Applying fuzzy integral for evaluating intensity of knowledge work in jobs

Article history: Received February 2 2013 Received in revised format May 28 2013 Accepted May 3


Introduction
In today's world, work in organizations has become complex and knowledge-intensive, considerably (Eppler et al., 1999).The growing trend towards knowledge workers in the labor market is, indeed, one of the primary features of the economy and society (Drucker, 1995;Lavoie et al, 2003;Overbeek, 2007).Measuring and increasing the productivity of knowledge workers are the biggest management challenges during the 21 st century (Drucker, 1991(Drucker, , 1999)).In order to improve the performance of knowledge workers in a systematic manner, it is necessary to have a clear understanding of knowledge work and knowledge workers in the first place (Ramirez, 2008).Up to now, there is still no effective way to define knowledge work, which is the primary requirement of knowledge work productivity (Shi-You, 2008).Ramirez (2006) states "Some researchers (Helton, 1998;Drucker, 1999;Agarwalet al., 2011) argue that knowledge workers account for roughly 75% of the workforce.Although a lack of a clear definition of what constitutes a knowledge worker creates doubts on the reliability of that figure, we can assume that the number is high enough that, even if it is overestimated, it is significantly high." Most of the researches in knowledge work area have been very general and vague in definition of the knowledge work or knowledge workers (Akhavan 2010;Heidary et al., 2011).Since there have been few researches, which present a quantifiable definition of knowledge work, it can be claimed that there is currently no clear definition that is generally accepted in literature or in practice (Ramirez, 2004(Ramirez, , 2006)).With respect to particular attributes of this group of workers, this paradox results serious problems in defining of human resource management's systems (recruitment, compensation, productivity measurement, etc.).
In this article, a characteristic based definition of knowledge work is adopted and an appropriate framework is proposed to quantify knowledge work intensity of jobs.The rest of this paper is organized as follows: section 2 provides literature review in the field of knowledge work definitions and knowledge work quantification frameworks.Section 3 presents characteristics of knowledge work used in the developed framework.In Section 4, the framework is introduced and its steps are explained.In section 5, KWIS is calculated for two sample jobs to illustrate applicability of the framework.Finally section 6 draws conclusions and future researches.

Literature review
Despite the growing trend in knowledge workers' population and the increasing number of researches in this field, there is still not a unique definition for knowledge work and knowledge workers and the definition of knowledge work remains elusive (Guns & Valikangas, 1998;Pyoria, 2005;Shi-you, 2008).Most of these definitions are descriptive and hard-to-use in the practice of management (Shiyou, 2008).Heidary et al. (2011)  -Some dimensions and characteristics associated with the nature of the job are considered in order to define KW.
-KW is a job that has several (or all) of the aforementioned attributes.
-KW is a continuum and each job can have its own score.

Occupation based 2
-A list of occupations is prepared and each entry is regarded as a KW (e.g.researcher, engineer, teacher, and accountant) -KWrs have specific professions and other workers cannot be grouped in the same category.

