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Fuzzy Delphi Method to Design a Strategic Plan (CON). Is This a New Inequality Theorem in Fuzzy Logic?

As I mentioned in my previous article of “Fuzzy Delphi Method to Design a Strategic Plan”, I would like to continue the debate on Distance Method.


But before going to the distance method, let me explain my story as follows:

While I was working on discrepancy between basic and distance method on driving forces, I encountered to a phenomena. Now, let me depict this phenomenon in the framework of a theorem below cited:


Inequality Theorem in Fuzzy Logic 


Assume, there is the fuzzy subset A of X where X is a universal set. Then, we define the fuzzy set of A by its membership function (MF=Membership Function) as follows:

MFA:  X   -------      [0, 1]     

It means that a real number MFA (x) in the interval [0, 1] is assigned to each element x where x is a member of X and also the value of MFA (x) at x presents the grade of membership of x in A.

We consider below conditions for the fuzzy set A:

-Fuzzy set A is a convex and normalized fuzzy set in which we can say the fuzzy set A is a fuzzy number.

- Fuzzy set A is a central triangular fuzzy number where we have:

For central triangular fuzzy number A= (a, b, c):   MFA (x) = 2(x-a)/c-a   If   a < x < b

                                                                           MFA (x) = 2(x-c)/a-c   If   b < x < c

                                                                           b = (a + c)/2

Now, we assume the set of S is included all central triangular fuzzy numbers as follows:

S = [Ai],             i = 1, 2, 3,…….n

In fact, we have:


You can review the continuation of this article on below link:

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