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Questions tagged [fuzzy-logic]

Fuzzy logic is a form of many-valued logic that deals with approximate, rather than fixed and exact reasoning.

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Mathematical interpretation and Fuzzy logic interpretation of d err/dt or change of error

Thank you for the possibility to ask a question. I am new at this forum. Currently I am scratching the surface of fuzzy logic with the idea to go deeper an deeper. From calculus, I understand that a ...
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Is there exists a fixed valued formula in infinite value logic?

EDIT: We have three kinds of famouse fuzzy logic name: Godel, Luaksiewicz and product logic (see 1). We can define infinite valuation semantics for each of them in $[0,1]$, i. e. we can define a ...
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Can we conclude provibility from semantically equavalency?

Let $\varphi$ be formula that $\varphi \equiv \perp$, i. e. for all valuaition $V$ we have $V(\varphi) = \varphi(\perp) = 0$. Can we conclude that $\vdash \varphi \leftrightarrow \perp$? Does it ...
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Proving the minimum t-norm is a joint possibility distribution

A t-norm is an operator $T:[0,1]^2\rightarrow[0,1]$ which is comutative, monotonic, associative and has 1 as an identity element, that is, $T(1,x)=T(x,1)=x$. A joint possibility distribution (JPD) of ...
Gustavo de Souza's user avatar
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ANFIS Model, tips about improving performance [closed]

I have a question regarding about improving the performance of an ANFIS (adaptive neuro Fuzzy inference system) model. In MATLAB, I have been training a model with 5 inputs, with 816 data point for ...
jocelyn matus ancavil's user avatar
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Interpretation of "If A, then B" as "A coupled with B": Context and Applicability

It is known that the meaning of a conditional statement in fuzzy logic can vary depending on the interpretation and context. In certain fuzzy logic books, I have come across the interpretation that &...
hasanghaforian's user avatar
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Equality of fuzzy sets

Is there a definition for "equality of fuzzy sets" ? My current thinking : Say we have two fuzzy sets $A = \{(x,\mu_{A}(x)):x \in X\}$ and $B = \{(y,\mu_{B}(y)):y \in Y\}$ When we consider ...
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something like an integral but for fuzzy logic OR rather than summation

I'm not well-versed in analysis. I want to OR together an infinite number of fuzzy truths of infinitesimal significance. I mean the following: I have an arbitrary function $t(v)$ with a range on $[0,...
Michael Saunders's user avatar
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About consistency and maximality in Łukasiewicz logic

Suppose that we define consistency in Łukasiewicz logic as follows: We say formula $\varphi$ is consistent if $\nvdash \neg \varphi$. We say a finite set $\Gamma= \{\psi_1, \dotsc, \psi_n\}$ is ...
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Proving a property about alpha cut $ (A')_\alpha \neq (A_\alpha)', unless \\ \alpha = 0.5 $

I recently came accross this property about alpha (or lambda) cuts $$ (A')_\alpha \neq (A_\alpha)', unless \\ \alpha = 0.5 $$ where A is a fuzzy set with membership function $\mu_A(x)$ I am curious ...
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The definition of fuzzy sets using logical and set operators.

I wrote this definition of fuzzy sets and fuzzy logic for a college assignment and was wondering if it is correct: Let a be any ordinary element of the universal superset U and A be a subset of U, ...
Matt Schramm's user avatar
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How to find Zadeh's extension of a function like this?

I'm learning fuzzy logic and i don't find many examples explaining Zadeh's extension principle I found this one but i don't know how to solve it. Can you help me ? Let us consider two fuzzy subsets $A$...
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Randomness vs Fuzziness

As the title suggests, What is the difference between randomness and fuzziness? My take: They are two-sides of the same coin - they are two different ways of expressing uncertainty. Consider a ...
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Associativity of join and meet in MV-algebra lattice

I'm trying to prove that MV-algebra is a lattice, where join and meet operations are defined as follows: $$x \vee y = (x \odot \neg y) \oplus y,$$ $$x \wedge y = x \odot (\neg x \oplus y).$$ I've ...
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Fuzzy Entropy, what is the correct exponential term?

When computing the Fuzzy Entropy measure, most works use an Exponential fuzzy function. Yet, there are two deviations between the works. For the exponential membership function, some use the term $\...
Lazaros Moysis's user avatar
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Truth Value of 0.5 in Fuzzy Logic

Suppose that I have a proposition, represented by variable $p$. It is my understanding that in fuzzy logic, $p$ may have a truth value $x$ where $\{x \in \mathbb{R} \mid 0 \leq x \leq 1\}$. Now ...
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How do I express that I iterate over all instances of my knowledge base to assign any combination of variables to in logic formula to find true ones?

