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-2
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0answers
40 views

Does anyone can explain continuous t-norms to me in simple terms? [closed]

I need to solve an example of this.
0
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1answer
13 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
9 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 ...
0
votes
0answers
8 views

Fuzzy logic, arithmetic operations

Consider the closed intervals $A=[a_l,b_s],B=[b_l,b_s],E=[e_l,e_s],F=[f_l,f_s]$ where $l$ represents the lower limit of the range and $s$ represents the upper limit of the range, knowing that ...
0
votes
1answer
13 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
20 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) ...
1
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0answers
25 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 $a=1$ ...
4
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0answers
69 views

Vague predicates in standard predicate logic [closed]

I'm trying to work out if a sentence of the form: 'Bob is larger than Maureen and almost as large as Chris' can be adequately formalised in predicate logic. One could just write: ...
2
votes
2answers
137 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
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0answers
18 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
197 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
113 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 ...
0
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0answers
48 views

Determine set of t-norms verifying a property

As recalled in Scholarpedia, a t-norm $\top(a,b)$ is a function from $\mathbb{R}^{2}$ to $[0,1]$ verifying the following properties: Commutativity: $\top(a,b)=\top(b,a)$ Associativity: ...
1
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0answers
39 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 ...
0
votes
0answers
22 views

fuzzy computation

I am completely new to fuzzy set theory and fuzzy logic and maybe i am way off the subject, but I was wondering about the following. Suppose i have a statement: "X is about the same as Y and equal ...
0
votes
0answers
17 views

Maximum likelihood estimation algorithm

I have problem with Gath-Geva algorithm. 1.Choose initial values for h(i|Xj),the probability of selecting i-th cluster givng the j-th feature vector In multivariate case,if I have 144 points(with two ...
0
votes
1answer
849 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 ...
0
votes
2answers
57 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
31 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
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1answer
73 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
84 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
89 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
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0answers
124 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
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1answer
53 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
116 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
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1answer
1k 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
164 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
102 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
37 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 ...
3
votes
1answer
568 views

Fuzzy C Means mathematics tutorial [closed]

Hello I am looking for help on understanding the maths of Fuzzy C Means as explained here: Fuzzy C Means I was hoping for a broken down explantion of the actual math. I have tryed googling for ...
2
votes
1answer
254 views

Is Fuzzy Logic Needed? [closed]

I had a very big doubt in my mind about Fuzzyness. When statistics is answering all the questions, which we see generally in Fuzzy theory. Then why one SHOULD learn Fuzzy Theory. Or is there any gap ...
1
vote
1answer
3k views

What is the difference between mamdani and sugeno in fuzzy logic?

I realise that the difference lies in the way the defuzzification happens but I don't fully understand it. I've read some papers comparing the outputs from the two models but I'm still not really sure ...
-2
votes
1answer
128 views

Fuzzy logical and integer programming

Is there any way of formulating linear/non-linear programming problems in terms of YES, NO, and MAYBE instead of just $0-1$ programming?
22
votes
4answers
879 views

Is there anything deep about Fuzzy sets/Fuzzy logic?

I keep coming across the term "fuzzy". I browsed around a bit and read a few articles.. It seems to me that there's absolutely nothing deep or foundational about fuzzy set theory or fuzzy logic. I ...
0
votes
1answer
309 views

Can someone explain definition of operation $\rightarrow$

It turns out that most frequently set of truth values comprises the so-called residue lattice in other words L is a partiar order set, which includes maximum element(1) and minimum(0), where each ...
1
vote
1answer
205 views

Representing non-fuzzy memberships

I'm trying to model an input for a FIS in Matlab, unlike other inputs this value is a boolean Yes / No Do I use two membership functions that do not overlap but cover the entire domain e.g NO (0 - ...
0
votes
2answers
791 views

What is the difference between Centroid of area and Bisector of area?

We got this fuzzy course in the university, there was a problem which it's result led to multiple overlapping fuzzy values. in order to conclude a value out of that there was different approaches ...
-1
votes
1answer
196 views

Applying fuzzy logic to determine the degree to which a project is complete

I have a Project made up of tasks. Each task has an estimated completion percentage. I realise I could treat each tasks completion percentage as a representation of the degree of membership to the ...
2
votes
1answer
287 views

Study material for fuzzy logic

Can you please suggest some good study material on fuzzy logic. any good books, articles, video material would be appreciated. I am doing my Master's Diploma in Information Systems, and I need some ...
10
votes
1answer
702 views

Fuzzy logic and topos theory

Why doesn't one develop fuzzy logic by extending topos theory, by simply extending the subobject classifier $\Omega$ to the unit interval [0,1]? Have people done that?
1
vote
1answer
113 views

Possibilistic clustering- what exectly is $\eta$ and how to calculate it

I'm curently studing the topic of Possibilistic shell clustering and I have a hard time with understanding the concept of variable $\eta$. Can somebody in simpe words explain me what exectly this ...
3
votes
1answer
557 views

About the pointwise infimum of a continuous piecewise linear function

I am reading the logic paper "Interpolation in fuzzy logic" by Matthias Baaz and Helmut Veith http://www.springerlink.com/content/654wl9u5mcj7qtva/ On page 479 it is claimed that "It suffices to show ...
4
votes
1answer
393 views

Lukasiewicz Logic Tautology

Suppose a statement form $\varphi$ always has value T or U. Show $\varphi$ is a classical tautology.
3
votes
1answer
163 views

Help needed on method to use for anomaly detection in Computer Science

I think people here could guide me in solving a problem related to anomaly detection. The term anomaly here refers to some undesired event occurring in the system like a virus infection. I could get ...
3
votes
0answers
179 views

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): ...
4
votes
1answer
391 views

Fuzzy Logic vs Logic

well i was wondering if, there s a way in which one could compare these two theories on the ground that which one will provide more accurate answers to a given problem. Fuzzy logic always focuses on ...