MAGDMMethod with Pythagorean 2-Tuple Linguistic Information and Applications in the HSE Performance Assessment of Laboratory

There is a significant gap between the safety management in the Chinese colleges and many renowned colleges in other countries. The subject of this study is how to assess the performance of health, safety, and environment (HSE) in Chinese college laboratories. The assessment system is established by three parts. First of all, HSE performance assessment indicators for laboratories in Chinese colleges are identified based on the previous studies. Then set valued iteration is used to calculate the weights of the various indicators. Following that, multiple attribute group decision-making (MAGDM) method with Pythagorean 2-tuple linguistic operators is used to assess the laboratory HSE performance in colleges. Finally, taking a college in Sichuan Province as an example, the proposed method is used to assess the laboratory HSE performance. The assessment result shows that the proposed method used in this study is practical and feasible.


Introduction
Laboratories are important locations in colleges where experimental teaching, scientific research, and social services are conducted.They cover a wide range of disciplines, involving a large number of students, pathogenic microorganisms, inflammable and explosive chemicals, highly toxic substances, wastes, machining, electrical and electronic materials, instrument, and equipment which pose certain potential safety risks and hazards [1,2].Although laboratory safety management and risk precautions are highlighted in colleges [3], accidents have occurred frequently in laboratories in recent years causing casualties and property losses, which threaten the life and property safety of the students, teachers, and the teaching and scientific research environment [1].There is a significant gap between the safety management in laboratories of the Chinese colleges and many renowned colleges in other countries, where HSE management system is implemented and the gap is reflected in various aspects of the HSE management [3].HSE performance assessment is an important part of the safety management, which can fully assess the safety management effects and identify any inadequacy so that rectification can be made to ensure to implement dynamic and effective safety management and improve the safety performance continuously [4].
So far significant studies have been conducted and a sound assessment system and method have been formed on the HSE performance assessment, which are widely used in the safety management, risk assessment, environmental protection, occupational health, etc. in the petrochemical, foodstuff, textile, iron and steel, mining, nuclear power industry, etc. [4,5].The studies on laboratory HSE in colleges also focus on the establishment of HSE management system [6] and safety culture building [7].Little concern is given to the study of HSE performance assessment of college laboratories.Previously mainly analytic hierarchy process [8,9] is used to calculate the weights in terms of assessment methods, and quantitative comparative strategic management model [10], fuzzy comprehensive evaluation [11], dynamic fuzzy assessment [5], fuzzy cognitive map and relative risk analysis [12], etc. are used for the assessment.
We have the following concerns on the HSE assessment for college laboratories in China despite the increasingly proven assessment systems and methods.
(1) There is lack of HSE performance assessment indicators for the college laboratories.No dedicated HSE management institution or committee is created in the Chinese colleges.No specific law, regulation, and operation standard is available.And health, safety, and environmental protection are managed separately by different departments.Collaborative management and law enforcement are inadequate and systematic management is not formed which results in the absence of HSE performance assessment indicators for the college laboratories.
(2) Although the indicator weights are identified in the previous HSE system [11], the weights of the HSE indicator system of laboratories in the Chinese colleges should be redetermined due to the different assessment objects and purposes, the social value of assessment factors, management purpose of the decision-makers, the perception of the evaluators, etc.The element of the judgment matrix is the ratio between two assessment indicators for the previous analytic hierarchy process [8].The ratios are given by the experts, which make it hard for the judgment matrix to meet the consistence test due to the influence of the experts' perception and preference [13].In particular, it is harder to pass the consistence test when a number of assessment indicators are present [14].
(3) In addition, HSE performance assessment is conducted prior to actual work.Normally, the experts would conduct the subjective measurement based on the HSE management assessment system [15].Uncertainties, inadequacies, the experts' indecision, absence of clear boundary and denotation, etc. may have an impact on the accuracy and reliability of the assessment results [5].Fuzzy comprehensive evaluation method has overcome the disadvantages and has been widely used [16].The fuzzy sets theory [17] can contain more expert decision-making information, which makes the assessment results more reliable.Only membership is considered in the classical fuzzy multiattribute decision-making [18].Nonmembership is not considered and the indecision of the decision-makers is not fully reflected.Intuitionistic fuzzy set (IFS) [19] consider membership degree, nonmembership degree, and hesitation to the decision-making preference at the same time.But they are limited to cases where the sum of membership and nonmembership is less than 1 [20], while cases where the sum of membership and nonmembership exceed 1 and the sum of the squares is less than 1 cannot be assessed.
Therefore, first of all, an indicator system is established in this paper for HSE performance assessment of laboratories in Chinese colleges to solve the problems above.Second, the experts tend to provide an interval value for some indicators in terms of the indicator weight calculation comparing with a point value for the individual indicator based on the conventional thinking mode.Set valued iteration [21] has provided the solution, so it is used in this study to determine the indicator weights.Third, Pythagorean 2-tuple linguistic operator [20] can simultaneously meet the conditions of the preferences of membership, nonmembership, and indecision fuzziness; the sum of membership and nonmembership may exceed 1 and the sum of the squares is less than 1, which has extended the range of the previous fuzzy assessment.Since more than one expert is involved in the decision [22], multiple attribute group decision-making (MAGDM) method [23] with Pythagorean 2-tuple linguistic operators is used for the study of the HSE performance assessment of college laboratories.

