This paper proposes a personalized comprehensive cloud-based method for heterogeneous multi-attribute group decision-making (MAGDM), in which the evaluations of alternatives on attributes are represented by LTs (linguistic terms), PLTSs (probabilistic linguistic term sets) and LHFSs (linguistic hesitant fuzzy sets). As an effective tool to describe LTs, cloud model is used to quantify the qualitative evaluations. Firstly, the regulation parameters of entropy and hyper entropy are defined, and they are further incorporated into the transformation process from LTs to clouds for reflecting the different personalities of decision-makers (DMs). To tackle the evaluation information in the form of PLTSs and LHFSs, PLTS and LHFS are transformed into comprehensive cloud of PLTS (C-PLTS) and comprehensive cloud of LHFS (C-LHFS), respectively. Moreover, DMs’ weights are calculated based on the regulation parameters of entropy and hyper entropy. Next, we put forward cloud almost stochastic dominance (CASD) relationship and CASD degree to compare clouds. In addition, by considering three perspectives, a comprehensive tri-objective programing model is constructed to determine the attribute weights. Thereby, a personalized comprehensive cloud-based method is put forward for heterogeneous MAGDM. The validity of the proposed method is demonstrated with a site selection example of emergency medical waste disposal in COVID-19. Finally, sensitivity and comparison analyses are provided to show the effectiveness, stability, flexibility and superiorities of the proposed method.
Multi-attribute group decision-making (MAGDM) refers to a decision situation where a group of decision-makers (DMs) provide their own opinions on a given set of alternatives under a set of attributes, and then select the optimal alternative(s) by aggregating their opinions [
Qualitative evaluations are not easy to be computed directly, especially when DMs use diverse forms of qualitative evaluations. At present, some models have been developed to deal with the calculations of qualitative evaluations, such as linguistic symbolic model [
Although the above mentioned cloud-based methods [ Some previous studies [ Few studies took DMs’ personalities into account during the transformation process. Wang et al. [ The comprehensive clouds in existing approaches [ Methods in [
To overcome the above limitations, this paper develops a personalized comprehensive cloud-based method for heterogeneous MAGDM, in which the evaluations of alternatives on attributes are represented as LTs, PLTSs and LHFSs. Regulation parameters of entropy and hyper entropy are proposed to reflect the DMs’ personalities. Two approaches are put forward to transform PLTS and LHFS into comprehensive cloud of PLTS (C-PLTS) and comprehensive cloud of LHFS (C-LHFS), respectively. The cloud almost stochastic dominance (CASD) relationship and CASD degree are initiated to compare clouds and further rank the alternatives. In addition, a novel approach is presented to obtain DMs’ weights and a comprehensive tri-objective programing model is constructed to determine the attribute weights. The proposed method is employed to the site selection of emergency medical waste disposal in COVID-19. Compared with existing studies, the major contributions of this paper are highlighted in the following four aspects:
Regulation parameters of entropy and hyper entropy are defined objectively. By incorporating regulation parameters into the transformation process, DMs’ personalities are reflected well. Moreover, DMs’ weights are objectively determined based on the proposed regulation parameters. From the perspectives of probability and membership degree, two approaches are put forward to transform PLTS and LHFS into C-PLTS and C-LHFS, respectively. The modified ratios of LTs decrease the loss and distortion of evaluation information. CASD relationship and CASD degree are defined and used to compare clouds. Based on the proposed comparison approach for clouds, the alternatives are ranked and the ranking results are stable and effective. A comprehensive tri-objective programing model is constructed to determine the attribute weights. In this model, three perspectives are considered, including differentiation between evaluation values, relationship between attributes and the amount of information contained in evaluation values. The setting of balance coefficients enables DMs to make a tradeoff in the three perspectives, which can improve the flexibility of the proposed method.
The remainder of this paper is organized as follows:
This section briefly introduces some concepts related to LTs and reviews cloud model as well as AFSD.
Let Ordered set: Negation operation:
In linguistic evaluation scales, the absolute deviation of semantics between any two adjacent LTs may increase, decrease or remain unchanged with increasing linguistic subscripts. To reflect various semantics deviation, linguistic scale functions (LSFs) [
Three kinds of LSFs are shown below:
In LFS1, the absolute deviation between adjacent LTs remains unchanged with increasing linguistic subscripts. Take
Lots of experimental studies [
LSF3 is defined based on prospect theory's value function and the DMs’ different sensation for the absolute deviation between adjacent linguistic subscripts.
