INTERNATIONAL JOURNAL OF MODERN EDUCATION (IJMOE), Dec 25, 2023
This work is licensed under CC BY 4.0 Mathematical domains refer to specific sets or areas of mat... more This work is licensed under CC BY 4.0 Mathematical domains refer to specific sets or areas of mathematics that focus on particular types of objects, structures, or functions. Whilst mathematical concepts are fundamental ideas or principles in mathematics that help us understand and describe various phenomena. This study aims to explore the specific domain of mathematics namely numbers, arithmetic operations, geometry, and measurement that exist in the Quran using an exploratoryqualitative research approach. The investigation reveals that there are a number of verses in the Quran that mentioned about mathematical domains and concepts such as numbers in surah al-Baqarah, an-Nisa', al-Maidah, an-An'am, al-Anfal, al-Furqan, as-Sajdah, as-Saffat; arithmetic operations in surah al-A'raf, al-Baqarah, al-'Ankabut, al-Anfal, an-Nisa'; geometry in surah al-Baqarah; and measurement in surah al-Kahf, Yunus, al-Hajj, al-Baqarah, an-Najm. The findings can be used as a supplement idea for the teachers or educators to attract students to enjoy learning mathematics as it relates to their religion and real-life situations.
In a normal situation, a university is constantly utilizing standard statistical analysis tools t... more In a normal situation, a university is constantly utilizing standard statistical analysis tools to provide a student's ranking through their academic achievement. The tools provides analysis of pairwise comparison among students on their academic performance but unfortunately visualization of the results is limited to the use of line graph, histogram, tables and boxplot which are not easily explained. In this study, another way of analyzing the pairwise comparison of academic performance on Mathematics among students is introduced that is by using interaction graph which is based on a weighted directed graph approach. The ranking of student's performance in Mathematics is calculated using Page Rank (PR) algorithm. A sample of final examination result for twenty-one students whom enrolled in Mathematics courses in Fakulti Sains Komputer dan Matematik (FSKM), UiTM Shah Alam are investigated. Their performance by marks in two Mathematics courses taken before the pandemic and three Mathematics courses taken during the pandemic are analyzed. The graph with twenty-one nodes represent the students, while the directed links between two students represent the Mathematics relative performance is established. The rank of the students' Mathematics performance is obtained from PR value of the graph. The largest PR value indicates the highest performance of the respective student. The result revealed that 62 percent of the students have shown better Mathematics performance even though the learning platforms before and during Covid-19 pandemic were drastically changed. Although this result does not indicate the whole picture of FSKM students' Mathematics performance, it gives a good insight to the academic administrator in making better decision. Besides, the interaction graph provides an easy way to explain the result only by looking into the graph.
Malaysian Journal of Fundamental and Applied Sciences, 2015
Dynamical changes of chemical reactions which occurred during combustion process in Circulating F... more Dynamical changes of chemical reactions which occurred during combustion process in Circulating Fluidized Bed boiler (CFB) has been modelled using adjacency matrix of Fuzzy Autocatalytic Set (FACS) of fuzzy graph type-3. Analysis of sequence of changes in the reactions at time t through Perron-Frobenious eigenvector (PFE) of the matrix in the Graph Dynamic Algorithm (GDA) shows that end-product of the combustion process in the CFB namely Water and Hydrogen is not really potrayed the real process. Therefore, in this study, transition matrix of FACS is utilized to analyse the dynamical changes of the reactions and the GDA is modified and improvised and known as Interactive Graph Dynamics (IGD) is subsequently use to facilitate the analysis. The result shows that by using the transition matrix of FACS, the end-product of the combustion process in CFB is in accordance to the real process. Whilst the IGD is able to reduced computer running time as compared to the existing GDA. This pape...
International Journal of Evaluation and Research in Education (IJERE)
COVID-19 has put a large impact on the education system all around the world. School, college and... more COVID-19 has put a large impact on the education system all around the world. School, college and university students are forced to attend hybrid learning (HL) classes. This has posed challenges to the learners to adapt with the new learning system. The objective of this case study is to examine students’ perception on HL, in particular, the impacts on students’ learning experience. This study used survey as the methodology and the instrument for data collection is questionnaire. Data was collected from 93 students of five mathematics classes at Universiti Teknologi MARA (UiTM), Malaysia. Their perceptions in five learning aspects were analyzed, namely the accessibility to the online learning system, the effectiveness of both HL and face-to-face (f2f) learning, the pedagogical, technical and social aspects. The results have shown positive acceptance on HL and they enjoyed the new learning experience which uses both f2f and online mediums. This finding indicated that HL has a good po...