My knowledge base consists of the following instances: ...
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Meaning of cardinality of fuzzy sets & intuitionistic fuzzy sets

We know that the cardinality of a finite crisp (or, classical) set $A$ can be considered as a measure of "number of elements" of $A$. However, if $X$ is a universe of discourse and $\tilde A$...
Usual_Learner's user avatar
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An exercise in fuzzy logics built from a t-norm

(I also asked this in MathOverflow) Consider the following t-norm: $ a * b = \begin{cases} \text{$2ab,$} &\quad\text{if $a, b$}\le1/2\\ \text{$min\{a, b\}$} &\quad\text{...
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Book request: fuzzy sets and logic

There are requests for this topic already, though I am looking for a particular kind of book on the topic. I got part of the way through Trillas' and Eciolaza's book Fuzzy Logic: An Introductory ...
Mark's user avatar
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Which branch of mathematics is the fuzzy logic?

Fuzzy logic comes close to boolean algebra but is the upper branch of fuzzy logic (or fuzzy mathematics) still algebra?
Max Hager's user avatar
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Prove that two fuzzy sets are disjoint if and only if their supports are disjoint

Prove that two fuzzy sets are disjoint if and only if their supports are disjoint. Given two fuzzy sets $A,B$ of a reference set $X$,then : $$ \begin{align} \\ &\text{Supp}(A) \cap \text{Supp}(B)=...
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Is almost-naive set theory in fuzzy logic with comprehension limited to continuous connectives consistent?

I've heard the result before that naive set theory is consistent in infinite-valued Łukasiewicz logic. This answer contains a citation. In this logic, every connective is continuous (w.r.t the product ...
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What is the difference between "Fuzzy Logic" and "General Predicate Logic with Identity and Function Symbols"?

I understand the Fuzzy Logic is a infinite-value logic. But can GPLIF's function symbols in conjunction with predicates be used as an alternative to the degrees of truth provided by fuzzy logic? What ...
Vivek Joshy's user avatar
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Fuzzy Logic Composition

I want to know when to use max-min composition and max product composition. I'm pretty sure I understand how to compute them, but I notice that even though they're both supposed to be performing ...
J J's user avatar
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Do this integral really means an integral? (random set representation of a fuzzy set) If yes, can someone explain to me intuitivily why this is true?

Let's suppose that I have a crisp set like: \begin{equation} A^\alpha = \{x \mid A(x) \geq \alpha \} \end{equation} and let's define a function \begin{equation} f_\alpha(x) = \begin{cases} 1, &...
Matheus Bento de Souza's user avatar
2 votes
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117 views

help replicating fuzzy equations from a paper

I'm trying to replicate Zhou's Paper on quantifying UX using Fuzzy Math. In their model, there is a weight vector $A$ for a set of characteristics. in the paper's test case the characteristics were ...
carlo's user avatar
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"De Morgan’s laws" vs "De Morgan's principles"

In the book Fuzzy Logic with Engineering Applications by Timothy J. Ross, it is written we can't write "De Morgan's laws"; instead, it should be "De Morgan's Principles". The ...
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What's a set of sentential formulas satisfied by $\aleph_0$ assignments in $\{0,1\}$-logic but $2^{\aleph_0}$ assignments in $\{0,1/3,2/3,1\}$-logic?

$\{0,1/3,2/3,1\}$ logic has the following connectives: $\neg r= 1-r$ $r\wedge s=min\{r,s\}$ $r\vee s=max\{r,s\}$ $r\rightarrow s=min\{1,1+s-r\}$ $r\oplus s=min\{r+s,2-r-s\}$ $r\leftrightarrow s=min\{1+...
Jun Xu's user avatar
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upper semi-continuous of fuzzy set [closed]

Let $u:\mathbb{R^n}\to [0,1]$ be a fuzzy set. (fuzzy set is a set of ordered pairs $(x,u(x)), x\in \mathbb{R^n})$. Please give an example such that $u(x)$ be upper semi-continuous. thanks
user809500's user avatar
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model fuzzy assignment problem [closed]

i wanna ask something about fuzzy assignment, why in fuzzy assignment problem specially in min z form didn't using $tilde{x}$ in $x_{ij}$ meanwhile it is used in $c_{ij}$ and also $z$. \begin{align*} ...
John Person's user avatar
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1 answer
175 views

Is there a logic with quantifier "almost always".

