Fuzzy Sets in HR Management

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1 Acta Polytechnica Hungarica Vol. 8, No. 3, 2011 Fuzzy Sets in HR Manageent Blanka Zeková AXIOM SW, s.r.o., Zlín, Czech Republic Jana Talašová Faculty of Science, Palacký Univerzity, Oloouc, Czech Republic Abstract: The ai of this paper is to deonstrate the different possible applications of fuzzy sets in HR anageent. This project is currently being carried out by the AXIOM SW copany, which specializes in the ipleentation of the Microsoft Dynaics NAV inforation syste. The evaluation of eployees is based on ultiple criteria evaluations. The criteria are derived fro typical copetencies of the eployees. A copetency odel has been created for any given role with different noralized weights assigned to various copetencies. The evaluation proceeds in the following anner: Firstly, the appointed evaluators fill in a questionnaire indicating to what extent, in their view, the tested eployee eets his/her copetencies. These evaluations are expressed using fuzzy scales. Noralized weights assigned to the evaluators of any given eployee are set based on the intensity of cooperation between the eployee and his/her evaluators. The level of fulfilent of each copetency by the given eployee is calculated as a weighted average of the fuzzy evaluations, conducted by each of his/her evaluators. Then, the overall fulfilent level of the eployee s working role, again as a weighted average of fuzzy nubers, is calculated according to a specified odel. This produces an overall evaluation of the eployee. The evaluation process is followed by an interview where the eployee is infored of his/her evaluation results, the eployees gaps are discussed, and possibilities for iproveent are proposed. Keywords: evaluation; fuzzy sets; huan resources 1 Introduction Evaluation has becoe part of our lives. In soe areas, evaluation is easier (based on easurable characteristics), while in others, ore coplex. There are any different concepts or types of evaluation. The eployees evaluation presented in this paper is essentially a ultiple criteria evaluation. 113

2 B. Zeková et al. Fuzzy Sets in HR Manageent In psychoetrics, it is coon to use discreet scales with sharp real values. The theory of fuzzy sets allows for the use of such linguistic fuzzy scales, where the various scale values are expressed linguistically and odelled by fuzzy nubers. The purpose of using the instruents of linguistic fuzzy odelling is, on the one hand, an exact atheatic data processing that excludes unwanted subjective influence, and, on the other hand, the natural expression of the expertly defined vague evaluations using natural language. The application of fuzzy sets in psychoetrics has been studied by Michael Sithson (see [4]). A siilar proble the eployees evaluation is also solved e.g. in the article A ulti-granular linguistic odel for anageent decisionaking in perforance appraisal (see [1]). 2 Applied Notions and Methods 2.1 Fuzzy Set A fuzzy set A in a universal set U is uniquely deterined by its ebership : U 0,1 A = x U, A x α, α 0,1 are called α-cuts of function: A [ ]. Sets α { ( ) } [ ] the fuzzy set A, a set A = { x U, A( x) > 0} set A, and a set A = { x U, A( x) =1} Supp is called a support of the fuzzy Ker is called a kernel of the fuzzy set A. The fuzzy set A is called noral if KerA. 2.2 Fuzzy Nuber A fuzzy nuber C is a fuzzy set defined in the set of real nubers R with the following properties: Ker C, Supp C is bounded, α-cuts C α are for all α (0, 1] closed intervals. A fuzzy nuber C is said to be defined in an interval [ A, B], if its ebership function is equal to 0 outside the interval. In the presented odel, trapezoidal fuzzy nubers defined in an interval [ A, B] are used. A trapezoidal fuzzy nuber C in the interval [ A, B] is defined by four points, ( x 0),( x,1),( x,1),(,0), where A x x x x B 1, 2 3 x ; the ebership function of C depends on the paraeters x 1, x2, x3, x4 in the following way: for any x [ A, B] it holds that C ( x) = 0 for x < x1 ; C( x) = ( x x1 )/( x2 x1 ) for x1 x x2 ; C ( x) = 1 for x 2 < x < x3 ; C( x) = ( x4 x) /( x4 x3 ) for x3 x x4 ; C ( x) = 0 for x 4 < x. 114