The International journal of Multimedia & Its Applications
Baling Tin is one of Malaysia’s popular traditional children’s games. However, as time passes, Ba... more Baling Tin is one of Malaysia’s popular traditional children’s games. However, as time passes, Baling Tin has practically almost vanished. Children nowadays are more interested on digital games. This study aims to preserve the traditional games by digitalising it in tandem with the current interest. The challenge in this study is to re-create the physical game play into a digital game play. The game application which was developed for primary and middle school childrenalso includes interactive 3-D objects, images, sounds, and suitable theme colours.Furthermore, the user can explore many other captivating pages, including Shop and Quest. Even though the game was designed for Malaysian community, it comes with dual language to enhance user preference. The functionality of the game mechanics was tested. The game fulfils game characteristics and imitate the traditional physical gaming.This application is believed to help younger generations become more familiar with one of Malaysia’s tr...
Directed Laplacians For Fuzzy Autocatalytic Set Of Fuzzy Graph Type‐3 Of An Incineration Process.... more Directed Laplacians For Fuzzy Autocatalytic Set Of Fuzzy Graph Type‐3 Of An Incineration Process. [AIP Conference Proceedings 1309, 112 (2010)]. Tahir Ahmad, Sabariah Baharun, Sumarni Abu Bakar. Abstract. Fuzzy Autocatalytic ...
Fuzzy Autocatalytic Set is a concept emerged from integration of graph theory, fuzzy theory and A... more Fuzzy Autocatalytic Set is a concept emerged from integration of graph theory, fuzzy theory and Autocatalytic Set theory. The concept has been used in modelling complex system such as clinical waste incineration process where the model is represented in a form of weighted directed graph. On the other hand, potential graph is a weighted directed graph represented by Difference Bound Matrix (DBM) which is used to represent timed automata in real time system. Since there is a similarity between potential graph and FACS, further investigation on the other matrix representation of FACS is made to expand the existing matrix representation of FACS by looking into the DBM. This paper provides a new definition on the DBM of FACS which leads to the formation of several theorems and corollaries. The representation of FACS by using DBM in modelling the clinical waste incineration system is also presented.
Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates the concept of fuzzy, graph ... more Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates the concept of fuzzy, graph and autocatalytic set. It was initially defined and used in the modeling of a clinical waste incineration process which has produced more accurate results than using crisp graph. As it is a newly developed theory, FACS seems to have great potentials in generating new mathematical theory. This paper employs Markov chain to the evaluation of steady state of an incineration process. Novel definition of transition probability matrix of FACS is presented. Steady state vector of Markov chain for incineration process is determined and graph of convergence of its norm difference is presented. This study led to some relation of Markov process and Perron-Frobenius Theorem.
Fuzzy Autocatalytic Set of Fuzzy Graph of Type-3 looking at its adjacency matrix was introduced i... more Fuzzy Autocatalytic Set of Fuzzy Graph of Type-3 looking at its adjacency matrix was introduced in the modeling of clinical waste incineration process. Several properties had been developed through that investigation particularly on its relations to Perron-Frobenius theory. We anticipate that many results and properties can be further scrutinized looking at the FACS in the light of its transition probability matrix representation. With this in mind, we have embarked into this approach. This paper highlighted our findings on the investigation on FACS and relates to fundamental Ergodic theorem for Markov Chain and show the existence of Perron vector. Similarity between properties of adjacency matrix and transition matrix is discussed.
... i. Bersetuju mehiluskan cadangan penyelidikan yang telah dikemukakan oleh tuan/puan, dan Puan... more ... i. Bersetuju mehiluskan cadangan penyelidikan yang telah dikemukakan oleh tuan/puan, dan Puan Roselah Osman serta Puan Wan Noraini Wan Jaafar. ii. ... b) Kaedah Cara umum untuk mendapatkan jalan penyelesaian.(ms 103; Nik Azis, 1996) c) Kaedah Graf ...
This paper exploits an interval valued fuzzy matrix in representing combustion process of clinica... more This paper exploits an interval valued fuzzy matrix in representing combustion process of clinical waste incineration system which previously modelled by using Fuzzy Autocatalytic Set (FACS). We defined a membership degree of interval-valued fuzzy edge connectivity using concept of infimum and supremum and proposed a mapping from FACS of clinical waste incineration process to an interval valued fuzzy matrix of FACS. Basic characteristics of the matrix are observed and some proven theorems are derived.
INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2021
Diabetes is referred to a group of metabolic disorder that is caused by irregular amount of insul... more Diabetes is referred to a group of metabolic disorder that is caused by irregular amount of insulin produced in body. There are two types of diabetes in major clinical cases that is type 1 diabetes (T1D) and type 2 diabetes (T2D). Most of the cases reported is T2D and this is caused by a number of people that are unaware of their possibility in having T2D and lack of knowledge regarding its risks. It is important to perform an early diagnosis of T2D to ensure that people will become more aware and also reduce the chances of them getting high risk or complications such as stroke, blindness and damage to body and nerves. To do a classification task, a tool namely machine learning will be used. This tool is used by researcher to analyze a large amount of data to obtain a data pattern. This pattern then will be interpreted to get a knowledge that can help in decision making process. For the medical diagnosis, there are two things that is important which is accuracy and comprehensibility...
Fuzzy Autocatalytic Set of Fuzzy Graph Type-3 (FACS) has provided a graphical model of an inciner... more Fuzzy Autocatalytic Set of Fuzzy Graph Type-3 (FACS) has provided a graphical model of an incineration process. Six important variables identified in the incineration process are represented as nodes and the catalytic relationships are represented by fuzzy edges in the graph. In this paper a non-coordinated FACS of the model is transformed into coordinated FACS. Preliminary analysis of the new graph revealed some relations to left Perron vector of transition matrix for fuzzy graph of FACS. Key-Words: Fuzzy Autocatalytic Set, Fuzzy Graph, Incineration Process, Directed Laplacian for FACS.
Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates the concept of fuzzy, graph ... more Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates the concept of fuzzy, graph and autocatalytic set. It was initially defined and used in the modeling of a clinical waste incineration process which has produced more accurate results than using crisp graph. As it is a newly developed theory, FACS seems to have great potentials in generating new mathematical theories and structures that would enrich the theory itself. With this in mind, we have embarked the study into the Markovian approach. This paper applies the theory of classical Markov chain to the evaluation of steady state of an incineration process. New definition for transition probability matrix of FACS is presented. Two methods for obtaining steady state vector of Markov chain for incineration process are implemented. Our study on FACS with regard to the system led to some relation of a Markov process and Perron-Frobenius Theorem for stochastic matrix.
A number of studies have proposed a method of ranking a smartphone due to the fact that newly sma... more A number of studies have proposed a method of ranking a smartphone due to the fact that newly smartphones in the market are offering more features which could give more benefit to the user and thus become increasingly important as a tool in helping them to make everyday decisions. But most of the studies have exhibited shortcoming associated to level of confidence of decision makers’ in giving a judgement, which significantly influences final ranking result. This study proposes Graph Theory and Matrix Approach (GTMA) on ranking smartphone alternatives that ensures consideration of uncertainty and confidence level upon their judgement towards smartphone selection. A Generalized Triangular Fuzzy Number (GTFN) is used in the calculation of interrelation matrix which leads to give more meaningful value of importance weights of the attributes. Selection index is then calculated to rank the smartphone through fuzzy determinant. A numerical example is provided to illustrate the proposed ap...
In this paper, criteria within the most significant domain of manufacturing in automotive industr... more In this paper, criteria within the most significant domain of manufacturing in automotive industry in Malaysia is analysed and prioritized. This paper aims to propose a multi criteria decision making (MCDM) procedure using concept of fuzzy theory, graph theory and Laplacian matrix approach which is embedded into Graph Theory and Matrix approach (GTMA). The manufacturing domains are ranked using Laplacian energy while the criteria within the most significant domain is prioritized using method of graph drawing whereby the criteria’s is ranked based on the average distance among other criteria in Cartesian coordinate system. The result indicates that cost, quality and service in economic domain are among significant criteria’s that practitioners should give an attention in developing a quality sustainable manufacturing framework so that the industry could sustain for a longer period of time.
INTERNATIONAL JOURNAL OF MODERN EDUCATION (IJMOE), Dec 25, 2023
This work is licensed under CC BY 4.0 Mathematical domains refer to specific sets or areas of mat... more This work is licensed under CC BY 4.0 Mathematical domains refer to specific sets or areas of mathematics that focus on particular types of objects, structures, or functions. Whilst mathematical concepts are fundamental ideas or principles in mathematics that help us understand and describe various phenomena. This study aims to explore the specific domain of mathematics namely numbers, arithmetic operations, geometry, and measurement that exist in the Quran using an exploratoryqualitative research approach. The investigation reveals that there are a number of verses in the Quran that mentioned about mathematical domains and concepts such as numbers in surah al-Baqarah, an-Nisa', al-Maidah, an-An'am, al-Anfal, al-Furqan, as-Sajdah, as-Saffat; arithmetic operations in surah al-A'raf, al-Baqarah, al-'Ankabut, al-Anfal, an-Nisa'; geometry in surah al-Baqarah; and measurement in surah al-Kahf, Yunus, al-Hajj, al-Baqarah, an-Najm. The findings can be used as a supplement idea for the teachers or educators to attract students to enjoy learning mathematics as it relates to their religion and real-life situations.
