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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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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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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How can compose fuzzy rules in 1-D and 2-D?

fuzzy implication function based on the interpretation "A entails B" can be expressed as : $$R_{s}=A \longrightarrow B=\int_{X\times Y} sgn[\mu_{B}(y)-\mu_{A}(x)]/(x,y),$$ or, alternatively, $$f_{s}(a,...
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Structure of a fuzzy subspace

Let $V$ be a vector space over a field $F$ and let $f$ be a function from $V$ to the interval $I:=[0,1]$ satisfying the condition that for any $a \in I$ the set $V_a:=\{v \in V | f(v) \ge a\}$ is a ...
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Fuzzy owa operator

I am reading about the allocation of OWA weigts from the article here In it one way of finding weights is through Here with varying values for a,b they have shown this. Three situations are ...
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Are the following standard five connectives { “and”, “or”, “not”, “implies”, “if and only if”} complete in fuzzy logic?

I am currently in a Logic class and was assigned this question. In class we define complete as a set of connectives that could generate every truth function. My answer to this question is no, the ...
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Mixing Fuzzy Logic and Probabilistic interpretation of a dataset

A probabilistic data cloud is a set $M$ of data points $\{m_i\}_i$, where each data point $m_i$ is associated to an event $E_i$ expressing the set of the occurrences of $m_i$ in any possible non-...
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Unit of Probabilities with uncertainties and contradictions

I want to built a unit of information, somewhat like a qubit, but it should encode besides the real-valued 'value' also the measure of 'uncertainty' (inverse of confidence) and measure of '...
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Why does the natural extension of a lower prevision dominate it?

On p. 48 in Troffaes and de Cooman's Lower Previsions there's a claim that "It is clear that" the natural extension $\underline{E}_\underline{P}$ of lower prevision $\underline{P}$ dominates (42) it, ...
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Valuation of a fuzzy logic with missing values

Usually, in fuzzy logics, values from $[0,1]$ are considered. There are some three values logics for missing values such as Kleene's logic (http://www.filozof.uni.lodz.pl/bulletin/pdf/43_12_4.pdf). ...
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How to allocate weights in OWA operator in fuzzy logic

I am reading about OWA operators in fuzzy logic from the article here In the example provided in page 21 it says that the weights associated with the linguistic quantifier are for $a=1.2$ are <...
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Notation of functional relationships in Fuzzy Logic

I would like to know how to put the following ideas in to a more formal mathematical notation: Traditional methods implement a direct functional relationship between input and output signals: ...
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56 views

Write down a linear programming problem

I want to replicate a linear programming problem.I have the following information, for the background." A fuzzy regression analysis with only one independent variable X results in the following ...
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What is the difference between a MIMO and multiple MISO fuzzy logic classifiers?

If I have 10 independent inputs and 5 independent outputs, can I say that a multiple MISO fuzzy logic classifiers equal to the function of a MIMO fuzzy logic classifier?
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Is there a crisp number membership degree in fuzzy logic model when it is defuzzified?

I am working on a GA implementation for a fuzzy job-shop scheduling problem for my final project. I have a model that explains the performance graph of a machine during the process. This model is ...
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Understanding Fuzzy Composition operations

There are two common forms of composition operation in Fuzzy Theory: max–min composition max–product composition Let R be a relation that relates elements from ...
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Designing a fuzzy system to analyze projectile motion

I realize this is probably going to be considered off-topic for this site, but I'm going to ask anyway: I have the following assignment: Design a fuzzy system which, for the given distances between ...
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an evidence finding

could anyone help me to solve this? I am not able to think where to start this..please help and give hints Rain causes bus failure. The bus failure causes Anil and Hari to be absent. P(Anil absent ...
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Fuzzy sets: extension principle

I am a little bit confused about fuzzy set theory extension principle description. Most sources define extension principle in a following way: Suppose $f:X\to Y$ and fuzzy set $A\in X$ such that $A=\...
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Hamacher product in fuzzy logic

I was reading the article here Hamacher product is In page 41 in the article it describes three properties of Hamacher product. I do not understand the difference in notations and meaning of the ...
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Finite Strong Completeness Theorem for BL logic

I need to prove the finite strong completeness theorem for Basic Logic, where $BL$ is: $\vdash_{BL} =\vDash_{FLew}$ + linearity + division. The strong completeness is: $$\varphi_1,...,\varphi_n \...
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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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131 views

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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23 views

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 $a=1$ ...
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Is the fuzzy conjunction function continuous?

As the question states, is the fuzzy conjunction (t-norm) function continuous? This was an exam question, the answer was no, but looking at the conjunctions we studied, this seems to be the case: ...
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a question in soft topology

The definition of soft topology is: My question is, isn't the soft topology in the folowing example lack the intersection and the union of two of it's sets? I mean, shouldn't the sets $\{\{\phi\},...