I would like to describe a reasoning with quantifier "almost always". For example, if probability of $Z$ is above $95$%, I would like to say that $Z$ is "almost always true". Is ...
Marina's user avatar
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Non continuous Fuzzy Set

I stuck in this question for a few hours now. Can anyone help me? $ A ̃ $ is a non continuous fuzzy set and is defined by: $ A ̃ = \{0.6/x_1 +0.5/x_2 + 1/x_3 + 0.75/x_4 + 0.7/x_5 + 0.8/x_6 + 1/...
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probabilistic and deterministic techniques and mathematical methods that exist for sensor fusion so far

I am not sure whether this is the right site on StackExchange to ask this question. I am relatively new in here at least as an active memeber. Nevertheless I thought mathematicians would know more ...
Noureddine Ouertani's user avatar
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Fuzzy number confusion in Data envelopment analysis R.

I was learning data envelopment analysis and I was confused when I started dealing with fuzzy data. How can I know if a variable in my dataset is a fuzzy number or not? They mentioned that with ...
tn99's user avatar
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Is there any relationship between K-Maps (Karnaugh Maps) and neural networks?

Recently, I've been studying neural networks to get a better understanding of how they work. I can't help but notice a vague similarity to K-Maps or Karnaugh Maps used for determining boolean ...
user148298's user avatar
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1 answer
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Meaning of "$\exp[ \cdot ]$" in mathematical equations [duplicate]

I am reading book "Fuzzy Logic With Engineering Applications, Wiley" written by Timothy J. Ross. I am reading chapter 7 and in this chapter, "Batch Least Squares Algoritm" has been defined. It ...
tahasozgen's user avatar
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Composition of a fuzzy set

I'm trying to learn about Fuzzy alone. I'm having difficulties with understanding intuitively the composition of a fuzzy set. According to the definition in the book:enter image description here ...
Rəşad Abdulxalıqov's user avatar
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Fuzzy logic t-norm

I am trying to understand fuzzy logic. I got to t-norms and trying to do some exercises on them. Can you explain to me how to make a t-norm of the following formulas and verify if they are ...
Adono's user avatar
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A map for fuzzy logics.

I'm studying metatheorems of fuzzy logics and I found this map of fuzzy logics that relates multiple fuzzy logics and I was wondering two things: First I would like to know if anyone knows where ...
Jose Moncayo's user avatar
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164 views

What are the real differences between "standard" boolean logic and fuzzy logic?

Fuzzy and Boolean Logics are equally expressive and one is nothing more than syntactic sugar for the other. I'm honestly trying to get convinced otherwise. Here's my argument: In Boolean logic, $x \...
Threnody's user avatar
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Evaluation of "Not" and "XOR" in Fuzzy logic rules

Consider we have three fuzzy variables A , B and D ,. Also , consider that the fuzzification process has been applied and A has been evaluated to 0.5 and B has been evaluated to 0.1. Now , we know ...
AAA's user avatar
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How can I compute the complement of a mathematical membership function?

Considering fuzzy set A defined on real numbers by the membership functions: $\mu_A(x)=\frac{1}{x+1}, \mu_C(x)=\frac{1}{10^x}$ How can I determine mathematical membership function and graph of $ A \...
estamos's user avatar
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Intuition behind Zadeh / Lukasiewicz implication of fuzzy logic

I am studying fuzzy logic and the implication operator. Suppose we are given the implication "IF $x$ is $A$ THEN $y$ is B" with $A,B$ fuzzy sets so $A(x), B(x) \in [0,1]$ are the membership functions. ...
NightRain23's user avatar
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Example of membership function which does not equal 1 for any element in its domain

I'm learning about fuzzy logic and fuzzy sets, and it seems to me that there is no requirement that there be at least one element in the domain set for which the membership function is equal to 1. ...
Charlie's user avatar
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3 answers
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What references should I follow if I want to learn more about semantic entailment in multi-valued logics?

I am simply curious about this subject, and would like to learn more about it. I am an undergraduate student and in our studies we've always tackled classical logic and simply mentioned that other "...
Threnody's user avatar
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Why is causal influence between concepts in Fuzzy Cognitive maps represented by membership functions?

We Know that FCM are represented by concepts and Weights or causal influence between the concepts. In order to find the weights, we take the help of an expert that describes the relationship between ...
roaibrain's user avatar
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2 votes
1 answer
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Textbook (or similar) for finite multivalued logic

There are a few sources mentioned on some questions on this site regarding multivalued logics, but usually they are to original papers, or to texts on fuzzy logic. I have access to some fuzzy logic ...
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How can i use fuzzy logic to switch between two distinct states?

So I have a nice problem and I've been contemplating the use of fuzzy logic for this. I have attached a little diagram I have made to explain the problem--> Fuzzy logic image So I have a power demand ...
Akash Menon's user avatar
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150 views

Fuzzy logics, deduction theorem and strong conjunction

Hajek in Metamathematics of Fuzzy Logic (1998) states that for every extension of Basic logic a special version of the deduction theorem holds $$A\vDash B\Leftrightarrow\exists n:\vDash\underbrace{A\&...
Daniil Kozhemiachenko's user avatar