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)

learn more… | top users | synonyms

1
vote
0answers
32 views

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 ...
0
votes
1answer
21 views

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?
0
votes
0answers
38 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 ...
1
vote
0answers
39 views

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 ...
0
votes
0answers
34 views

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. ...
1
vote
1answer
20 views

Types of Uncertainty

There are three types of uncertainty. How can one illustrate different between fuzzy uncertainty, resolution uncertainty, and probability uncertainty?
0
votes
1answer
29 views

Fuzzy sets/logic free ebooks

I need to find a free e-book about fuzzy sets/logic. But there are some requirements: this book must be published after 2010 and its size must be about 250. I have a task at my university to translate ...
0
votes
0answers
7 views

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, ...
2
votes
0answers
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 ...
0
votes
0answers
16 views

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 ...
1
vote
0answers
18 views

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). ...
0
votes
0answers
18 views

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 ...
0
votes
0answers
57 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 ...
1
vote
0answers
18 views

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 ...
0
votes
0answers
22 views

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 $\sigma$ ...
0
votes
0answers
16 views

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 ...
0
votes
0answers
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 ...
1
vote
0answers
27 views

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: ...
0
votes
0answers
31 views

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 ...
0
votes
0answers
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 ...
-1
votes
2answers
89 views

What is the formal negation of the statement “There is much X in Y”. [closed]

What is the formal negation of the statement "There is much X in Y"? The answer to me is that "It is not the case that there is much X in Y" But I want a more useful negation. Can I say that its ...
0
votes
1answer
170 views

Reference help about fuzzy logic and fuzzy set

Good afternoon, I'm trying to learn about Fuzzy alone, I was using some texts on the Internet about it, but it was very difficult to learn. I want to learn about Fuzzy set as shaper of uncertainty. ...
0
votes
0answers
15 views

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 ...
0
votes
1answer
80 views

Fuzzy logic de morgan

i should show, that de morgan's law is also correct in the fuzzy logic: $\neg(A\vee B)$ could be written as: $1-max(a,b)$ $(\neg A) \land (\neg B)$ as: $min(1-a, 1-b)$ But how could I show, that ...
1
vote
1answer
69 views

Set notation, what is the meaning of <dimension>[]?

I just ran across this notation in a lecture slide and unfortunately it was not explained, This is my first question and because of that I cannot post images, here's a link to an image containing ...
0
votes
0answers
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 ...
0
votes
0answers
7 views

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 ...
1
vote
1answer
22 views

How does associativity work for this fuzzy norm?

How to prove that $$\min\left(1,\min(1,x+y)+z\right)=\min\left(1,x+\min(1,y+z)\right)$$ where $x,y,z\in[0,1]$?
0
votes
0answers
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 ...
1
vote
1answer
237 views

defuzzification using centroid and weighted average

I was reading the book Fuzzy Logic by Timothy. J .Ross I don't understand how this difuzzification result was obtained. This is the example in the book. The centroid method equation is : I ...
0
votes
0answers
34 views

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) ...
0
votes
0answers
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 $a=1$ ...
2
votes
2answers
154 views

Is there an established method for assigning a truth value $0<t<1$ to undecidable statements?

Is there an established method for assigning a truth value $0<t<1$ to undecidable statements? Classical logic assumes every proposition is either true or false, i.e., the law of excluded ...
0
votes
0answers
37 views

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: ...
0
votes
1answer
903 views

Fuzzy Logic Question Help

so im working on a few questions for my discrete math class and i came up on this question: The truth value of the conjunction of $2$ propositions in a fuzzy logic is the minimum of the truth ...
0
votes
2answers
230 views

How to solve this fuzzy logic inference problem?

I'm having trouble solving an exercise involving fuzzy logic. It basically says something like that (pardon me if I made some mistake, I'm basing only on my poor memory) John goes to park if it is ...
1
vote
0answers
53 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 ...
2
votes
1answer
3k views

Troubles figuring out how to calculate the centroid for a defuzzification process

I am trying to implement a fuzzy logic system, but am having serious issues finding the centroid for the defuzzification process. This is what my output sets look like: My reference source gives ...
1
vote
3answers
99 views

Proof of a property of fuzzy extension principle

I'm looking for a proof of the following property of the fuzzy extension principle: $$ B \supseteq f(f^{-1}(B)) $$ ($f: X\rightarrow Y$ is an arbitrary crisp function, and $B$ is a fuzzy set). I ...
2
votes
1answer
41 views

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 ...
1
vote
1answer
117 views

Set Theory Symbols

I get easily confused when it comes to the symbol based terminology in Set Theory. Could someone please elaborate on what the following expressions mean? It would really help me out. $S_1$ = ...
0
votes
1answer
110 views

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, ...
4
votes
0answers
97 views

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 ...
0
votes
0answers
165 views

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 ...
2
votes
1answer
69 views

Linear fuzzy system

I need help if any one can help me How to define a crisp number or crisp system? Whats the difference between crisp number and fuzzy number? And if there is any references.
2
votes
1answer
138 views

Reference help for “fuzzy mathematics”

I want to study Fuzzy Sets and Fuzzy logic self. For that what would be better book to start from basic?
1
vote
1answer
2k views

Ranked Preference Matching Algorithm

first dropping the link that will serve as reference: NRMP Residency Matching I have a sort of side project (nothing riding on it, computational performance not an issue, so feel free to go wild, I ...
2
votes
3answers
171 views

Simplifying Equivalences in Łukasiewicz Logic

I am working on an inference system for infinite valued Łukasiewicz logic, using standard MV-algebras. As a pre-processing step, I would like to perform (non-exhaustive) simplification of formulae. ...
1
vote
1answer
114 views

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 ...
1
vote
1answer
46 views

How to implement fuzzy minimum function via fuzzy maximum

I know that I can represent fuzzy max via power function(i need it in neural network) i.e. def max(p:Double)(a:Double,b:Double) = pow(pow(a,p) + pow(b,p) , 1/p) // assumption a >=0 and b >=0 ...