Search results for: M.A. Lazim
11 A New Similarity Measure on Intuitionistic Fuzzy Sets
Authors: Binyamin Yusoff, Imran Taib, Lazim Abdullah, Abd Fatah Wahab
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Intuitionistic fuzzy sets as proposed by Atanassov, have gained much attention from past and latter researchers for applications in various fields. Similarity measures between intuitionistic fuzzy sets were developed afterwards. However, it does not cater the conflicting behavior of each element evaluated. We therefore made some modification to the similarity measure of IFS by considering conflicting concept to the model. In this paper, we concentrate on Zhang and Fu-s similarity measures for IFSs and some examples are given to validate these similarity measures. A simple modification to Zhang and Fu-s similarity measures of IFSs was proposed to find the best result according to the use of degree of indeterminacy. Finally, we mark up with the application to real decision making problems.Keywords: Intuitionistic fuzzy sets, similarity measures, multicriteriadecision making.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 282910 A New Condition for Conflicting Bifuzzy Sets Based On Intuitionistic Evaluation
Authors: Imran C.T., Syibrah M.N., Mohd Lazim A.
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Fuzzy sets theory affirmed that the linguistic value for every contraries relation is complementary. It was stressed in the intuitionistic fuzzy sets (IFS) that the conditions for contraries relations, which are the fuzzy values, cannot be greater than one. However, complementary in two contradict phenomena are not always true. This paper proposes a new idea condition for conflicting bifuzzy sets by relaxing the condition of intuitionistic fuzzy sets. Here, we will critically forward examples using triangular fuzzy number in formulating a new condition for conflicting bifuzzy sets (CBFS). Evaluation of positive and negative in conflicting phenomena were calculated concurrently by relaxing the condition in IFS. The hypothetical illustration showed the applicability of the new condition in CBFS for solving non-complement contraries intuitionistic evaluation. This approach can be applied to any decision making where conflicting is very much exist.Keywords: Conflicting bifuzzy set, conflicting degree, fuzzy sets, fuzzy numbers.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16689 An Interval Type-2 Dual Fuzzy Polynomial Equations and Ranking Method of Fuzzy Numbers
Authors: Nurhakimah Ab. Rahman, Lazim Abdullah
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According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.
Keywords: Dual fuzzy polynomial equations, Interval type-2, Ranking method, Value.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17558 The Effect of Nonnormality on CB-SEM and PLS-SEM Path Estimates
Authors: Z. Jannoo, B. W. Yap, N. Auchoybur, M. A. Lazim
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The two common approaches to Structural Equation Modeling (SEM) are the Covariance-Based SEM (CB-SEM) and Partial Least Squares SEM (PLS-SEM). There is much debate on the performance of CB-SEM and PLS-SEM for small sample size and when distributions are nonnormal. This study evaluates the performance of CB-SEM and PLS-SEM under normality and nonnormality conditions via a simulation. Monte Carlo Simulation in R programming language was employed to generate data based on the theoretical model with one endogenous and four exogenous variables. Each latent variable has three indicators. For normal distributions, CB-SEM estimates were found to be inaccurate for small sample size while PLS-SEM could produce the path estimates. Meanwhile, for a larger sample size, CB-SEM estimates have lower variability compared to PLS-SEM. Under nonnormality, CB-SEM path estimates were inaccurate for small sample size. However, CB-SEM estimates are more accurate than those of PLS-SEM for sample size of 50 and above. The PLS-SEM estimates are not accurate unless sample size is very large.
Keywords: CB-SEM, Monte Carlo simulation, Normality conditions, Nonnormality, PLS-SEM.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 51217 Measuring Teachers- Beliefs about Mathematics: A Fuzzy Set Approach
Authors: M.A. Lazim, M.T.Abu Osman
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This paper deals with the application of a fuzzy set in measuring teachers- beliefs about mathematics. The vagueness of beliefs was transformed into standard mathematical values using a fuzzy preferences model. The study employed a fuzzy approach questionnaire which consists of six attributes for measuring mathematics teachers- beliefs about mathematics. The fuzzy conjoint analysis approach based on fuzzy set theory was used to analyze the data from twenty three mathematics teachers from four secondary schools in Terengganu, Malaysia. Teachers- beliefs were recorded in form of degrees of similarity and its levels of agreement. The attribute 'Drills and practice is one of the best ways of learning mathematics' scored the highest degree of similarity at 0. 79860 with level of 'strongly agree'. The results showed that the teachers- beliefs about mathematics were varied. This is shown by different levels of agreement and degrees of similarity of the measured attributes.Keywords: belief, membership function, degree of similarity, conjoint analysis
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23336 Fuzzy Approach for Ranking of Motor Vehicles Involved in Road Accidents
Authors: Lazim Abdullah, N orhanadiah Zam
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Increasing number of vehicles and lack of awareness among road users may lead to road accidents. However no specific literature was found to rank vehicles involved in accidents based on fuzzy variables of road users. This paper proposes a ranking of four selected motor vehicles involved in road accidents. Human and non-human factors that normally linked with road accidents are considered for ranking. The imprecision or vagueness inherent in the subjective assessment of the experts has led the application of fuzzy sets theory to deal with ranking problems. Data in form of linguistic variables were collected from three authorised personnel of three Malaysian Government agencies. The Multi Criteria Decision Making, fuzzy TOPSIS was applied in computational procedures. From the analysis, it shows that motorcycles vehicles yielded the highest closeness coefficient at 0.6225. A ranking can be drawn using the magnitude of closeness coefficient. It was indicated that the motorcycles recorded the first rank.