In order to save all of the given information and facilitate calculation, the aforesaid functions can be extended into
In this paper, it is assumed that all PLTSs have already been normalized.
For simplicity, normal cloud is called as cloud hereafter. The degree of certainty of
There are two kinds of uncertainty: randomness and fuzziness. Randomness refers to the uncertainty contained in an event that has a clear definition but do not necessarily occur. Fuzziness refers to the uncertainty contained in an event that has appeared but it is difficult to define it accurately [
The AFSD is used to compare two stochastic variables. It was proposed by Leshno and Levy [
This section describes the heterogeneous MAGDM problem and introduces the improved transformation approach between LT and cloud in detail. Particularly, we developed two novel transformation approaches from PLTS and LHFS to comprehensive clouds.
A heterogeneous MAGDM problem is to find the best solution from all feasible alternatives assessed on multiple attributes by a group of DMs. The evaluation attributes in heterogeneous MAGDM can be classed into several subsets which are expressed by different kinds of forms.
For a heterogeneous MAGDM problem, suppose that DMs
Let
Generally, two kinds of approaches have been proposed for transformation from LTs to clouds so far. One is based on the golden radio [
Let
Entropy
It is obvious that
Obviously,
The determination of DM's hesitant degree is based on the average number of LTs that DM uses at a single evaluation in the form of PLTSs or LHFSs.
A great deal of experimental research has demonstrated that regulation parameter
In the following, an example is given to illustrate how to determine the value of
Calculate the average number of LTs used by DM
Calculate the hesitant degree of DM
Then, the value of
Hyper entropy
The closer the memberships for corresponding LTs are to 0, the larger indeterminacy degree DMs have for corresponding LT.
Clearly, it holds that
It is easily seen that
Take
Calculate the information entropy of each evaluation in the form of PLTSs by
Calculate the information entropy of DM
Calculate the indeterminacy degree of each evaluation in the form of LHFSs by
Calculate the indeterminacy degree of DM
Then, the value of
Then, the specific transformation procedures are shown as follows:
Calculate
Determination approaches for Calculate
Map
LSF2 Calculate
Calculate
Let
where
Calculate
Based on the above analyses, the corresponding cloud for LT
To illustrate the advantages of regulation parameters, an example is given below.
Based on
Based on
LT | |||||||
---|---|---|---|---|---|---|---|
0 | 0.2197 | 0.3812 | 0.5 | 0.6188 | 0.7803 | 1 | |
0.0000 | 2.1969 | 3.8122 | 5.0000 | 6.1878 | 7.8031 | 10.0000 | |
0.7323 | 0.6354 | 0.4672 | 0.3959 | 0.4672 | 0.6354 | 0.7323 | |
0.0258 | 0.0224 | 0.0164 | 0.0139 | 0.0164 | 0.0224 | 0.0258 |
LT | |||||||
---|---|---|---|---|---|---|---|
0 | 0.2197 | 0.3812 | 0.5 | 0.6188 | 0.7803 | 1 | |
0.0000 | 2.1969 | 3.8122 | 5.0000 | 6.1878 | 7.8031 | 10.0000 | |
0.8399 | 0.7288 | 0.5359 | 0.4541 | 0.5359 | 0.7288 | 0.8399 | |
0.2146 | 0.1862 | 0.1369 | 0.1160 | 0.1369 | 0.1862 | 0.2146 |
LT | |||||||
---|---|---|---|---|---|---|---|
0 | 0.2197 | 0.3812 | 0.5 | 0.6188 | 0.7803 | 1 | |
0.0000 | 2.1969 | 3.8122 | 5.0000 | 6.1878 | 7.8031 | 10.0000 | |
0.8399 | 0.7288 | 0.5359 | 0.4541 | 0.5359 | 0.7288 | 0.8399 | |
0.4657 | 0.4040 | 0.2971 | 0.2518 | 0.2971 | 0.4040 | 0.4657 |
Three sets of cloud generated by DMs
It can be seen from
In this sub-section, two approaches are brought forward to transform PLTS and LHFS into comprehensive clouds, respectively.