3 Acta Polytechnica Hungarica Vol. 8, No. 3, Fuzzy Scale (see [5]) We say that fuzzy nubers partition of the interval [ B] 1, S defined in the interval [ B] S T i i x 1 for any x [ A, B]. 1 T T = = A, if ( ) A, for a fuzzy A fuzzy scale is a set of fuzzy nubers T, TS A, B that for a fuzzy partition of this interval and are nubered according to their order. 2.4 Linguistic Variable (see [5]) 1 defined in the interval [ ] A linguistic variable is characterized by a quintuple ( V, T ( V ), X, G, M ), where V T is a set of its linguistic values, X R is a is a nae of the variable, ( V ) universal set in which the fuzzy nubers representing the eanings of the linguistic values are defined, G is a syntactic rule for generating linguistic values of V, and M is a seantic rule for setting atheatical eanings, i.e. fuzzy T V. nubers in X, to linguistic values fro ( ) 2.5 Linguistic Fuzzy Scale (see [5]) ( V, T V, A, B, G, M ) is a linguistic variable and that Let us suppose that ( ) [ ] eanings of its linguistic values for a fuzzy scale in [ A, B]. Then we stipulate that the linguistic variable represents a linguistic scale in [ A, B]. Linguistic scales eet the properties logically expected fro verbally defined scales: eanings of linguistic values that are odelled by fuzzy nubers are linearly ordered and each A, B either entirely pertains to a certain eleent of the scale, point of the interval [ ] or its pertaining is divided between two subsequent values on the scale. For odelled linguistic values, the above entioned trapezoidal fuzzy nubers defined by four points are suitable. 2.6 Weighted Average of Fuzzy Nubers (see [5]) The weighted average of fuzzy nubers C,,C A, B, with noralized weights v, v 0, j = 1,,, v = 1, is a fuzzy nuber C = = v j j C 1 j by the following relation 1 defined in the interval [ ] j j j = 1 j the ebership function of which is for any c [ A, B] defined { { 1 1 } [ ] j = 1 j j j } Cc ( ) = ax in C( c),..., C ( c ) c= v c, c AB,, j= 1,, The weighted average of fuzzy nubers (with real weights) defined in this way is a fuzzification of weighted average of real nubers according to the definition of 115

4 B. Zeková et al. Fuzzy Sets in HR Manageent the extension principle. In the presented eployee evaluation odel this definition of weighted average of fuzzy nubers will be used for the aggregation of partial evaluations given by different evaluators. 2.7 Fuzzy Weights (see [3]) Fuzzy nubers j, = 1,,, 0,1 are called noralized fuzzy weights, if for each α ( 0, 1] and for each i { 1,, } the following holds: for each vi V i α (an α cut of V i ) there exist v V, j = 1,,, i j, such that V j defined in the interval [ ] i + j = 1, j i v v = 1. j j jα 2.8 Fuzzy Weighted Average (see [3]) Fuzzy weighted average of fuzzy nubers [ B] on the interval [ B] C,,C 1 defined in the interval A, with noralized fuzzy weights V, j = 1,,, is fuzzy nuber C defined defined by the following relation j A,, the ebership function of which is for each c [ A, B] { C1( c1) C( c) V1( v1) V( v) } in,...,,,..., C( c) = ax. c = v, 1, 0, 1,...,, [, ], 1,..., j 1 j cj v j 1 j = vj j = cj a b j = = = In the presented fuzzy odel this definition of fuzzy weighted average of fuzzy nubers will be used for the aggregation of partial evaluations against different criteria. 3 Eployee Evaluation First, the procedure of the eployee perforance evaluation will be deonstrated. The evaluation of eployees is based on ultiple-criteria evaluations. The criteria are derived using the typical copetencies of the eployee. 3.1 Copetency Model Copetencies are the suary of the knowledge, skills, abilities, attitudes and values necessary for personal developent and self-assertion of every eber of society. The copetency odel is always created in ters of the work for a given working role. It reflects the copetency coposition that is necessary for carrying out a particular type of work. 116