In a normal situation, a university is constantly utilizing standard statistical analysis tools t... more In a normal situation, a university is constantly utilizing standard statistical analysis tools to provide a student's ranking through their academic achievement. The tools provides analysis of pairwise comparison among students on their academic performance but unfortunately visualization of the results is limited to the use of line graph, histogram, tables and boxplot which are not easily explained. In this study, another way of analyzing the pairwise comparison of academic performance on Mathematics among students is introduced that is by using interaction graph which is based on a weighted directed graph approach. The ranking of student's performance in Mathematics is calculated using Page Rank (PR) algorithm. A sample of final examination result for twenty-one students whom enrolled in Mathematics courses in Fakulti Sains Komputer dan Matematik (FSKM), UiTM Shah Alam are investigated. Their performance by marks in two Mathematics courses taken before the pandemic and three Mathematics courses taken during the pandemic are analyzed. The graph with twenty-one nodes represent the students, while the directed links between two students represent the Mathematics relative performance is established. The rank of the students' Mathematics performance is obtained from PR value of the graph. The largest PR value indicates the highest performance of the respective student. The result revealed that 62 percent of the students have shown better Mathematics performance even though the learning platforms before and during Covid-19 pandemic were drastically changed. Although this result does not indicate the whole picture of FSKM students' Mathematics performance, it gives a good insight to the academic administrator in making better decision. Besides, the interaction graph provides an easy way to explain the result only by looking into the graph.
Malaysian Journal of Fundamental and Applied Sciences, 2015
Dynamical changes of chemical reactions which occurred during combustion process in Circulating F... more Dynamical changes of chemical reactions which occurred during combustion process in Circulating Fluidized Bed boiler (CFB) has been modelled using adjacency matrix of Fuzzy Autocatalytic Set (FACS) of fuzzy graph type-3. Analysis of sequence of changes in the reactions at time t through Perron-Frobenious eigenvector (PFE) of the matrix in the Graph Dynamic Algorithm (GDA) shows that end-product of the combustion process in the CFB namely Water and Hydrogen is not really potrayed the real process. Therefore, in this study, transition matrix of FACS is utilized to analyse the dynamical changes of the reactions and the GDA is modified and improvised and known as Interactive Graph Dynamics (IGD) is subsequently use to facilitate the analysis. The result shows that by using the transition matrix of FACS, the end-product of the combustion process in CFB is in accordance to the real process. Whilst the IGD is able to reduced computer running time as compared to the existing GDA. This pape...
International Journal of Evaluation and Research in Education (IJERE)
COVID-19 has put a large impact on the education system all around the world. School, college and... more COVID-19 has put a large impact on the education system all around the world. School, college and university students are forced to attend hybrid learning (HL) classes. This has posed challenges to the learners to adapt with the new learning system. The objective of this case study is to examine students’ perception on HL, in particular, the impacts on students’ learning experience. This study used survey as the methodology and the instrument for data collection is questionnaire. Data was collected from 93 students of five mathematics classes at Universiti Teknologi MARA (UiTM), Malaysia. Their perceptions in five learning aspects were analyzed, namely the accessibility to the online learning system, the effectiveness of both HL and face-to-face (f2f) learning, the pedagogical, technical and social aspects. The results have shown positive acceptance on HL and they enjoyed the new learning experience which uses both f2f and online mediums. This finding indicated that HL has a good po...
The International journal of Multimedia & Its Applications
Baling Tin is one of Malaysia’s popular traditional children’s games. However, as time passes, Ba... more Baling Tin is one of Malaysia’s popular traditional children’s games. However, as time passes, Baling Tin has practically almost vanished. Children nowadays are more interested on digital games. This study aims to preserve the traditional games by digitalising it in tandem with the current interest. The challenge in this study is to re-create the physical game play into a digital game play. The game application which was developed for primary and middle school childrenalso includes interactive 3-D objects, images, sounds, and suitable theme colours.Furthermore, the user can explore many other captivating pages, including Shop and Quest. Even though the game was designed for Malaysian community, it comes with dual language to enhance user preference. The functionality of the game mechanics was tested. The game fulfils game characteristics and imitate the traditional physical gaming.This application is believed to help younger generations become more familiar with one of Malaysia’s tr...