In this paper,
The specific procedures to determine Let Use
If The modified ratio of According to Definition 5, three numerical characteristics
Based on the above analyses, the comprehensive cloud of PLTS
Based on
Let Based on Based on Based on
Finally, the C-PLTS of
The PDFCs and 5000 cloud drops of
From
The specific procedures to determine Let Use
If The modified ratio of According to Definition 5, three numerical characteristics
Based on the above analyses, the comprehensive cloud of LHFS
Based on
Let Based on Based on Based on
Finally, the C-LHFS of
The NCs and 5000 cloud drops of
From
Up till now, heterogeneous MAGDM matrices in which attribute values are expressed with LTs, PLTSs and LHFSs can be transformed into homogeneous MAGDM cloud matrices. For simplicity, homogeneous MAGDM cloud matrix is called as cloud matrix hereafter. Then, the individual cloud matrix
In this section, some related techniques are introduced, such as the comparison approach for clouds, the determination approaches of DM weight vector and attribute weight vector. Significantly, a personalized comprehensive cloud-based method for heterogeneous MAGDM problem is proposed.
As mentioned above, the regulation parameter
Solving
By
Based on
The evaluations from DMs have been transformed to clouds. As mentioned above, if
According to the characteristics of cloud, AFSD theory is used to compare the dominance relationship between clouds with characteristics
If
As mentioned above, the CASD relationship is adapted to compare two clouds. However, this relationship cannot quantify the degree for one cloud over another. To quantify the dominance degree, CASD degree is put forward.
Let
Case | Comparison for characteristics | CASD degree |
---|---|---|
Case 1 | ||
Case 2.1 | ||
Case 2.2.1 | ||
Case 2.2.2 | ||
\raisebox{20pt}{Case 2.2.3} | ||
\raisebox{10pt}{Case 2.2.4} | ||
\raisebox{3pt}{Case 2.3} | ||
Case 2.4 |
To rank the alternatives and select the optimal alternative, the comparison approach for clouds is applied to the collective cloud matrix. Alternatives
Based on the comparison approach mentioned above, the CASD degree for the alternatives
Let
Then, the collective overall CASD degree matrix
As mentioned in
Let
Next, let
According to maximizing deviation approach [
Let
Then, let
From the perspective of correlation coefficient [
Let
It has been mentioned in
Combining
To solve the comprehensive tri-objective optimization model, we add three balance coefficients
To solve
The global optimal solution can be derived by taking partial derivatives of
By solving
After normalizing
Model 4 enables DMs to make a tradeoff in the above three aspects. Multifaceted considerations enhance the stability of the proposed method and the setting of balance coefficients improves the flexibility of the proposed method.
Up till now, the collective overall CASD degree matrix
Based on the values of
A personalized comprehensive cloud-based method for heterogeneous MAGDM problem is proposed in this sub-section. Particularly, the resolution procedures of the proposed method are depicted in
As depicted in
DMs identify the feasible alternatives
Hesitant degree
Based on
Firstly, pairwise comparisons are made to judge the CASD relationships for alternatives
Set the balance coefficients
In this section, the proposed method is applied to an example of emergency medical waste disposal site selection in COVID-19. Furthermore, sensitivity analyses are conduced to demonstrate the stability and flexibility of the proposed method.
At the end of 2019, COVID-19 broke out in various provinces and cities in China. The amount of medical waste kept rising along with the number of confirmed cases. The explosive growth of medical waste occurred in many cities, and the lack of disposal capacity made the situation more serious. In such an emergency situation, medical waste disposal becomes a special battlefield in the fight against pneumonia. If these massive amounts of medical waste that may carry the virus were not disposed in a safe and timely way, it was likely to cause secondary infections and further spread of COVID-19, which may result in a series of unimaginable aftermaths. Generally, qualified medical waste disposal companies existed previously were completely at full capacity in many cities during the outbreak of COVID-19. In order to cope with the increasing amount of medical waste, many local governments adopted a series of emergency measures. One of these measures was converting other waste disposal companies, such as industrial hazardous waste disposal companies and solid waste disposal companies, to medical waste disposal sites temporarily for emergency disposal of medical waste. The selection for emergency medical waste disposal sites can be regarded as a heterogeneous MAGDM problem.