Laboratory HSE Performance Assessment Indicators
An appropriate HSE performance assessment indicator system for college laboratories is the basis of HSE performance assessment, first, the assessment indicators and indicator system should be established properly, objectively, and systematically to ensure the accuracy of the assessment results.
In this paper, experts and management responsible for the laboratory safety in colleges are invited and Delphi method is used to reach a consensus based on the actual HSE conditions in colleges considering the previous studies on the laboratory HSE management system [1,24], HSE performance assessment indicators [5,11], etc. as well as the new framework for HSE performance measurement and monitoring [25].A performance assessment system is established including 29 measurement indicators, i.e., organization, objectives and commitment, risk assessment, hazard control, continuous improvement, training, information communication, internal review, rectification, and improvement.This indicator system reflects the HSE management features which highlight precautions, continuous improvement, optimization and motivation, all staff involved, and process control [5,11,24].The specific indicators are shown in Table 1.

Pythagorean 2-Tuple Linguistic Operators
In this section, we shall give some definitions of Pythagorean 2-tuple linguistic information, which is the foundation for establishing corresponding group decision-making methods.
To compute with words without loss of information, the 2-tuple linguistic model based on the concept of symbolic translation was proposed in [26,27].The model uses a 2-tuple (  , ) to represent linguistic information, where   ∈ ,  denotes the value of symbolic translation, and  ∈ [−0.5, 0.5).The specific definition of 2-tuple linguistic model is given as follows.
Definition 1 (see [26]).Let  = { 0 ,  1 , ⋅ ⋅ ⋅ ,   } be a linguistic term set and  ∈ [0,] be a value representing the result of a symbolic aggregation operation; then the 2-tuple that expresses the equivalent information to  is obtained with the following function: with   ,  = () Safety responsibility systems of the college, institutes, departments and laboratories are in place and the responsibilities and obligations of the parties involved are identified.
Hazard identification, risk assessment and control and preventive and control measures are in place.
Conventional fund, ear-marked fund or self-financed fund and resources are available for HSE management each year to ensure that the safety measures can be implemented properly.
u 8 HSE management system manuals and procedures are in place and well maintained.
Management and control process records in details are available.
Relevant trainings and publicity on occupational health, safety and environmental protection management are conducted on a regular basis at the college.
The teachers and students respond to, participate in and follow the HSE management requirements.
The relevant laboratory personnel have undergone trainings and have the HSE management awareness and capabilities.Plans and procedures should be in place to prevent and correct any failure of the hazard control, emergency preparedness and response procedures.
Have the ability to conduct the incident or accident investigation and root cause analysis and reporting.
u 28 HSE management system is reviewed by the college leaders and relevant requirements are rectified on a regular basis if they are inappropriate.where round(⋅) is the usual round operation,   has the closest index label to , and  is the value of symbolic translation.