5 Acta Polytechnica Hungarica Vol. 8, No. 3, 2011 The copetency odel was created fro ultiple sources of inforation. 13 general copetencies were set as the basis (see [2]). A questionnaire was put together for the evaluators to express their opinion on what copetencies the eployees in their particular roles should have. To these general copetencies, specific copetencies were added as well for each specified role. Materials fro the Microsoft copany were used as the basis for the specified copetencies in the following roles: project anager, developer, and consultant. In the Axio SW copany, the following roles were identified: senior executive, project anager, analyst, consultant, developer, dealer, and arketing agent. Since the roles specified in the Microsoft aterials do not entirely atch with the roles in Axio, copetencies stipulated in these docuents were assigned to roles in the Axio copany according to the real classification of working activities. Figure 1 Copetency Model The copetencies are divided into three groups: INPUT (knowledge, skills), OUTPUT (results) and PROCESS (behaviour). The weights of copetencies can be represented either by real nubers or by fuzzy nubers (for the atheatical structure of noralized fuzzy weights see 2.7). 3.2 Evaluators The structure of the evaluators is based on the copany s organisational structure. A given eployee will always be evaluated by those eployees he/she ost closely cooperates with, i.e. his/her direct supervisor, and collaborators on the sae project, and in the case of anagers, also by their subordinates. 117

6 B. Zeková et al. Fuzzy Sets in HR Manageent Figure 2 Copany s Organizational Structure The significance attributed to the evaluators will be first divided according to groups, and then to the individual eployees in the groups. At both levels the division will be ipleented by the Metfessel Allocation ethod (see [1]). In the end, noralized weights of individual evaluators are set for each eployee. Figure 3 The Eployee s Card Structure of Evaluators Since the assignent of eployees to particular projects changes over tie, it is necessary also to keep the coposition of evaluators up-to-date. The division of weights aong groups of evaluators ust be deterined by experts (i.e. it is eaningful to express the with nubers). The division of weights aong the collaborators on the project in question ust be carried out on the worked hours the eployee reports to have spent on tasks in collaboration with the evaluator. (The syste of the working-hours record allows for this). In cases where the subordinates evaluate their supervisor, the weights are divided equally aongst the. 118

7 Acta Polytechnica Hungarica Vol. 8, No. 3, Evaluation Methodology The process of evaluation proceeds in several steps. First, an eployee receives a questionnaire which he/she copletes during preparation for the interview. In the questionnaire, the eployee articulates his/her self-evaluation. The sae questionnaire is handed out to all evaluators who then express their opinion to what extent they see the evaluated eployee eeting the stipulated copetencies. The questionnaire includes qualitative criteria that is part of the copetency odel for any given role. The evaluation against the quantitative criteria is taken fro the eployee s personal record (education, experience, certifications, etc.). For evaluation against the qualitative criteria, the evaluators have at their disposal a non-unifor six-eleent linguistic fuzzy scale (see 2.5). Using the scale values, the evaluator expresses to what extent, in his/her view, the evaluated eployee has et the required level of a given copetence. The individual scale values are odelled with trapezoidal fuzzy nubers that are always given by four points (for the fuzzy scale see 2.3 and Fig. 4). The scale was intentionally set as a non-unifor one. The reason for this is that people tend rather to avoid extree values and prefer centre values. Therefore, if anyone chooses an extree value, it ay be assued that the person is ore certain about his/her decision. The extree values of the used fuzzy scale are therefore less uncertain. The uncertainty rises towards the centre-values. Table 1 Evaluation Scale Points Descriptors Distinctive points 1 Does not eet at all In the ost part does not eet Rather doesn t eet Rather eets Nearly eets Very well eets Figure 4 Applied Fuzzy Scale 119