To select a suitable emergency medical waste disposal site from five alternatives
The procedures are summarized in the following steps:
According to the proposed transformation approaches from LTs, PLTSs and LHFSs to clouds, C-PLTSs and C-LHFSs, the individual original normalized evaluation matrices
DM | Alternative | Attribute | ||||
---|---|---|---|---|---|---|
DM | ||||||
---|---|---|---|---|---|---|
2.05 | 0.2929 | 0.3163 | 0.6033 | 1.2258 | 0.5388 | |
1.6 | 0.2286 | 0.1783 | 0.325 | 1.1329 | 0.3214 | |
1.25 | 0.1786 | 0.0591 | 0.055 | 1.0567 | 0.08 | |
1.5 | 0.2143 | 0.1962 | 0.305 | 1.1115 | 0.3213 |
DM | Alternative | Attribute | ||||
---|---|---|---|---|---|---|
(7.8031, 0.7788, 0.3423) | (5.4413, 0.5195, 0.2283) | (6.6099, 0.6331, 0.2783) | (5.6086, 0.5319, 0.2338) | (7.8031, 0.7788, 0.3423) | ||
(5, 0.4853, 0.2133) | (9.293, 0.854, 0.3754) | (7.8031, 0.7788, 0.3423) | (7.0278, 0.6877, 0.3023) | (5.5683, 0.5289, 0.2325) | ||
(6.1878, 0.5727, 0.2517) | (6.9734, 0.6808, 0.2992) | (3.9486, 0.5742, 0.2524) | (5.5797, 0.5298, 0.2329) | (1.0657, 0.8421, 0.3702) | ||
(3.8122, 0.5727, 0.2517) | (4.2722, 0.5405, 0.2376) | (9.5102, 0.8726, 0.3835) | (8.9592, 0.8435, 0.3707) | (4.3713, 0.5334, 0.2344) | ||
(5, 0.4853, 0.2133) | (8.4004, 0.8129, 0.3573) | (5.7278, 0.5405, 0.2376) | (7.9979, 0.7609, 0.3344) | (5.6323, 0.5336, 0.2345) | ||
(7.8031, 0.7198, 0.2042) | (10, 0.8296, 0.2354) | (5.4474, 0.4806, 0.1363) | (5, 0.4485, 0.1272) | (5, 0.4485, 0.1272) | ||
(10, 0.8296, 0.2354) | (7.8031, 0.7198, 0.2042) | (8.7712, 0.7701, 0.2185) | (8.9227, 0.7777, 0.2206) | (8.8599, 0.7746, 0.2197) | ||
(6.1878, 0.5293, 0.1502) | (7.8031, 0.7198, 0.2042) | (4.8092, 0.4625, 0.1312) | (6.1878, 0.5293, 0.1502) | (4.384, 0.4921, 0.1396) | ||
(3.8122, 0.5293, 0.1502) | (2.8373, 0.651, 0.1847) | (7.8031, 0.7198, 0.2042) | (7.0257, 0.6353, 0.1802) | (7.8031, 0.7198, 0.2042) | ||
(2.1969, 0.7198, 0.2042) | (9.3789, 0.8001, 0.227) | (9.8327, 0.8218, 0.2331) | (8.8812, 0.7756, 0.22) | (7.0036, 0.6327, 0.1795) | ||
(7.8031, 0.6714, 0.0508) | (5, 0.4184, 0.0317) | (7.6838, 0.6599, 0.05) | (3.8122, 0.4937, 0.0374) | (10, 0.7738, 0.0586) | ||
(10, 0.7738, 0.0586) | (5.9868, 0.4818, 0.0365) | (7.8031, 0.6714, 0.0508) | (7.0012, 0.5899, 0.0447) | (7.8031, 0.6714, 0.0508) | ||
(6.1878, 0.4937, 0.0374) | (5, 0.4184, 0.0317) | (3.8122, 0.4937, 0.0374) | (5, 0.4184, 0.0317) | (5, 0.4184, 0.0317) | ||
(3.8122, 0.4937, 0.0374) | (3.8122, 0.4937, 0.0374) | (7.9834, 0.6804, 0.0515) | (7.8031, 0.6714, 0.0508) | (3.8122, 0.4937, 0.0374) | ||
(2.1969, 0.6714, 0.0508) | (7.8031, 0.6714, 0.0508) | (10, 0.7738, 0.0586) | (7.8031, 0.6714, 0.0508) | (6.9955, 0.5893, 0.0446) | ||
(5, 0.4401, 0.1272) | (4.2757, 0.4899, 0.1416) | (5.4488, 0.4716, 0.1363) | (3.8122, 0.5193, 0.1501) | (3.8122, 0.5193, 0.1501) | ||
(6.1878, 0.5193, 0.1501) | (6.7982, 0.5968, 0.1725) | (7.8031, 0.7062, 0.2041) | (6.1878, 0.5193, 0.1501) | (4.4396, 0.4791, 0.1385) | ||
(7.8031, 0.7062, 0.2041) | (7.8031, 0.7062, 0.2041) | (4.345, 0.4854, 0.1403) | (5.6031, 0.4819, 0.1393) | (1.0895, 0.7624, 0.2204) | ||
