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, $$f_{s}(a,b)=sgn(b-a)=\begin{cases} 1 &\mbox{if } b\geq a \\ 0 & \mbox{if } otherwise, \end{cases} $$ where $a=\mu_{A}(x)$ and $b=\mu_{B}(y)$ and $\mu_{A}(x)=\mu_{B}(x)=bell(x,4,3,10)$ and $z=f_{s}(a,b)$ and $(\mu_{Rs}(x,y)= sgn[\mu_{B}(y)-\mu_{A}(x)])$. I want using above identities to show the fuzzy rule "if x is A or y is B then z is C" which is equivalent to the union of two fuzzy rules "if x is A then z is C" and "if y is B then z is C" under max-min composition. I would be grateful if anyone help to solve this problem? How can I obtain $\mu_{C}(z)$ and how can I obtain $\mu_{R}(x,z)$, $\mu_{R}(y,z)$? I would be grateful if anyone help to solve this problem?
2026-03-25 09:25:44.1774430744
How can compose fuzzy rules in 1-D and 2-D?
272 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in FUZZY-LOGIC
- Verifying De Morgan's laws for two given fuzzy sets
- What properties does fuzzy logic preserve?
- Applications of fuzzy logic/set theory in pure math?
- Fuzzy logics, deduction theorem and strong conjunction
- How can i use fuzzy logic to switch between two distinct states?
- Textbook (or similar) for finite multivalued logic
- Why is causal influence between concepts in Fuzzy Cognitive maps represented by membership functions?
- What references should I follow if I want to learn more about semantic entailment in multi-valued logics?
- Troubles figuring out how to calculate the centroid for a defuzzification process
- Write down a linear programming problem
Related Questions in FUZZY-SET
- Verifying De Morgan's laws for two given fuzzy sets
- Operations on Fuzzy Power sets
- Proof from Fuzzy Intersection
- A Question on Definition of Fuzzy Numbers
- Applications of fuzzy logic/set theory in pure math?
- How can i use fuzzy logic to switch between two distinct states?
- Property of INF-w_i Composition of Fuzzy Relation
- Why does Spivak define the realization functor from fuzzy simplicial sets to extended pseudo metric spaces the way he does?
- Troubles figuring out how to calculate the centroid for a defuzzification process
- Conceptually: A set whose elements can only be probabilistically characterized?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?