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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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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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, ...
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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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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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40 views

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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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 ...
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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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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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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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39 views

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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Can anyone tell me what are the prerequisites for learning fuzzy logic?

I am an undergraduate student and want to do an internship on fuzzy logic.So, it will be very helpful if someone can tell me what are the prerequisites for it and recommend me some introductory books. ...
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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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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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19 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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21 views

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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Fuzzy Logic - Defuzzification

Given the fuzzy set describing temperature (Frio - Cold ; Calor - Hot) And knowing it's 18 ºC, how do I go about calculating the Certainty Factor of Calor(Hot)? I'm almost sure I have to use the ...
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25 views

Lattice of a Fuzzy Number?

Can somebody define what is a fuzzy lattice? How to computer lattice of a fuzzy number? Please try to be generic and basic in the explanation as I'm a beginner in studying fuzzy theory and soft ...
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Weighted Decision Making on the basis of Two Significance Indexes

I'm trying to make the best decision for assignment of books(some of the books have multiple authors that belong to different organizations).Only one author can be represented by a single book. I have ...
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54 views

Sugeno and Madani membership functions

Neural networking,genetic algorithms are these used only with Sugeno Type Inference? Aren't these used with Mamdani Inference method. If so for Mamdani what is the way to develop membership ...
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Morgans Law, fuzzy logic

I wonder how to make proofs in fuzzy logic, working with classic sets I can do, but I'm having trouble with fuzzy. How I can proof that $$\eta(a)\bigtriangleup \eta(b) = \eta(a\bigtriangledown b) ...
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48 views

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 ...