8 B. Zeková et al. Fuzzy Sets in HR Manageent The evaluation against the quantitative criteria is not part of the questionnaire as values are taken fro a personnel record of the eployee. Based on eeting the set criteria the eployee is given a certain aount of points. For each of the quantitative criterion the axiu aount of points is set. The evaluation itself is then expressed as a level, in which the given eployee eets the axiu value. The points are given in the following way (see Table 2): Table 2 Evaluation against the Quantitative Criteria Education Points Note Secondary school 1 Higher Vocational School (DiS.) 2 College (Bc.) 3 College (Mgr., Ing.) 5 College (PhDr., RNDr. etc.) 6 College (PhD., CSc.) 8 Experience Nuber of onths of relevant 0-60 experience Certification Nuber of certifications point for each certification Language Knowledge Reading coprehension 1 Ability to ake oneself 1 understood Writing 1 In case of ore languages, the points are added, axiu is 6 points For each evaluated eployee, there are available evaluations against the qualitative criteria in the for of questionnaires filled in by appointed eployees (see Figure 3). The evaluations based on the quantitative criteria are exactly defined. The aggregation of those evaluations is carried out in several steps. First, the qualitative criteria is assigned an evaluation as a weighted average (see 2.6) of evaluations given by individual eployees, where the weights of the coworkers depend on the intensity of collaboration with the eployee in question (see Figure 3). The resulting fuzzy nuber expresses an evaluation of the eployee against the given criterion. Other qualitative criteria shall follow the sae procedure analogically. It is possible to carry out a linguistic approxiation of the resulting evaluation concerning various criteria. Now we add to the evaluation quantitative criteria based on the specified conditions (education, experience, certification, language skills). 120

9 Acta Polytechnica Hungarica Vol. 8, No. 3, 2011 In the next stage, the partial evaluations are aggregated to for an overall evaluation. Firstly, there is the aggregation within groups INPUT, OUTPUT, PROCESS, subsequently followed by the aggregation of these groups. The evaluation tree is defined in accordance with a specified copetency odel. The evaluation is calculated as a fuzzy weighted average of the partial evaluations against the criteria (see chapter 2.8). For the purpose of this paper, the evaluation aggregation was carried out using the deo version of the FuzzMe Prograe (see Figure 5 Aggregation of a Partial Evalutions of a Developer 3.4 Outcoes of the Evaluation The output includes a partial fuzzy evaluation of an eployee against the copetencies, then the aggregated fuzzy evaluation for the areas INPUT, OUTPUT, and PROCESS, and finally, the overall fuzzy evaluation of the eployee (see Table 2, Figure 6). Figure 6 Aggregation against the Groups and Overall Evaluation 121

10 B. Zeková et al. Fuzzy Sets in HR Manageent Table 2 An Exaple of Partial Evaluations (Crisp Weights) The evaluations in all entioned levels are represented by fuzzy nubers or, ore exactly, by their linguistic approxiations. For further work with the eployee the evaluation in groups INPUT, OUTPUT, and PROCESS is particularly iportant, since interrelations aong these evaluations deterine the type of the eployee, which allows the anageent to choose the appropriate strategy (Table 3). Processing the outcoes is followed by a otivation interview with the evaluated eployee. First, the eployee is asked for his/her self-evaluation. Then the supervisor infors the evaluated eployee of the evaluation outcoes. If a striking discrepancy between the self-evaluation and the evaluation by the other eployees occurs, an explanation is sought. Then the eployee sets his/her objectives for the following tie period which he/she ust defend before the supervisor. An evaluation of fulfilent of these objectives shall be included into the eployee s evaluation for a following tie period. 122

