# DEVELOPMENT OF FUZZY LOGIC MODEL FOR LEADERSHIP COMPETENCIES ASSESSMENT CASE STUDY: KHOUZESTAN STEEL COMPANY

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3 This kind of assessment reduce the rater opportunity to express points of view and causes a rigid feedback. The logic of traditional mathematical methods has two states 1 or 0. That mean each proposition must either be false or true. In 1965, Zadeh introduced fuzzy logic as means to model and handle uncertainty in natural language [9]. Fuzzy logic describes the qualitative nature aspects of the object while Boolean logic systems focus on their quantitative aspects. Fuzzy set theory appears as an important tool to include inaccurate judgements inherent in L.C.A. process. Fuzzy logic has two main components: membership functions and fuzzy rules. Using them it is possible to move a qualitative to a quantitative description, for example, to represent linguistic expressions as mathematic expressions. Fuzzy membership function express the certainty than an element of the universe belongs to a fuzzy set. It represents the degree of truth as an extension of the valuation [9]. These membership functions can take different shapes according to expertise and preferences of the model designer. In this paper because of the ambiguity of verbal statements the fuzzy logic approach is used to describe 360-degree work behaviour feedbacks, 360-degree frequency of work behaviour feedbacks, work behaviour passing scores, and work behaviour scores. III. METHODOLOGY AND THE MODEL In the traditional non-fuzzy approach (crisp approach) the 360 work behaviour feedbacks are considered and assessed on a fixed scale (0,25,50,75,100). The work behaviour scores can be evaluated as the average of 360-degree work behaviour feedbacks. Leader s work behaviour scores over 50, would be regarded as areas of strength otherwise would be regarded as need to improve [2]. In this paper, because of the ambiguity of verbal statements, the fuzzy logic approach and Mamdani F.I.S. is used to assess work behaviour scores. K.S.C. leadership competency model was used and a questionnaire was developed which gives self, superiors, colleagues, subordinates and customers of each leader, the option to answer questions using on a numeric scale (from 1 to 100). Mamdani model which is one of the most common fuzzy inference techniques takes crisp inputs and produces crisp outputs [10]. It performs this depending on expert-defined fuzzy rules on expert-defined fuzzy variables membership functions. Membership functions and fuzzy rules make it possible to move the experiences and human preferences from a qualitative description to a quantitative description. Membership functions and rules can take different forms according to the experts knowledge, experiences and preferences. Below are the main steps: A. Step1:Creating Mamdani F.I.S. and defining fuzzy inference mechanism. 3 Fig. 1. F.I.S. editor B. Step2:Fuzzification: This step is to take the crisp inputs and determine the degree to which these inputs belong to each of the appropriate fuzzy linguistic values. 360 work behaviour feedbacks, refers to the percentage indicating how well the leader s behaviour matches the competency definition. Here each of ten identified 360 work behaviour feedbacks have been given a range of [0 100] and have been fuzzified with five linguistic variables (unacceptable, below average, average, above average, excellent) using Gaussian curve membership functions, by experts. Fig. 2. Fuzzy sets for linguistic input variable: 360 work behaviour feedback 360 frequency of work behaviour feedbacks, refers to the percentage of times they observe that work behaviour. Each of ten identified 360 frequency of work behaviour feedbacks have been given a range of [0 100] and have been fuzzified with four linguistic variables (never, seldom, sometimes, always) using Gaussian curve membership functions, by experts. Fig. 3. Fuzzy sets for linguistic input variable: 360 frequency of work behaviour work behaviour passing scores, refers to the percentage which is determined by organization for each position. Each of ten identified work behaviour passing scores have been given a range of [0 100] and have been fuzzified with three linguistic variables (low (L), average (A), high (H) ) using Gaussian curve membership functions, by experts. Fig. 4. Fuzzy sets for linguistic input variable: work behaviour passing score

4 Each of ten identified work behaviour scores have been given a range of [0 100] and have been fuzzified with nine linguistic variables (unacceptable (1), extremely poor(2), poor (3), need to improve (4), average(5), above average (6), good (7), extremely good(8), role model (9)) using Gaussian curve membership functions, by experts. calculate partial areas value, calculate each partial area centroid, and calculate total centroid. Fig. 7. Rule viewer Fig. 5. Fuzzy sets for linguistic output variable: work behaviour score C. Step3: Rules evaluation: Fuzzy rules combine one or more input fuzzy sets and associate them with one or more output fuzzy set. In this paper, work behaviour scores, 360 frequency of work behaviour feedbacks and work behaviour passing scores are input variables and work behaviour score is fuzzy output variable. The fuzzy rules are shown in table 1. IV. COMPARISON OF SIMULATION RESULTS (FUZZY APPROACH) WITH TRADITIONAL OR CRISP RESULTS (NON-FUZZY APPROACH) Traditional or non-fuzzy results: The results are shown in table 3. Table 3. Traditional (crisp) results Table 1. Fuzzy Logic Control Rules base Here, the overall crisp leadership competency score is, fuzzy logic results: The simulation (t=10sec) results are shown in fig. 8. As can be seen from the table above there are sixty rules which are defined by experts. With the help of surface viewer we can easily determine the value of output work behaviour score corresponding to inputs. A surface viewer for F.I.S., 1-10 is shown in fig. 6. Fig. 6. Surface viewer for F.I.S D. Step4:Aggregation of rule outputs and defuzzification: The membership functions of all rule consequents previously clipped or scaled are combined into a single fuzzy set, as shown in fig. 7. Inference system output is a fuzzy output not a numerical or crisp data. To make it possible and translate it to numerical data, this article used centroid or gravity center defuzzification method. This method divide total area in partial areas, Fig. 8. Simulation results 4

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