Perc Decision Making Theory

This paper provides a new solution method for group multi-criteria decision making problems using Perceptual Computer (Per-C) theory. The Perceptual Computer (Per-C) is an instantiation of Zadeh’s CWW paradigm, as applied to assisting people in making subjective judgments. The Per-C consists of three components: an encoder, which maps words into IT2 FS models; a CWW engine, which operates on the input words and whose outputs are FOU(s); and a decoder, which maps these FOU(s) into a recommendation. Conceptual structure of Per-C, which was proposed to make subjective judgments by CWW, is shown in Fig. 1.

These three components are described in as follows:

CWW: There are different kinds of CWW engines.

ZADEH coined the phrase “computing

. . , n

2) For each α ∈ [0, 1], compute the α-cut of the FWA by recognizing that it is an IWA, i.e., Y_FWA (α) = Y_IWA (α), where
Y_IWA (α) = [l(α), r(α)]

In which: l(α)=■(min@∀ w_i (α)∈[c_i (α),d_i (α)] ) (∑_(i=1)^n▒〖a_i (α) w_i (α)〗)/(∑_(i=1)^n▒〖 w_i (α)〗)

r(α)=■(max@∀ w_i (α)∈[c_i (α),d_i (α)] ) (∑_(i=1)^n▒〖b_i (α) w_i (α)〗)/(∑_(i=1)^n▒〖 w_i (α)〗)

And the KM or EKM algorithms [29], [43], [77] are used to compute l(α) and r(α).

3) Connect all left coordinates (l(α), α) and all right coordinates (r(α), α) to form the T1 FS YFWA.

C. Linguistic Weighted Average (LWA):

The LWA is defined as [73], [75]

Y ̃_LWA= (∑_(i=1)^n▒〖 W ̃_i×X ̃_i 〗)/(∑_(i=1)^n▒〖 W ̃_i 〗)

where X ̃_i and W ̃_i are IT2 FSs, and Y ̃_LWA is also an IT2 FS. Again, (A12) is an expressive way to describe the LWA. To compute Y ̃_LWA, one only needs to compute its LMF ▁Y_LWA and UMF ¯Y_LWA.
Let W ̃_i be an embedded T1 FS [43] of W ̃_i , as shown in Fig. 13. Because in, X ̃_i only appears in the numerator of Y ̃_LWA,

Xi and an α-cut. The dashed curve is an embedded T1 FS of X