# Tagged Questions

Fuzzy logic is a form of many-valued logic that deals with approximate, rather than fixed and exact reasoning. (Def: http://en.m.wikipedia.org/wiki/Fuzzy_logic)

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### Is Fuzzy Set/Measure Theory an Active Area for Research?

I came across the notion of a fuzzy set the other day and since then, I've been reading about fuzzy measures and the Sugeno/Choquet integrals. While I certainly do not claim to have fully wrapped my ...
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### Definition of functions based on “fuzzy” truth table

I'm stuck on this problem: I have a "truth-table" (well, I don't know if it can be called truth table, if there aren't true/false values only): ...
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### Fine-grained notions of deduction for fuzzy logic

In the presentations of fuzzy logic that I've seen, $A \vdash B$ is understood as meaning that in any interpretation where $A$ is 1, $B$ is also 1. If we are reasoning meta-theoretically about fuzzy ...
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### Approximate function from sample data

Let $f\colon\mathbb{R}^n\to\mathbb{R}$ be a function. I don't have function definition. It's described as a fuzzy inference system. I have the inference system and can manipulate sample data for each ...
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### How should I refer to “volume-like” measures in a dimensional-free way?

When I try to model diffuse defined objects, I Frequently found myself in the need to refer to a measure in a way independent of the dimensional attributes of the space of definition of the objects. ...
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### Making sense of a symbol manipulation in fuzzy logic

I'm reading Bede's Mathematics of Fuzzy Sets and Fuzzy Logic and encountered the following proof for the absorption law: where $\land$, $\lor$ and $\leq$ stand for "intersect", "union", and "...
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### Fuzzy logic vs probability

In reading about fuzzy logic it says that fuzzy logic is different from probability. Can some one please explain how these two differ. How can this be explained to a person with no mathematical ...
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### Given a fuzzy set, find the level set

If you are give a fuzzy set $A = \frac{0.1}{x_{1}}+ \frac{0.3}{x_{2}} + \frac{0.6}{x_{3}} + \frac{1}{x_{4}}$ How do you find the level set?
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### Using fuzzy sets, can the total degree of membership of $x$ in $A, B,$ and $C$ determine the degree of membership of $x$ in $D$?

In fuzzy sets, can $x$'s total degree of membership in the three sets, $A, B, C$, collectively determine $x$'s degree of membership in $D$? For an example, it seems that the degree to which an ...
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### Fuzzy Logic Calculations for Non-Intersecting membership values

So i am not a fuzzy logic expert but wanted to see if what I am trying to do falls into something that I can solve using fuzzy logic. I have 3 categories A, B & C and for each category I have 4 ...
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### Concentration , Dilation in fuzzy Logic

I have several questions regarding concentration and dilation in fuzzy logic. 1) If I have a variable that affects hugely to the final outcome than other variables should I concentrate that ...
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### Definition of structarality for predicate logics

A logic $L$ in a propositional language $\mathfrak{L}$ is said to be structural if $\Gamma\vdash_{L}\phi$, then $\sigma({\Gamma})\vdash_{L}\sigma({\phi})$ for each $\mathfrak{L}$ substitution $\sigma$ ...
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### Multiple imputation for fuzzy logic

In my data set I have missing values for all variables and one particular variable has 12 out of 25 data points missing. So I used multiple imputation method to handle the missing values. What I want ...
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### Fuzzy logic operators

This is the first time I am working with fuzzy logic. So I need some help.I have 5 input variables and for each of them I have created membership functions based on literature review. Now I want to ...
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### Fuzzification of Data

I am using the triangular method of fuzzification to place data from a set of heights into three different categories: (tall, medium & short). What weights should I assume (I think we have to use ...
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### Assign an utility function for fuzzy evaluation grades on a $[0,\infty]$ scale

I have a score $x$ on a scale $[0,\infty]$. I know that if $0\leq x \leq 1.3$ the fuzzy grade is "None". If $1.3\leq x \leq 2.1$ the fuzzy grade is "MILD". If $2.1\leq x \leq 3.5$ the fuzzy grade ...
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### Laws of fuzzy logic

I need help to prove the following equality in fuzzy logic. Proof that $A\cup A^c=U$ where $U$ represents a classic set, but is valid considering the T-norm drastic $T_D=${$a$ if $b=1$ , $b$ if $a=1$ ...