(5, 0.4401, 0.1272) | (4.0077, 0.5071, 0.1466) | (7.346, 0.6587, 0.1904) | (7.8031, 0.7062, 0.2041) | (2.1969, 0.7062, 0.2041) | ||
(6.1878, 0.5193, 0.1501) | (10, 0.8139, 0.2353) | (10, 0.8139, 0.2353) | (10, 0.8139, 0.2353) | (6.988, 0.619, 0.1789) |
Alternative | Attribute | ||||
---|---|---|---|---|---|
(7.0959, 0.6585, 0.1963) | (6.1492, 0.5814, 0.1718) | (6.3498, 0.5691, 0.1596) | (4.4651, 0.4975, 0.1449) | (6.7577, 0.6468, 0.1845) | |
(8.0437, 0.6825, 0.1719) | (7.301, 0.6584, 0.2152) | (8.044, 0.7275, 0.2156) | (7.2794, 0.6457, 0.1912) | (6.773, 0.6309, 0.1685) | |
(6.5953, 0.5778, 0.1707) | (6.7972, 0.632, 0.1975) | (4.2219, 0.5013, 0.1495) | (5.563, 0.4864, 0.1469) | (3.0776, 0.6328, 0.2113) | |
(4.1119, 0.5069, 0.1507) | (3.7104, 0.5491, 0.1599) | (8.0814, 0.7271, 0.2227) | (7.8396, 0.7092, 0.2161) | (4.509, 0.62, 0.1796) | |
(3.7613, 0.6157, 0.1609) | (8.8683, 0.7701, 0.2301) | (9.1087, 0.7569, 0.1994) | (8.6644, 0.7531, 0.2214) | (6.7245, 0.5976, 0.1662) |
- | 0.4259 | 0.5036 | 1.0000 | 1.0000 | - | 0.4676 | 0.4638 | 1.0000 | 0.0000 | - | 0.5000 | 0.6141 | 0.5000 | 0.0000 | |
0.5741 | - | 0.5000 | 1.0000 | 1.0000 | 0.5324 | - | 0.5409 | 1.0000 | 0.5000 | 0.5000 | - | 1.0000 | 0.4959 | 0.4097 | |
0.4964 | 0.5000 | - | 1.0000 | 1.0000 | 0.5362 | 0.4591 | - | 1.0000 | 0.5000 | 0.3859 | 0.0000 | - | 0.0000 | 0.0000 | |
0.0000 | 0.0000 | 0.0000 | - | 0.5759 | 0.0000 | 0.0000 | 0.0000 | - | 0.0000 | 0.5000 | 0.5041 | 1.0000 | - | 0.4132 | |
0.0000 | 0.0000 | 0.0000 | 0.4241 | - | 1.0000 | 0.5000 | 0.5000 | 1.0000 | - | 1.0000 | 0.5903 | 1.0000 | 0.5868 | - | |
- | 0.0000 | 0.3669 | 0.0000 | 0.0000 | - | 0.4968 | 1.0000 | 1.0000 | 0.5000 | ||||||
1.0000 | - | 0.5000 | 0.4624 | 0.4547 | 0.5032 | - | 1.0000 | 1.0000 | 0.5000 | ||||||
0.6331 | 0.5000 | - | 0.0000 | 0.0000 | 0.0000 | 0.0000 | - | 0.2076 | 0.0000 | ||||||
1.0000 | 0.5376 | 1.0000 | - | 0.4319 | 0.0000 | 0.0000 | 0.7924 | - | 0.0000 | ||||||
1.0000 | 0.5453 | 1.0000 | 0.5681 | - | 0.5000 | 0.5000 | 1.0000 | 1.0000 | - |
0.7324 | 0.4828 | 0.4035 | 0.0917 | 0.7492 | |
0.7685 | 0.6433 | 0.6014 | 0.6043 | 0.7508 | |
0.7491 | 0.6238 | 0.0965 | 0.2833 | 0.0519 | |
0.1440 | 0.0000 | 0.6043 | 0.7424 | 0.1981 | |
0.1060 | 0.7500 | 0.7943 | 0.7784 | 0.7500 |
With the obtained attribute weight vector, the total CASD degrees of
Thus, the ranking order is
LSFs are strictly monotonously increasing with respect to the subscript
No. | LFS | Balance coefficients | Total CASD degrees | Ranking of alternatives |
---|---|---|---|---|
1 | LFS1 | |||
2 | ||||
3 | ||||
4 | ||||
5 | LFS2 ( |
|||
6 | ||||
7 | ||||
8 | ||||
9 | LFS3 ( |
|||
10 | ||||
11 | ||||
12 |
As can be seen from
Furthermore, the proposed method can handle various decision situations and meet different DMs’ preferences by taking different LSFs and balance coefficients. Thus, the flexibility of the proposed method can be reflected by the acquired ranking results derived by various selections of LSFs and balance coefficients.
