Kybernetes 1 Expertons and uncertain averaging operators versus correlational approaches : A case study on Corporate Social Responsibility and effectiveness

Purpose 
 
 
 
 
The purpose of this paper is to explore the relationship between corporate social responsibility (CSR), work-life balance (WLB) and effectiveness by comparing a correlational approach, expertons method and uncertain averaging operators (uncertain average [UA], uncertain weighted average [UWA], uncertain probabilistic aggregation [UPA] and uncertain probabilistic weighted averaging [UPWA]). 
 
 
 
 
Design/methodology/approach 
 
 
 
 
Participants were 814 employees from two Chilean companies with different levels of development on CSR policies. The Survey work–home Interaction – Nijmegen for Spanish Speaking Countries and the balanced scorecard were used. Results showed differences between companies with different levels of CSR development on individual effectiveness and relations between WLB and individual effectiveness. 
 
 
 
 
Findings 
 
 
 
 
Expertons methodology and uncertain averaging operators allow more accurate results than correlational statistics. 
 
 
 
 
Originality/value 
 
 
 
 
Expertons method and uncertain averaging operators (UA, UWA, UPA and UPWA) are common in the field of economics and engineering but very innovative in the human resources research, allowing more accurate analyses of workers’ perceptions.

The most used aggregation operators based on exact numbers are weighted average and the probabilistic aggregation.The first operator aggregates the information by giving different levels of importance to each argument in the problem.On the other hand, the probabilistic aggregation uses probabilities to aggregate the data.Merigó (2009) proposed a combination of both previous operators, the probabilistic weighted average (PWA) that considers the degree of importance of each concept in the analysis including the objective and the subjective information of the environment.
However, organizations are complex realities where information is not always so clear.To deal with this reality, Moore (1966) proposed interval numbers as a useful technique for representing uncertainty because it considers the minimum and the maximum results that may occur.When using interval numbers to aggregate the avalaible information we form uncertain aggregation operators.One operator based on interval numbers is the experton methodology.It enhances scientific rigor by measuring subjectivity and pooling the opinion of several experts to establish a single valuation (Gámez-González et al., 2010).It is regarded as a major step forward in the development of fuzzy subsets, given that it seeks objectivity, thanks to the use of aggregation as a solution (Gil Lafuente, 1997).This methodology has shown its suitability as an analysis tool in such different fields as quality assessment (Barreiro et al., 2007;Levrat et al., 1997), monitoring of stocks management (Reig and González, 2002), marketing (Zalila et al., 2005) and business ethics (Gámez-González et al., 2010).
Other operators based on interval numbers are the uncertain average (UA), the uncertain weighted average (UWA) and the uncertain probabilistic aggregation (UPA).Several studies use this kind of aggregation operators, such as the interval grey linguistic variables (Jin and Liu, 2010), the linguistic aggregation operators such as the linguistic probabilistic weighted average (LPWA) (Merigó et al., 2016), decision making under risk, interval vague set and the TOPSIS method (Liu, 2009(Liu, , 2010;;Zeng and Xiao, 2016), the induced and uncertain heavy OWA operators (Merigó and Casanovas, 2011), the Hungarian algorithm with the induced ordered K y b e r n e t e s 3 weighted averaging distance (HAIOWAD) (Vizuete-Luciano et al., 2015), the uncertain linguistic hybrid geometric mean operator (Wei, 2009), or the uncertain induced Minkowski ordered weighted average distance (UIMOWAD) operator (Zeng, 2013).Merigó (2011b) proposed a new decision making approach based on an operator that is the result of the union between the uncertain weighted average (UWA) and the uncertain probabilistic aggregation (UPA) operators.This result considers not only the subjective part of the assessment of the individual but also the objective of the subject being treated, and it is called the uncertain probabilistic weighted averaging (UPWA) or the interval probabilistic weighted average (IPWA).