Activity based 3
-A specific group of activities and tasks are considered to be the essential part of the KW.
-Two categories are considered by researchers: -Mental and high cognitive activities (like reasoning and refining).
Although the majority of thinkers believe two styles describe one entity and even some researchers simultaneously use two styles in their definition of knowledge work; but it seems that each style refers to various groups of jobs (Heidary et al., 2011).We can see this difference in survey of some knowledge work classifications.These differences must be considered in knowledge work quantification.Few studies have discussed knowledge work quantification.Jackson (1989) determined the parameters, which influence expected task completion time developed a method to calculate target time of knowledge work.This study can be categorized as the first paradigm of knowledge work definition (Heidary et al., 2011).
Shi-You (2008) presented a framework for analyzing content of knowledge work in a certain position.As a result, he divided the analysis model of position knowledge structure into two modules: "Core Content" and "Ability Application".The "Ability application" comprises ability of knowledge application, ability of skill application and ability of self-determination in working and three types of indexes are applied in "Core Content" module, including information collection and disposal, information and knowledge application, planning, reasoning and decision-making.Then by application of Position Analysis Questionnaire (PAQ) and empirical testing data, he selected 10 important subdivided indexes to six indexes of knowledge characteristic and calculated knowledge characteristic value (KCV) of position based on them (Shi-You, 2008).In this study both paradigm of knowledge work definition was applied (Heidary et al., 2011).Sen- Wang (2008) used Rough Set Theory for evaluation of Knowledge worker value.He attempted to evaluate work efficiency by determining 13 attributes knowledge work, which are important for its accomplishment (Sen- Wang, 2008).This study can be categorized as job-oriented and characteristic based.Ramirez (2006) defined knowledge workers on the basis of four knowledge work principles (Ramirez, 2006(Ramirez, , 2008)): -Knowledge work can be stated as a continuum, which varies from 0% to 100% knowledge work.
-Knowledge work is defined based on job characteristics (what the worker does) with no regarding of "who is knowledge worker".-Work or job that a worker does is defined by tasks that compose the job.
-Knowledge work characteristics can be used for measuring the knowledge work level in a task.He used literature review methodology and shapes a systematic review for 591 publications.He used frequency analysis to evaluate the characteristics and finally selected 8 characteristics for defining knowledge work.In addition, he proposed a mathematical model to quantify knowledge work (Ramirez, 2008).This study can be categorized as job-oriented and characteristic based.Heidary et al. (2011) proposed a structure to identify different kinds of activities that comprise a worker's job, and provide a framework for quantitative definition and segmentation of knowledge work.They postulated that every knowledge work has two main parts: working with knowledge and establishing communication.Thus, in order to provide an exact definition for the knowledge work it is necessary to calculate the knowledge intensity score of a job (JKIS) and communication intensity score of a job (JCIS).For determining these two parameters precisely, jobs were broken hierarchically to tasks and then activities.To identify these activities, an initial list of activities mentioned in the literature was created and then completed with generalized work activities of O*NET.A six-step framework for calculating of JKIS and JCIS was proposed and finally, different groups of knowledge workers with respect to JKIS and JCIS were identified by using a clustering method (Heidary et al., 2011).Three research gaps identified in the previous characteristic based knowledge work quantification frameworks are as follows: -former researchers did not use specific methodology for identifying tasks that compose the job; -weights of tasks is determined by only the ratio of time spent on the tasks, while other factors like importance of task must be considered, as well.-For calculating knowledge work intensity of tasks, former researchers use only simple average method.While it's obvious that criteria used for calculation do not have equal weight and there are interactions among them.Therefore, applying the simple average method is not appropriate.
In this article, a characteristic based framework for evaluating intensity of knowledge work in jobs that covers identified gaps is proposed.For covering these gaps, four principles presented by Ramirez (2006) are accepted and a mathematical model is presented for determining knowledge work intensity.

Knowledge work characteristics
Eight characteristics that were presented by Ramirez are: high level of autonomy, knowledge, creativity and innovation and complexity and low level of structure, tangibility, routine and repetitiveness and physical effort (Ramirez, 2006).Since Ramirez (2006) used a clear and acceptable approach for defining these characteristics, in the first step, we use his approach (literature review methodology) for identifying knowledge work characteristics.Ramirez (2006) reviewed studies published before 2007, thus we analyze other articles that he did not cover in his dissertation (especially cases that published after 2006).We gather 84 new articles in this field and analyze lists, categories, factors or characteristics, which can be implemented to differentiate knowledge work from manual work and then adjust them with characteristics introduced by Ramirez.Results revealed that these eight characteristics will cover all new characteristics, and then we accept Ramirez' eight characteristics in this article as criteria used for evaluating in the framework

Framework
In this section, the developed framework is introduced.As depicted in Fig. 2 the framework consists of five major steps.Explanation of each step is as follows: 4.1.Identifying job tasks by using FJA One of the gaps discovered in the literature is the absence of a methodology for task identification.Job analysis is a process for task identification, job specification distinction, etc. Table 2 presents some job analysis methods and their functions.