To justify the advantages of our proposal, comparison analyses with methods based on cloud and other classical MAGDM methods are conducted. Besides, a summary of transformation approaches with different evaluation forms is presented.
Peng et al. [ The cloud in [ The method in [ The proposed approach to determining DMs’ weights is superior to [
It can be seen that The ranking of alternatives is based on the expected score values of clouds in [
Lin et al. [ Solve the adapted example of this paper by the methods in [
Since Lin et al.'s method just cloud handle the MAGDM problems with PLTSs, we only retain the evaluations on
Method | Ranking result |
---|---|
TOPSIS-ScoreC-PLTS method in [ |
|
VIKOR-ScoreC-PLTS method in [ |
|
Proposed method of this paper |
It is easy to find that Solve the example in [
The proposed method could handle MAGDM problems with LT, PLTS, LHFS or one of them. As a result, the proposed method could settle the example in [
DM weight vector:
Attribute weight vector:
The total CASD degrees:
Therefore, the final ranking order is
The ranking order by method in [
Previous studies [
Approach | The form of evaluation | Probability | Membership | Interval concept | Personality of DMs |
---|---|---|---|---|---|
Wang et al. [ |
LT | - | - | - | - |
Wang et al. [ |
LT | - | - | - | Yes |
Zhu et al. [ |
LT and LHFS | - | Yes | - | - |
Peng et al. [ |
LT and PLTS | Yes | - | - | - |
Zhou et al. [ |
LT and HFLTS | - | - | - | - |
Mao et al. [ |
LT and Interval- |
Yes | Yes | ||
Peng et al. [ |
LT and Uncertain Z-number | - | - | Yes | - |
Jia et al. [ |
LT, Atanassov's interval-valued Intuitionistic fuzzy sets and Z-numbers | - | Yes | Yes | - |
Wang et al. [ |
LT and Unbalanced linguistic distribution assessments | Yes | - | - | - |
Wang et al. [ |
LT and PLTS | Yes | - | - | - |
Transformation approaches of this paper | LT, PLTS and LHFS | Yes | Yes | - | Yes |
In summary, we find that most existing studies can only process LTs, or LTs with probability, or LTs with membership or LTs with interval concept. However, this paper provides the transformation approaches for LTs, LTs with probability and LTs with membership, simultaneously. Moreover, there are few studies that take DMs’ personalities into account during the transformation process. Although Wang et al. [
This paper develops a personalized comprehensive cloud-based method for heterogeneous MAGDM, in which the evaluations of alternatives on attributes are represented as LTs, PLTSs and LHFSs. The validity of the proposed method is demonstrated with a site selection example of emergency medical waste disposal in COVID-19. The effectiveness, stability, flexibility and superiorities of the proposed method are proven by sensitivity and comparison analyses, respectively. Compared with the existing methods, the proposed method of this paper has the following prominent superiorities:
With the proposed regulation parameters, the width and thickness of clouds for the corresponding LTS are different for different DMs, which makes the DMs’ personalities can be reflected in clouds. Besides, a novel approach to obtaining DM weight vector is constructed based on the proposed regulation parameters. The new transformation approaches from PLTS and LHFS to C-PLTS and C-LHFS decrease the loss and distortion of evaluation information. CASD relationship and CASD degree are initiated in this paper to compare clouds. With CASD relationship and CASD degree, alternatives in the form of clouds can be ranked and the ranking results are stable and effective. This innovation provides new perspective for pairwise comparisons of clouds. The comprehensive tri-objective programing constructed in this paper enables DMs to make a tradeoff among three different aspects. Multifaceted considerations enhance the stability of the proposed method and the setting of balance coefficients improves the flexibility of the proposed method.
Although an example of emergency medical waste disposal site selection in COVID-19 is illustrated to the effectiveness of the proposed method, and it is expected to be applied to more real-life decision-making problems, such as investment selection, supply chain management, and so on. More effective transformation approaches for other evaluation forms, especially LTs with interval concept are waiting for us to come up with and apply them to heterogeneous MAGDM problems. Additionally, how to extend some classical decision-making methods to heterogeneous MAGDM based on cloud is also very interesting and deserves to be studied in the future.