can use any number of pairs to determine your fuzzy number. For example, you can define fuzzy number Z, NOC, more concretely: Z =({50;0}, {70;1}, {75;1}, {85;0.5}, {100;0}).

So, one way to represent fuzzy number is to create the set of pairs as it was done above. Another way- and may be the most convenient one- is to use Belief graph. For example, the fuzzy number Z could have the following Belief graph: Note: In InrecoLAN FuzzyMath there are five Belief graph types, which can be used as defaults during the Creating Fuzzy Number process.

Each fuzzy number has Centroid. It is determined as the balancing point of Belief graph. Centroid is used to display fuzzy number in the sheet cell.

## InrecoLAN FuzzyMath Functions

Using InrecoLAN FuzzyMath you can create, edit, deffuzify fuzzy numbers and display Belief graph. Also, InrecoLAN FuzzyMath performs operations on both fuzzy numbers and crisp numbers. When both fuzzy and crisp operands are used in formula, InrecoLAN FuzzyMath returns crisp.

To create fuzzy number there are two methods: easy and advanced methods.

InrecoLAN FuzzyMath allows using of an extensive set of Calc functions (Mathematical and Financial functions) with fuzzy arguments.