Keywords: Road accidents, decision making, closeness coefficient, fuzzy number
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15325 A New Objective Weight on Interval Type-2 Fuzzy Sets
Authors: Nurnadiah Z., Lazim A.
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The design of weight is one of the important parts in fuzzy decision making, as it would have a deep effect on the evaluation results. Entropy is one of the weight measure based on objective evaluation. Non--probabilistic-type entropy measures for fuzzy set and interval type-2 fuzzy sets (IT2FS) have been developed and applied to weight measure. Since the entropy for (IT2FS) for decision making yet to be explored, this paper proposes a new objective weight method by using entropy weight method for multiple attribute decision making (MADM). This paper utilizes the nature of IT2FS concept in the evaluation process to assess the attribute weight based on the credibility of data. An example was presented to demonstrate the feasibility of the new method in decision making. The entropy measure of interval type-2 fuzzy sets yield flexible judgment and could be applied in decision making environment.Keywords: Objective weight, entropy weight, multiple attributedecision making, type-2 fuzzy sets, interval type-2 fuzzy sets
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16484 Jacobi-Based Methods in Solving Fuzzy Linear Systems
Authors: Lazim Abdullah, Nurhakimah Ab. Rahman
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Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.
Keywords: Fuzzy linear systems, Jacobi, Jacobi Over- Relaxation, Refinement of Jacobi, Refinement of Jacobi Over- Relaxation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24013 New Fuzzy Preference Relations and its Application in Group Decision Making
Authors: Nur Syibrah Muhamad Naim, Mohd Lazim Abdullah, Che Mohd Imran Che Taib, Abu OsmanMd. Tap
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Decision making preferences to certain criteria usually focus on positive degrees without considering the negative degrees. However, in real life situation, evaluation becomes more comprehensive if negative degrees are considered concurrently. Preference is expected to be more effective when considering both positive and negative degrees of preference to evaluate the best selection. Therefore, the aim of this paper is to propose the conflicting bifuzzy preference relations in group decision making by utilization of a novel score function. The conflicting bifuzzy preference relation is obtained by introducing some modifications on intuitionistic fuzzy preference relations. Releasing the intuitionistic condition by taking into account positive and negative degrees simultaneously and utilizing the novel score function are the main modifications to establish the proposed preference model. The proposed model is tested with a numerical example and proved to be simple and practical. The four-step decision model shows the efficiency of obtaining preference in group decision making.Keywords: Fuzzy preference relations, score function, conflicting bifuzzy, decision making.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14212 Sensory Evaluation of the Selected Coffee Products Using Fuzzy Approach
Authors: M.A. Lazim, M. Suriani
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Knowing consumers' preferences and perceptions of the sensory evaluation of drink products are very significant to manufacturers and retailers alike. With no appropriate sensory analysis, there is a high risk of market disappointment. This paper aims to rank the selected coffee products and also to determine the best of quality attribute through sensory evaluation using fuzzy decision making model. Three products of coffee drinks were used for sensory evaluation. Data were collected from thirty judges at a hypermarket in Kuala Terengganu, Malaysia. The judges were asked to specify their sensory evaluation in linguistic terms of the quality attributes of colour, smell, taste and mouth feel for each product and also the weight of each quality attribute. Five fuzzy linguistic terms represent the quality attributes were introduced prior analysing. The judgment membership function and the weights were compared to rank the products and also to determine the best quality attribute. The product of Indoc was judged as the first in ranking and 'taste' as the best quality attribute. These implicate the importance of sensory evaluation in identifying consumers- preferences and also the competency of fuzzy approach in decision making.Keywords: fuzzy decision making, fuzzy linguistic, membership function, sensory evaluation,
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27691 Cold Flow Investigation of Primary Zone Characteristics in Combustor Utilizing Axial Air Swirler
Authors: Yehia A. Eldrainy, Mohammad Nazri Mohd. Jaafar, Tholudin Mat Lazim
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This paper presents a cold flow simulation study of a small gas turbine combustor performed using laboratory scale test rig. The main objective of this investigation is to obtain physical insight of the main vortex, responsible for the efficient mixing of fuel and air. Such models are necessary for predictions and optimization of real gas turbine combustors. Air swirler can control the combustor performance by assisting in the fuel-air mixing process and by producing recirculation region which can act as flame holders and influences residence time. Thus, proper selection of a swirler is needed to enhance combustor performance and to reduce NOx emissions. Three different axial air swirlers were used based on their vane angles i.e., 30°, 45°, and 60°. Three-dimensional, viscous, turbulent, isothermal flow characteristics of the combustor model operating at room temperature were simulated via Reynolds- Averaged Navier-Stokes (RANS) code. The model geometry has been created using solid model, and the meshing has been done using GAMBIT preprocessing package. Finally, the solution and analysis were carried out in a FLUENT solver. This serves to demonstrate the capability of the code for design and analysis of real combustor. The effects of swirlers and mass flow rate were examined. Details of the complex flow structure such as vortices and recirculation zones were obtained by the simulation model. The computational model predicts a major recirculation zone in the central region immediately downstream of the fuel nozzle and a second recirculation zone in the upstream corner of the combustion chamber. It is also shown that swirler angles changes have significant effects on the combustor flowfield as well as pressure losses.
Keywords: cold flow, numerical simulation, combustor;turbulence, axial swirler.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2195