Table 2
Job analysis methods and their attributes (Madani, 2007) Job analysis method Focus level Input/output classification Personnel specification Job structural needs Mental processes Whereas these methods are developed for all types of works, we must select one method to first focus on the task level and then be appropriate for knowledge works.Among the techniques mentioned in Table 2, FJA is a method, which focuses on job tasks.In addition, this method presents tasks associated with the job, and, based on working with people, working with things, and working with data, scales the functions of workers.Furthermore this method is based on Subject Matter Experts (SMEs) like knowledge workers themselves and this is close to their autonomy discussed in the literature (Madani, 2007).FJA defines the exact tasks of a specific job or occupation.FJA is based on the premise that every job needs a worker to function in relation to things, data and people in different degrees.Task actions may be Physical (for example, operating an electrical typewriter), Mental (for example, analyzing data) or Interpersonal (for example, consulting another person).In FJA method, tasks consist of basic elements of job and they are defined in pursuit of organizational goals.Thus in first step of this method, analyst must define expected outputs of job and then describe tasks that provide these outputs (Fine, 1999;Levin et al., 1983).

Determining scores of tasks in each characteristic
After identifying job tasks, each task must be measured based on eight characteristics of knowledge work.Whereas these eight characteristics can't be measured quantitatively and have fuzzy attitude, then fuzzy variables are used for measurement.Table 3 lists the semantics (Herrera et al., 2000;Chang et al., 2006).
For determining TKIS, each SME notes a linguistic value that indicates the intensity or frequency in a particular characteristic for a particular task based on Table 3.Then we must derive fuzzy numbers that are comparable with linguistic terms (Fig. 3).For example, the linguistic term "Medium" is converted into a linguistic rating of 0.5 (Chang et al., 2006).For determining the score for a particular task (j) in a characteristic ( ) , it is necessary to classify these characteristics as regular or irregular (Ramirez;2006).Autonomy, knowledge, creativity and innovation and complexity are regular characteristics and then ) ( ) (i j x f for this characteristics are equal to linguistic values.Structure, tangibility, routine and repetitiveness and physical effort are irregular and then ) ( ) for these characteristics calculate based on Eq. 1.

Determining task's knowledge intensity score (TKIS)
As mentioned earlier, one of the deficiencies in the previous works was application of the simple average method in calculating knowledge intensity (regarding that these criteria don't have equal weight and there is interaction between them).Furthermore, scores of characteristics are fuzzy and then an appropriate approach must be selected.Five most often used aggregation operators are as below (Detyniecki, 2001;Grabisch, 1996) Each of these operators has mathematical and behavioral properties that can help researchers in selection of an appropriate operator (Detyniecki, 2001;Grabisch, 1996).The characteristics in our problem have following properties (Ramirez, 2006): -The dependency and interaction among characteristics must be considered.
-Each characteristic has a weight (relative importance) in compared with other characteristics.
-There are Substitutive/ Complementary relation between characteristics.
As Grabisch (1996) states, the fuzzy integrals are useful operators to model these conditions.
According to literature, the fuzzy integrals used in many situations like prediction of wood strength (Ishii & Sugeno, 1985), evaluation of strategies (Narukawa & Torra, 2007), evaluation of the capability of supplier (Kong et al., 2007), evaluation the students' performance (Shieh et al., 2009), warehouse location selection (Demiral et al., 2010), evaluating customer service perceptions on fast food stores (Hu.C, 2010), etc.There are two types of commonly used fuzzy integrals; Choquet and Sugeno integrals.In this article we use Choquet integral because this type is proposed for qualitative setting (Wagholikar & Deer, 2007).Definition 1: Let µ be a fuzzy measure on X. the choquet integral of a function where .(i) indicates that the indices have been permuted so that 1 ) ( ... ) ( 0 (Detyniecki, 2001;Demiral et al., 2010).More complete definitions can be found in (Detyniecki, 2001;Grabisch, 1996).Let X be the set of the characteristics that participate in TKIS and ) ( ) x 's score.Then it's enough to define fuzzy measures match to the set of the characteristic.