Calculation of Objective Attribute
Assume If an indicator is never selected by any expert, it is insignificant and its weight coefficient is adjusted to

MAGDM Method with Pythagorean 2-Tuple Linguistic Weighted Average Operator
Step 1 (establishing Pythagorean 2-tuple linguistic decision matrix).Let evaluation experts score according to Pythagorean 2-tuple linguistic weighted average operator (P2TLWA).First, the grade of evaluation is selected according to the linguistic assessment, and the scope of the deviation is given.Then the degree of membership and nonmembership is scored for the number of 2-tuple linguistic information.
It combines the 2-tuple linguistic operator which allows the use of natural language for scoring and Pythagorean fuzzy number which contains more information.This method is used for scoring and integration, which is closer to the actual conditions.Pythagorean 2-tuple linguistic set consists of 2-tuple linguistic variable and degree of membership and nonmembership.2-tuple linguistic variable ( () , ) is used to show the specific score of a certain indicator in a certain scheme.Then Pythagorean membership  P() is used to express the support extent for the score and nonmembership V P() is used to express the opposition extent [20].
If the expert has already determined the score of the number of 2-tuple linguistic information, the membership degree is 1, and the nonmembership degree is 0.
Mark the score of the  expert on the  index as p = ⟨(  ,   ), (  , V  )⟩ and establish the corresponding Pythagorean 2-tuple linguistic decision matrix  = ( p ) × ..
Step 4 (calculation of the assessment result).According to the results of Step 3, the assessment result is Q.
The final results are assessed based on the calculation result Q and assessment rating.

Case Study
Taking the HSE performance management of the laboratory in a certain college in Sichuan Province of China as an example, the method above is used and five experts are invited to select and assess the performance indicators shown in Table 1.One expert is the safety person-in-charge of the college experiment equipment section.One expert is a professor specializing in safety management.The other three experts are the directors of chemical, biological, and engineering laboratories.The weight calculation and assessment are as follows.

Weight Calculation.
First, the experts are asked to select the most significant 5 indicators from the assessment indicators and then the second most significant 5 indicators from the remaining indicators, etc., until the last 4 indicators are left.The five experts select the indicator sets as per the rules, which are shown in Table 2.
Set valued iteration is used to calculate the indicator scores based on Table 2 using ( 9) and (10).The results are shown in Table 3.

MAGDM Method with P2TLWA Operator
Step 1 (establishing Pythagorean 2-tuple linguistic decision matrix).The linguistic assessment is rated uniformly.In this assessment activity, the linguistic assessment is rated as  = { 1 = very poor,  2 = poor,  3 = odinary,  4 = good,  5 = very good}.The linguistic sets are rated in many different ways, which are suitable for different assessment systems, areas, specifications, etc.An appropriate assessment rating helps reflect the actual conditions.The laboratory HSE performance is scored in the form of Pythagorean 2-tuple linguistic number by the five experts based on the 29 indicators.The weights and assessment scores are consolidated and shown in Table 4.
Step 2. The expert scores are integrated based on Table 4 to obtain each expert's Pythagorean 2-tuple linguistic weighted averages which are shown in Table 5.
Step 3. Calculate the scores of each expert's assessment which are shown in Table 6.
Step 4. The weights of the five experts are assumed as  = (0.15, 0.25, 0.15, 0.25, 0.2), respectively, due to their different knowledge background and experience.According to (14), we can get the result as follows.
The final result ( 3 , −0.2205) is obtained according to the proposed method.The final assessment result is lower than the ordinary level.
The assessment result is communicated with the relevant safety persons in charge of the college laboratory; ordinary level was evaluated by the college operation evaluation committee.Most previous evaluations mainly focused on the responsibility and obligation of the organization, the construction of experimental conditions, safety training, operational records, risk assessment, without involving the organizational system, management plans and procedures, information communication, accident investigation and analysis, internal review, and so on.The evaluation method was determined according to the experts' opinion.
Using the proposed method, not only the general level evaluation is given, but also the specific grade of the level is further reflected, so that the administrators can know more about the HSE management and take corresponding management decisions.Therefore, the assessment method of this study is more informative and exact.

