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)

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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 ...
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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 is ...
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2answers
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What is the formal negation of the statement “There is much X in Y”. [on hold]

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 ...
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1answer
30 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. ...
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10 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 ...
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1answer
58 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 ...
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1answer
60 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 ...
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13 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 ...
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2 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 ...
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1answer
19 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 $x,y,z\in[0,1]$?
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25 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 ...
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1answer
79 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 ...
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25 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) ...
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32 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 $a=1$ ...
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2answers
142 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 ...
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26 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: ...
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1answer
311 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 ...
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2answers
151 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 ...
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49 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: ...
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43 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 ...
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26 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 ...
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1answer
2k 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 ...
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2answers
68 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 ...
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1answer
32 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 ...
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81 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. $S_1$ = ...
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90 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, ...
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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 ...
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137 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 ...
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1answer
54 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.
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1answer
125 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?
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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 ...
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3answers
167 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. ...
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1answer
107 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 ...
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38 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 ...
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1answer
625 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 ...
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1answer
274 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 ...
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1answer
4k 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 ...
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1answer
131 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?
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4answers
934 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 ...
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1answer
332 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 ...
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1answer
245 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 - ...
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2answers
869 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 ...
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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 ...
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1answer
302 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 ...
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1answer
738 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?
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1answer
115 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 ...
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1answer
588 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 ...
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410 views

Lukasiewicz Logic Tautology

Suppose a statement form $\varphi$ always has value T or U. Show $\varphi$ is a classical tautology.
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164 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 ...
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183 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): ...