11 Acta Polytechnica Hungarica Vol. 8, No. 3, 2011 OUTPUT (Perforance) Table 3 The exaple of Working Types and their Manageent Strategies INPUT (Potential) PROCESS (Behaviour) WORK TYPE MOTIVATION STRATEGY Star He/She should be given ore abitious tasks, his/her inforal authority should be encouraged, should be given as an exaple, should be delegated to, prooted Enfant terrible Proisi ng Intellig ent idler and a badgere r Agreea ble Hard Worker Free Spirit Nice Lubber should be ore involved in group tasks or on the contrary trusted with independent tasks, depending on the personality type; requires consistent, unforgiving approach, not-ignoring any assets; needs acceptance by the others, without being preachy; ore support, stiulate courage, resilience and self-confidence; liits need to be set as well as deadlines for change with clear iplications in case of non-copliance; as uch feedback as possible; to instruct and create conditions for selfeducation; shape up; if tutoring by others (of the infant terrible type) fails, consider redeployent; Spoiler probleatic choice; it is necessary to speak expressly about the possibility of departure; the initiative of iproveent is to be left solely to the person in question; deadline for visible iproveents needs to be pinpointed. Conclusions In this paper, the possibilities of the application of fuzzy sets in eployee evaluation has been deonstrated. In psychoetrics it is coon to use discreet scales with sharp integer values. The theory of fuzzy sets allows for the use of linguistic scales where scale values are expressed linguistically and odelled by fuzzy nubers. Siilarly, expertly defined weights of criteria can as well be odel ore adequately by fuzzy nubers, as was shown. The resulting evaluation could also be back-transfored to linguistic expression by eans of a procedure 123

12 B. Zeková et al. Fuzzy Sets in HR Manageent called linguistic approxiation. The advantage of the linguistic fuzzy approach is, on the one hand, a atheatical data process excluding subjective bias, and, on the other hand, a natural process of evaluation and natural expression of evaluation resulting in language natural to the evaluator. References [1] de Andrés, Rocío, García-Lapresta, José, Martínez, Luis. A Multi-Granular Linguistic Model for Manageent Decision-Making in Perforance Appraisal. Soft Coputing - A Fusion of Foundations, Methodologies and Applications. Springer Verlag, Heidelberg 2010, pp , ISSN [2] Hroník, František. Hodnocení pracovníků. Praha : Grada Publishing, a. s., ISBN [3] Pavlačka, Ondřej, Talašová, Jana. The Fuzzy Weighted Average Operation in Decision-Making Models. Proceedings of the 24 th International Conference Matheatical Methods in Econoics, Septeber 13-15, 2006, Plzeň (Ed.L. Lukáš) Typos, Plzeň 2006, pp [4] Sithson, Michael. Fuzzy Set Analysis for Behavioral and Social Science. New York : Springer - Verlag, 1987, ISBN [5] Talašová, Jana. Fuzzy etody vícekriteriálního hodnocení a rozhodování. Oloouc : Vydavatelství UP, 2003, ISBN [6] Talašová, Jana. Fuzzy přístup k hodnocení a rozhodování. Proceedings of the 5 th Conference Apliat (Ed.: Kováčová, M.), Bratislava, February 7-10, 2006, Slovak University of Technology in Bratistava, Bratislava, 2006, pp [7] Zeková, Blanka. Application of Fuzzy Sets in Eployees Evaluation. Apliat Journal of Applied Matheatics. Bratislava 2008, pp , ISSN [8] Ján Vaščák, Ladislav Madarász: Adaptation of Fuzzy Cognitive Maps a Coparison Study, in Acta Polytechnica Hungarica, Vol. 7, No. 3, 2010, pp [9] Márta Takács: Multilevel Fuzzy Approach to the Risk and Disaster Manageent, in Acta Polytechnica Hungarica, Vol. 7, No. 4, 2010, pp

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