Discussion
The establishment and implementation of HSE management system in college laboratories can protect the environment, improve the safety and health of the laboratories and the experiment conditions, and maintain the legitimate rights and interests of the teachers and students [24].The implementation of the system will help optimize the laboratory management, enhance the laboratory image, and create a better experimental environment and safety atmosphere.The establishment, implementation, and promotion of HSE management system in the Chinese colleges have been lagging behind.In particular, the Chinese colleges are pursuing the world first-class universities and disciplines in recent years.Most colleges are highlighting the building of laboratories while neglecting the HSE management.The systematic and structured HSE internal management mechanism has not formed.An appropriate HSE management performance assessment system is absent.
Pythagorean 2-tuple linguistic set assessment method [20] is used considering the uncertainty of expert assessment.Both membership (support) and nonmembership (opposition) are considered in the assessment of the indicators.And cases where the sum is greater than 1 but the sum of the squares is less than 1 are considered.This method properly reflected the hesitation when people conduct the assessment and considered the different preference of the decision-makers.In theory, it can obtain more informative and exact results for the HSE performance assessment of college laboratories.
But, on the other hand, there are still some limitations with the proposed method.(1) In the proposed method, it contains 29 assessment indicators that are indicative and reflect the comprehensive assessment of the HSE performance.However, there may be some deficiencies affected by the knowledge and the HSE concept of the experts.(2) And the weights of assessment indicators should be recalculated during assessment for laboratories of different disciplines and majors due to the different highlights of HSE management.(3) In addition, each indicator's assessment rating, membership, and nonmembership should be available when completing the forms and they should meet the appropriate value range requirements.The assessment experts may feel that they are complicated.

Conclusion
The college laboratory HSE performance assessment system is established based on the previous studies considering the current state of the HSE management of the college laboratories.
The assessment system contains three important parts including (1) creation of the indicator system, (2) determination of the indicator weight, and (3) assessment of the HSE performance.In terms of the assessment indicators, it is tailored for the college laboratory HSE management.Set valued iteration [21] is used to determine the weights.And MAGDM method with Pythagorean 2-tuple linguistic operators [20] is used for assessment.
The proposed assessment system in this study is used to carry out an empirical study on the HSE performance management taking the laboratory in a certain college as an example.The results have indicated that the assessment system proposed in this study is informative and exact.In our future work, we shall continue to do laboratory HSE performance assessment in college with other fuzzy decisionmaking methods according to its limitations [29][30][31][32][33][34].

u 29
Management measures are modified based on the changes of the laboratory and external circumstances.

Step 1 .
Weight.The system above indicates that all the indicators are in the same hierarchy.So set valued iteration[21] characterized by easy operation and calculation can be used to determine the weights of the indicators.It is a "function-driven" weight calculation method with preference.It corresponds to the weights based on the relevant impotence of the indicators, which can eliminate the personal subjective factors of the evaluators.Assuming the indicator set  = { 1 ,  2 , ⋅ ⋅ ⋅ ,   } and expert L, the indicator weights are calculated as per the steps of the set valued iteration.4.1.1.Selection of Indicator Subset.Selecting a positive integer (1 ≤  ≤ ), each expert selects the indicators strictly as per the following steps.Take expert  as an example.The expert selects the top  indicators he believes from set  to obtain the indicator set  1, = { 1,,1 ,  1,,2 , ⋅ ⋅ ⋅ ,  1,, }.Step 2. The expert selects the top 2 indicators he believes from set  to obtain the indicator set  2, = { 2,,1 ,  2,,2 , ⋅ ⋅ ⋅ ,  2,,2 }. . . . . . .Step s.The expert selects the top  indicators he believes from set  to obtain the indicator set  , = { ,,1 ,  ,,2 , ⋅ ⋅ ⋅ ,  ,, }.If natural numbers s and r(1 ≤  ≤ ) exist, and  ⋅  +  = , then the indicator selection of expert  is completed and  indicator sets are obtained.4.1.2.Calculation of (Indicative) Function.Function   (  ) is used to calculate the times of the various indicators in all the indicator sets selected by the experts:

Table 1 :
HSE performance indicators for college laboratories.College leaders are committed to the HSE management objectives and have clarified the HSE missions.

Table 3 :
Set valued iteration calculation results.

Table 4 :
Performance indicator scoring based on Pythagorean 2-tuple linguistic numbers.

Table 6 :
The scores of each expert's assessment.