Theoretical background: CSR and effectiveness
The Corporate Social Responsibility (CSR) approach has grown in importance and has become a possible answer to the necessity of developing a world class culture of responsible businesses, accompanied by more government regulation and the claim that every company must take into account all its stakeholders (Bolton et al., 2011).It seems that the era of world economic crisis and recessions may be a favourable scene to develop a business concept in which not only financial improvement is important, but also sustainable growth (Ali et al., 2010).
The use of CSR and its focus inside the organization generates competitive advantages in order to improve the organizational effectiveness.There exists theoretical and empirical evidence to accept that this affirmation is valid (Aharon et al., 2011;Ali et al., 2010;Brammer et al., 2007;Galbreath, 2010;Kim et al., 2010;Skudiene and Auruskeviciene, 2012;Turker, 2009;Vitaliano, 2010); however, in the opinion of some authors, there is little evidence regarding the internal impact of CSR (Bolton et al., 2011;Rodrigo and Arenas, 2008;Wolf, 2013).
The CSR addresses the strategic level of the organization, which in turn includes the development of different policies.In this paper we will focus on the analysis of familyresponsible policies and their effect on perceived balance between the personal and work areas (WLB).The analysis of this relationship has scarcely been studied from the scientific literature and some of the research has limitations in measuring the perception of WLB from the negative and one-dimensional side (Yuile et al., 2012).In order to overcome this weekness, in this paper we propose the Geurts and Demerouti model of WLB (2003, in Geurts et al., 2005).The authors defined WLB as a process in which an employee is affected positively or negatively by the interaction of both labour and non-labour ambits.In addition, this definition may be complete because it considers the interactions of both the labour and non-labour aspects in four different directions: negative work-home and home-work interaction, positive work-home and positive home-work interaction.
Related to effectiveness, Matthews (2011) indicates that there are several ways to understand it, however, this can be understood in terms of accomplishment of objectives, while performance is the measure by which organizations know if they are or not effective.In this way, a measure of effectiveness assesses the capacity of an organization to achieve its planned goals (Keh et al., 2006).
One of the most influential frameworks to assess effectiveness is the Balanced Scorecard (BSC) (Evans, 2004).The BSC is designed to provide companies with a measureable roadmap with so that they may know if they are achieving their goals (Kang and Fredin, 2012).Thus, with the use of the BSC companies define their strategic objectives and arrange them on a map according to the four perspectives: financial, customers, internal processes, and growth and learning (Kaplan and Norton, 1992;2004).

Procedure and sample
Two Chilean companies were chosen according to their external CSR reputation and family friendly policies using the following criteria: (1) National CSR rankings, (2) National CSR awards, (3) International CSR awards, and (4) IFREI level (Carlier et al., 2012;Chinchilla and Torres, 2006;2007).As a result, companies were classified according to CSR policy development.
Company 1 is a company in the lumber industry with 1,712 employees in total.It has a highlevel CSR policies development because it appears in the first 25 positions in a CSR national ranking and has several national and international awards and a B level on IFREI (Company has does not appear in any CSR national ranking and does not have any national or international awards.This company obtained a C level on IFREI (Company has some policies but their use is limited).
A non-probability for convenience sampling method was used.Instruments were sent to employees from both companies by the online platform QuestionPro in June and July 2012.
-Effectiveness.Balanced Scorecard (BSC) (Kaplan andNorton, 1992, 2004;Becker et al., 2001).The Balanced Scorecard is a business management model to help organizations to translate their strategy into measurable objectives.This model allows companies to design a performance appraisal based on their own key performance indicators to measure objectives accomplishment and strategic competencies development at the employee level (Becker et , 2001).In this study, in order to know this indicator the following question was added: "Please, report the result of the performance appraisal you obtained in 2011".Participants answered according to a five points scale (1= Critical to 5= Excellent).

Data analyses
A three data analysis strategy was employed: (a) correlational approach by t-test and correlations, (b) data analysis based on expertons method developed by Kaufmann and Gil-Aluja (1993), and (c) uncertain averaging operators (UA, UPA, UWA, and UPWA).
From expertons methodology the WLB scale establishes confidence intervals based on five anchors (Zalila et al., 2005).In this study, a group of ten academic and professional experts, with a minimum of 10 years' experience in the field of CSR, was asked to establish confidence intervals based on the five anchors.To do this, they used a 11-point scale (11 values between 0 -Null and 1-Totally) and considered confidence levels as [0,1].They allocated the Strongly agree response the value of 1, the value of 0 to Strongly disagree.Likewise, the responses Disagree, Neither agree nor disagree and Agree, being an uncertain level, were ascribed the values of [0.1, 0.4], [0.5, 0.5] and [0.6, 0.9] respectively.In this way, the imprecision in the validation corresponds to a specific situation that is semantically acceptable (Kaufmann et al., 1994, p. 45).
Finally, we considered the UA (uncertain average), as the basis for using the UPA, UWA and the UPWA operators, because they can analyse situations with subjective and objective information in the same formulation.For the UPA and UWA weights, each expert gives their own opinions.These opinions are consensuated in order to form the collective weights to be used in the aggregation process.The UPA operator use de following vector P = (0.2, 0.1, 0.4, 0.3) and for UWA V = (0.1, 0.1, 0.4, 0.4).It is important to note that the experts consensuated, on one hand, higher coefficients for the interaction Work-Home versus the interaction Home-Work.On the other hand, they consensuated higher coefficients for the positive interactions than for the negative ones.The UPWA operator uses UPA vector with a 40% of importance and the UWA vector with a 60%.

Correlational analyses
The t-test analyses, shown in Table 1, evidence that there is no statistical difference between both companies in any dimension of work-life balance (WLB).However, there is significant statistical evidence to support company differences in individual effectiveness which is favourable for company 1 with high-level in CSR and better level in family-friendly policies.2 shows the results obtained with the Pearson's correlation coefficient.As it is possible to see, coefficients for each dimension and individual effectiveness are close to zero with values between r = -.09(p = .01)and r = .004(p = .46).Only one of the four dimensions (negative HWI) has significant and negative correlation with individual effectiveness, however, the effect size calculated through the explained variance is small (r 2 = .008).

