The first thing I would like to mention is if there is no uncertainty in the data, then there is no need to introduce fuzzy set theory in it. If the problem has a simple solution, then why to introduce complexity?

Still, if you really need fuzziness, then I will try to explain it by an example concerning normal life. There are not fixed numbers representing the ages so that we say that a person with age 18 is young. Sometimes a person with age 16 also looks young and sometimes a person of age 19 also does not look young. Similar remarks apply to old, middle age etc. If we are instructed to boil the water at low temperature, then we cannot exactly say that up to what degree of temperature, we will say that it is low? So, people divide the range, say 0 to 100 in our example, in several parts such as low, medium and high or such as very low, low, medium, high, very high etc. How many partitions to take? It is our choice. Naturally more partitions than necessary will introduce more complexity. Corresponding to each of them, one has to define membership function solely dependent on our choice. Of course, the choice must be realistic.

Thus, for every variable which are uncertain, you first have to identify the range and then decide the appropriate partitions. Then membership functions.

I would recommend a book: "Fuzzy logic with engineering applications" by Timothy Ross. Another book is "Fuzzy sets, uncertainty and information" by G Klir.

Use ANFIS in matlab. Via anfisedit  command you can upload your crisp data and make automatic fuzzy rules and save them as, data.fis.

I am agree with Sanghavi. If there is no uncertainty in data, no point to use fuzzy or intuitionistic fuzzy. But if some  non-determinism (Non-stochastic)  is found in data, IFS theory can be used . And for this first you fuzzify the data and then  consult research paper to convert of  A. Jurio, D. Paternain, H. Bustince, C. Guerra, G. Beliakov, A Construction Method of Atanassov’s Intuitionistic Fuzzy Sets for Image Processing, Paper presented at the Intelligent Systems (IS), 5th IEEE International Conference, 7-9 July 2010, London to convert fuzzy sets to intuitionistic fuzzy sets.

Fuzzy rules in the fuzzy set part of matlab toolbox is the very instructive document to understand fuzzy data  concepts;

I agree with Pr. Mahmoud;

Sanjay Kumar Dr please ,In your paper that was entitled "Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making" .I need to know how can I convert table 1 to table 2 or how can I fuzzify the data before convert of  A. Jurio,

Sara Sami Alkafaas To do this we have constructed fuzzy sets for each criteria with increasing or decreasing graph as membership functions. Then numerical values were associated with corresponding membership grades.

Sanjay Kumar Dr please , I need too any source to clear the fuzzification which was used in your paper or any clear example .

Mubashar Hussain Shah I already shared my problem but no one replied .

To convert crisp to intuitionstic

Normalize the data according the typ of each criterion. Let the normalized value equal the membership degree .The non membership degree equal (1- membership degree ) .In this case the hesitancy degree equal zero.

Sanjay Kumar Dear Dr , Normalized value equal the membership degree .It is the method which you used in your paper .

Mubashar Hussain Shah Thanks

Mohamed Fattouh Abd Elhameed Dear Dr , this is a good answer and I took your way and I found Some researchers actually used this method but I tried to apply it in this paper and did not get the correct results.Thanks

Sara Sami Alkafaas In Step 1 you will find four fuzzy sets A1, A2, A3 and A4 those are used to fuzzify the crisp value of criterion.

Mubashar Hussain Shah Thanks my problem is solved

Sanjay Kumar Thanks a lot dr.sanjay for your help.

Put your data set to construct a Bell Shaped Gaussian Probability Curve. This Function will be your Membership function. Construct another function which looks like turned upside down of the Gaussian curve ( near Complement of the membership function ) , it may treated as non-membership function. There are many ways to develop membership functions, It may be taken as Triangular when you are able to get < mean , Median, Mode > of the crisp data set; and likewise you may have Non membership function. If your data representing a single value, then consider its maximum and Minimum deviations ( lower and upper bounds etc.) that might appear in practice to get your answer. Thanks.

First of all you have to know the basic characteristic of the said data. Then go for its spread, means how much extent it can relax, if it may deviate 0% to +/-100% then its fuzzification is meaning less. Generally , fuzzification requires a small change of the given data which are parts of strong fuzzy , otherwise it will be treated as weak fuzzy. So you should think its real application while you fuzzify them.

Yucheng Dong

Physical measurements are prone to error and thus we require the fuzzy number to represent the uncertainties arose. There are many methods available in the literature, some of which are using the concept entropy or defining the left and right spread function. It all goes back to the characteristic of data available. If it is a monthly data for a year only, you can resort to the entropy that make use the maximum value and maybe the average to find the spread value. Otherwise, you can obtain the distribution of your data (maybe gaussian or s or z-shaped) like Sujit Kumar De suggested. Bear in mind that sometime the distribution obtained might not be unimodal, it could be two modes or any possibilities.

The construction is again of course and approximation and prone to fuzziness itself.

In order to construct intuitionistic data set from your data, you can consider the concept of complement instead where your v(x) is obtained by 1-\mu(x). I guess that is suitable and practical for the data available.

How can l transform crisp data to fuzzy data