# 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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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 &...
1 vote
167 views

### 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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1 vote
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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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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 $\tilde A$...