Expertons methodology
Table 3 shows the expected value of the expertons for each company related to individual effectiveness for WLB dimensions: NWHI, NHWI, PWHI and PHWI.
Results indicate that in the company with high levels of CSR policy development and family-friendly policies (Company 1) there is a positive relationship between the perception of balance and employee effectiveness.Thus, employees who obtain higher levels of effectiveness are those evaluated by experts as with lower NWHI ([0.22, 0.39]) and NHWI ([0.12, 0.30]) and with higher PWHI ([0.68, 0.83]) and PHWI ([0.70, 0.90]).
Instead, in the company with lower development of policies (Company 2) the results do not show a clear relationship between the perception of WLB and effectiveness.Thus, contrary to expectations, it was observed that high levels of PWHI ([0.53, 0.73]) and PHWI ([0.57, 0.71]) are related to lower levels of effectiveness (levels 1 and 2).Likewise, low levels of NWHI ([0.36, 0.5]) and NHWI ([0.13, 0.24]) are related to intermediate levels of effectiveness (do not take into account missing and non evaluated cases).

Uncertain operators
The results obtained in Table 3 can be aggregated in order to find a single result than permits us to known how the perceived balance between work and home domains is related with effectiveness (Table 4).
As previously, in Company 1, with high levels of CSR and family-friendly policy development, the higher the perceived levels of WLB, the higher the effectiveness (do not taking into account missing cases).By contrast, in Company 2, with lower levels of CSR and family-friendly policy development, the higher perceived levels of WLB, the lower the effectiveness.

CONCLUSIONS
The present study had as a purpose to go deeper in to the influence of CSR within the organization, particularly, on WLB and individual effectiveness using three methodological approaches: (a) the correlational approach, (b) expertons method (Kaufmann and Gil-Aluja, 1993), and (c) uncertain averaging operators (UA, UWA, UPA, and UPWA) (Merigó, 2011b).
It was expected to find differences in WLB and effectiveness between companies but this was not confirmed for WLB from the correlational approach.Our results point out that in spite of the fact that one company shows a better level in family-friendly policy development than another company, there are no differences between both companies on WLB.These findings are different from Yuile et al. (2012) who using different measures and method, found a significant relationship.
Knowing to what extent employees' WLB has an impact on their individual effectiveness, results showed a significant negative relationship, although small, for the negative home-work interaction (NHWI) which is consistent with other previous studies showing negative relationships between WLB and other measures of effectiveness such as productivity (Wallace and Young, 2008) or intention to quit (Parkes and Langford, 2008).Additionally, the low relation in this study could be explained because of the difficulties of giving a nominal and operational definition of this variable (Cameron, 1986;Richard et al., 2009).In this sense, the use of Balanced Scorecard could not only assume the weaknesses related with its capacity to compare companies with each other (Richard et al., 2009), but also could be affected by the difficulty of what is evaluated at the individual level as a performance appraisal (Kang and Fredin, 2012).Another plausible explanation could be found in the methodology based on the correlational approach, which assumes that the data are unambiguous and clearly known (Merigó, 2011b).
However, the methodologies based on the uncertain aggregation operators, namely expertons, UA, UPA, UWA and UPWA have allowed us a better approach to a complex reality from the multi-person evaluation.Following Merigó (2011b) we can affirm that these operators allows us to "unify decision-making problems under objective risk and under subjective risk in the same formulation and considering the degree of importance that each concept has in the analysis" (p.6101).
For the UPA and UWA weights, each expert of our selected group gives their own opinions, and these had been consensuated in order to form the collective weights to be used in the aggregation process.They decided higher coefficients for the interaction Work-Home versus the interaction Home-Work.On the other hand, they consensuated higher coefficients for the positive interactions than for the negative ones.This is aligned with the perspective related to the optimal functioning of individuals and groups in organizations, as well as the effective management of wellbeing at work and the development of healthy organizations (Seligman, K y b e r n e t e s 9 1999).In this sense, our work gives priority to management decisions oriented to the improvement of WLB against those directed towards reducing the negative effects of imbalance.
We applied common methodologies in the fields of economics and engineering, but very innovative in the field of human resources research, facilitating the analysis of the perception of workers.In the future, we should include organizations from other sectors, sizes and countries in order to get a deeper insight into the explored relationships.

7
With regard to the relation between WLB and individual effectiveness, Table

Table 1 .
). Descriptive statistics for SWING-SSC and effectiveness in both companies

Table 3 .
Expected value of expertons for Company 1 and Company 2. Note: * corresponds to employees who failed indicating their performance appraisal.** corresponds to employees not evaluated in the 2011 performance appraisal.