Introducing an appropriate method for calculating Fuzzy measures
Definition 2: A fuzzy measure µ defined on the set X is a set function satisfying the following axioms (Wang & Shen, 2006): For any A, B ⊆ X and A ∩ B = ∅, fuzzy measure values do not always satisfy the additive relation (μ (A) + μ(B) = μ (A ∪ B)) and according to Tan and Chen (2010) and Wang and Shen (2006) it can be stated as follows, The most difficult part in using fuzzy integrals is determination of fuzzy measures.Some methods can be found for this purpose in literature (Wagholikar & Deer, 2007).In this article, we use fuzzy measure identification method by diamond pair wise comparisons and s  transformation.Fig. 4 outlines the fuzzy measure identification in this method (Takahagi, 2008).Pairwise comparisons between two characteristics are described in Fig. 5 at 2 axes.The horizontal axis (additive line) means the pairwise comparison with respect to relative importance (weights).In middle point of this axis, two characteristics have equal weights and to left increase weight characteristic A and wise versa (Takahagi, 2008).The vertical line is associated with interaction degrees.In the bottommost point of this axis, either A or B is important (Both are not needed) and it means that the two evaluation items are substitutive.Against, in upmost point of this axis, both A and B is important (Takahagi, 2008).
) are Shapley value of the μ and ij I is the Murofush and Soneda's interaction index (Murofushi & Soneda 1993).With respect to these equations, fuzzy measure values for the diamond are estimated as Eq. ( 8).
In this method interaction degree indexes ( ij  ) has been used instead of ij I .This interaction degree indexes compute based on equation and function s  is defined as Eq. ( 9) Fore computing the weights of characteristics, we use AHP's eigenvalue method that weight ratio matrix's elements define as Eq. ( 10).
After calculating interaction degree indexes ( ij  ) and characteristics weigh, we define dissimilarity measure among the characteristics as average distance to other characteristics.More with Applying ordinal agglomerative hierarchical clustering method pairs of clusters that have smallest dissimilarity are merged (Takahagi, 2008).Then, we simplify the diagram by procedure that presented by Takahagi (Takahagi, 2008).Finally fuzzy measures identified by s  transformation based on hierarchical clusters that obtained.

Calculating Fuzzy measures of knowledge work characteristics
For extracting i sv and ij I of the eight characteristics, a questionnaire is prepared.Then this questionnaire is sent to 60 experts in the field of human resource management and knowledge management.52 experts responded and returned their filled questionnaires.Table 4 presents average of their proposed values for i sv and ij I (up i sv and bottom ij I ).In this table, Index i indicates columns and index j indicates rows.Then weights and interaction degree are calculated based on the method explained in above.Agglomerative hierarchical clustering method is applied in 6 repetitions; results are shown in Fig. 6.The simplified hierarchy diagram of this example is depicted in Fig. 7 (threshold value is 0.5).Fuzzy measures based on this figure are presented in appendix 1.

Calculating TKIS
In this step, TKISs are calculated based on Choquet integral, fuzzy measures (appendix 1) and task scores for each one based on eight characteristics.For example while supposed {f j ( x(1) ), …, f j ( x(8) )}score set for task j in 8 characteristics as 0≤f j ( x(1) ), …, f j ( x(8) )≤1 then TKIS for task j ( j c  ) is calculated by Eq.

(with respect to Choquet integral definition). In this relationship A
is fuzzy measure for A (i) set such that their values are presented in Appendix 1.Workers need a different proportion of the total time to accomplish each task.However, a task comprising less proportion of the total time may play an essential role in accomplishing a job.Such tasks usually form some parts of a job mission.For example, ''writing reports'' is the most important task of a laboratory technician; but, it comprises less proportion of the total time compared to his/her other tasks (Heidary et al., 2011).Based on the required proportion of the total time and the importance, two types of weights are assigned to each task.

Determining the time proportion weights
Determination of time proportions of tasks needs to apply time study.Selection of the appropriate method for the time study depends mostly on the nature of the job.Jackson (1989) and Groover (2007) chose different approaches in order to select a method for the time study.Results obtained via these two approaches are very similar.The first approach is more accurate, but requires more computational time.In this article, approach proposed by Groover ( 2007) is followed.Fig. 8 presents job structure hierarchy (Groover, 2007).As this figure indicates, researcher must select appropriate time study method based on job level and time that he/she wants to spend.Based on Table 5 and with respect to this reality that our study focuses on the task level (level 2), Direct Observation Methods like Stop-Watch and work sampling are appropriate methods.As direct observation methods focus on task level, then, major use of methods in this family is on level 2 of job structure hierarchy (Marashi, 1997).Another factor that must be considered in selecting time study approach is nature of the job.As knowledge workers must be involved in their performance evaluation process (Roger G. Schroeder, 1985;Mary R. Lind, 2000;Josu Takala;2006;Ramirez, 2008) then in this article self reporting technique is selected for time study.In this technique, workers that their job is studied are requested to report their situation and tasks that they are doing, in distinct times.It means that only difference between this technique and work sampling method that presented first time (Trippett, 1935) workers involved in time study procedure (Ampt, et al., 2007, Bell, 1999, Agustinus, 2007).The ratio of needed time to accomplish each task to the total time required to accomplish the job is defined as time proportion weight ( j W 1 ).

