### I. Introduction

### II. Methods

### 1. General Anesthetics Parameters

#### 1) MAC (for inhaled anesthetics only)

#### 2) Blood:gas partition coefficient (for inhaled anesthetics only)

#### 3) Oil:gas partition coefficient (for inhaled anesthetics only)

#### 4) Onset of action (for both)

#### 5) Recovery time (for inhaled anesthetics only)

#### 6) Duration (for injected anesthetics only)

#### 7) Induction dose (for injected anesthetics only)

### 2. Fuzzy PROMETHEE and Application

*p*

*) denotes the difference between the evaluations obtained with two alternatives (*

_{j}*a*

*and*

_{t}*a*

*) with regards to a particular criterion, within a preference degree ranging from 0 to 1. There are 6 types of preference functions that can be used to implement the PROMETHEE method, namely, usual, U-shaped, V-shaped, level, linear, and Gaussian functions.*

_{t′}*j*, determine a specific preference function

*p*

*(*

_{j}*d*).

*w*

*= (*

_{T}*w*

*,*

_{1}*w*

*, …,*

_{2}*w*

*). At the discretion of the decision maker, the weights of the criteria can be taken equally only if their importance is equal. In addition, normalization can be used for the weights:*

_{k}*a*

*,*

_{t}*a*

*∈*

_{t′}*A*, define the outranking relation π:

*p*

*is the weighted average function,*

_{k}*A*is the alternative, and

*A*×

*A*denotes the set of all possible alternative pairs. Here, π(

*a*

*,*

_{t}*a*

*) denotes the preference index, which is a measure for the intensity of preference of the decision maker for an alternative*

_{t′}*a*

*in comparison with an alternative*

_{t}*a*

*while all criteria are considered simultaneously.*

_{t′}-
Leaving (or positive) flow for the alternative

*a*:_{t} -
Entering (or negative) flow for the alternative

*a*:_{t}

*n*is the number of alternatives. Here, each alternative is compared with

*n*-1 number of other alternatives. The leaving flow

*Φ*

^{+}(

*a*

*) expresses the strength of alternative*

_{t}*a*

*∈*

_{t}*A*, while the entering flow

*Φ*

^{-}(

*a*

*) denotes the weakness of alternative*

_{t}*a*

*∈*

_{t}*A*.

*a*

*is preferred to alternative*

_{t}*a*

*(*

_{t′}*a*

_{t}*Pa*

*) if it satisfies one of the following conditions:*

_{t′}*a*

_{t}*Pa*

*)*

_{t′}*if*

*a*

*and*

_{t}*a*

*have the same leaving and entering flows,*

_{t′}*a*

*is indifferent to*

_{t}*a*

*(*

_{t′}*a*

_{t}*Ia*

*):*

_{t′}*a*

*is incomparable to*

_{t}*a*

*(*

_{t′}*a*

_{t}*Ra*

*) if*

_{t′}*Φ*

*(*

^{net}*a*

*) value.*

_{t}^{2}), and type II diabetes. This patient would be assigned as Class 4E [22] according to the ASA physical status classification system. To apply fuzzy PROMETHEE to identify the most appropriate anesthetic to this individual, the weights were first selected and then the min/max preferences were rearranged after consultation with the anesthesiologists from various hospitals. The linguistic fuzzy scale was defined as shown in Table 7 (note the differences from Table 5 in terms of importance ratings of criteria), and the preferences were assigned as shown in Table 8 for inhaled and injected anesthetics.

### III. Results

### IV. Discussion

_{2}), whereas propofol has no effect on heart rate, and it decreases CBF and CMRO

_{2}[24]. On the other hand, based on its effect on CBF, propofol might be considered at lower doses for hemodynamically unstable patients. Thus, the choice of the “best” anesthetic depends on a number of criteria, and the proposed method provides a feasible solution.