Determining the importance weights
There are various methods for determining importance of tasks in a job.For example, some job analysis methods can be used for this reason.However these methods are to some extent complicated and time consuming.Heidary et al. (2011) proposed an effective and simple method for determining importance of tasks which is utilized in this article.To determine the importance of the tasks, job incumbent and other SMEs are asked to assign a number from the set   7 ,..., 2 1 to each task (Heidary et al.,2011).The importance weight of tasks ( j W 2 ) is calculated by Eq. ( 12).

Calculating knowledge work intensity score (KWIS)
The following information can be obtained from pervious steps of the framework: -Tasks of the job, -Tasks' knowledge intensity scores ( j C  ) , -Time proportion weight ( j W 1 ) of the tasks, -Importance weight ( j W 2 ) of the tasks.
Knowledge work intensity score (KWIS) of a job which has n tasks is calculated by Eq. ( 13) as follows,

Application of the framework
In this part, knowledge work scores are calculated for two jobs to illustrate the applicability of framework.We consider one managerial job (Deputy of Finance and support) and one technician job (Laboratory technician) in a power plant for this reason.The jobs had job description, which could be used for identifying tasks of these jobs.SMEs in each field and HRM's experts were interviewed to extracting scores of the tasks in each knowledge work characteristic ( ) ( ) ), of the tasks and Importance weight ( j W 2 ) of the tasks.Also, time proportion weights ( j W 1 ) is obtained by interviewing incumbents of the jobs and applying the self-reporting method.

Example 1: Deputy of Finance and support
Job description: Planning, supervision and coordinating finance activities, public services, commerce (Procurement & Contracts), foreign subscribers and legal rights based on regulations in order to meeting organizational goals and programs.Tasks and their scores in each knowledge work characteristic (as Linguistic variables) have been listed in appendix 2. TKISs and time and importance weights for the tasks of this job are presented in Table 6.As this table shows, KWIS for first job (deputy Finance and support) is equal to 0.6121.

Example 2: Laboratory technician
Job description: Responsibility for installation, testing and maintenance measurement accessories with the aim of correct utilization and providing better services to subscribers; Tasks and their scores in each knowledge work characteristic (as Linguistic variables) for this job have been listed in Appendix 3. Table 7 presents calculation of KWIS for this job which is equal to 0.5225.

Summary and Conclusions
Presenting a knowledge work quantifiable definition is very important for Development of human resources management tools, especially in the field of knowledge workers' productivity management.In this article a framework is presented for quantitative definition of knowledge work.The framework covers identified gap in literature review by using appropriate job analysis method (FJA) time study method (Self reporting), fuzzy variables, and fuzzy integral and fuzzy measures.Results of using this methodology for quantifying knowledge intensity of two jobs (deputy Finance and support and Laboratory technician) indicate applicability of the framework.Based on these examples, job of deputy Finance and support is more knowledge intensive as a laboratory technician and experts agree with this result.This study provides many starting points for Future researches.Some studies in this field can be used for Statistical analysis of the results of this methodology and validate it by the Statistical test (at business level), mapping KWISs with previous knowledge work classifications (like Davenport, 2005) and provide clearer definitions of each class of knowledge workers.

Fig. 3 .
Fig. 3. Linguistic rating on membership function corresponding to fuzzy numbers

Fig. 7 .
Fig. 7. Simplified identified hierarchy diagram Determining tasks' time proportions and importance weights

Fig. 8 .
Fig. 8. Definitions of orders of work units

jW 2 :
Importance weight of task j j s : Number assigned to task j by SME n: Number of the job's tasks

Table 1
identified two paradigms and four streams for definition of knowledge work summarized in Table1as follows, Definition Streams for Knowledge Work or knowledge worker(Heidary et al., 2011)

Table 3
Linguistic interval scale

Table 5
Appropriate time study methods based on orders of work units

Table 6
KWIS calculation for Deputy of Finance and support

Table 7
KWIS calculation for Laboratory technician