Directed Laplacians For Fuzzy Autocatalytic Set Of Fuzzy Graph Type‐3 Of An Incineration Process.... more Directed Laplacians For Fuzzy Autocatalytic Set Of Fuzzy Graph Type‐3 Of An Incineration Process. [AIP Conference Proceedings 1309, 112 (2010)]. Tahir Ahmad, Sabariah Baharun, Sumarni Abu Bakar. Abstract. Fuzzy Autocatalytic ...
Fuzzy Autocatalytic Set is a concept emerged from integration of graph theory, fuzzy theory and A... more Fuzzy Autocatalytic Set is a concept emerged from integration of graph theory, fuzzy theory and Autocatalytic Set theory. The concept has been used in modelling complex system such as clinical waste incineration process where the model is represented in a form of weighted directed graph. On the other hand, potential graph is a weighted directed graph represented by Difference Bound Matrix (DBM) which is used to represent timed automata in real time system. Since there is a similarity between potential graph and FACS, further investigation on the other matrix representation of FACS is made to expand the existing matrix representation of FACS by looking into the DBM. This paper provides a new definition on the DBM of FACS which leads to the formation of several theorems and corollaries. The representation of FACS by using DBM in modelling the clinical waste incineration system is also presented.
Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates the concept of fuzzy, graph ... more Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates the concept of fuzzy, graph and autocatalytic set. It was initially defined and used in the modeling of a clinical waste incineration process which has produced more accurate results than using crisp graph. As it is a newly developed theory, FACS seems to have great potentials in generating new mathematical theory. This paper employs Markov chain to the evaluation of steady state of an incineration process. Novel definition of transition probability matrix of FACS is presented. Steady state vector of Markov chain for incineration process is determined and graph of convergence of its norm difference is presented. This study led to some relation of Markov process and Perron-Frobenius Theorem.
Fuzzy Autocatalytic Set of Fuzzy Graph of Type-3 looking at its adjacency matrix was introduced i... more Fuzzy Autocatalytic Set of Fuzzy Graph of Type-3 looking at its adjacency matrix was introduced in the modeling of clinical waste incineration process. Several properties had been developed through that investigation particularly on its relations to Perron-Frobenius theory. We anticipate that many results and properties can be further scrutinized looking at the FACS in the light of its transition probability matrix representation. With this in mind, we have embarked into this approach. This paper highlighted our findings on the investigation on FACS and relates to fundamental Ergodic theorem for Markov Chain and show the existence of Perron vector. Similarity between properties of adjacency matrix and transition matrix is discussed.
... i. Bersetuju mehiluskan cadangan penyelidikan yang telah dikemukakan oleh tuan/puan, dan Puan... more ... i. Bersetuju mehiluskan cadangan penyelidikan yang telah dikemukakan oleh tuan/puan, dan Puan Roselah Osman serta Puan Wan Noraini Wan Jaafar. ii. ... b) Kaedah Cara umum untuk mendapatkan jalan penyelesaian.(ms 103; Nik Azis, 1996) c) Kaedah Graf ...
This paper exploits an interval valued fuzzy matrix in representing combustion process of clinica... more This paper exploits an interval valued fuzzy matrix in representing combustion process of clinical waste incineration system which previously modelled by using Fuzzy Autocatalytic Set (FACS). We defined a membership degree of interval-valued fuzzy edge connectivity using concept of infimum and supremum and proposed a mapping from FACS of clinical waste incineration process to an interval valued fuzzy matrix of FACS. Basic characteristics of the matrix are observed and some proven theorems are derived.
INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2021
Diabetes is referred to a group of metabolic disorder that is caused by irregular amount of insul... more Diabetes is referred to a group of metabolic disorder that is caused by irregular amount of insulin produced in body. There are two types of diabetes in major clinical cases that is type 1 diabetes (T1D) and type 2 diabetes (T2D). Most of the cases reported is T2D and this is caused by a number of people that are unaware of their possibility in having T2D and lack of knowledge regarding its risks. It is important to perform an early diagnosis of T2D to ensure that people will become more aware and also reduce the chances of them getting high risk or complications such as stroke, blindness and damage to body and nerves. To do a classification task, a tool namely machine learning will be used. This tool is used by researcher to analyze a large amount of data to obtain a data pattern. This pattern then will be interpreted to get a knowledge that can help in decision making process. For the medical diagnosis, there are two things that is important which is accuracy and comprehensibility...
Fuzzy Autocatalytic Set of Fuzzy Graph Type-3 (FACS) has provided a graphical model of an inciner... more Fuzzy Autocatalytic Set of Fuzzy Graph Type-3 (FACS) has provided a graphical model of an incineration process. Six important variables identified in the incineration process are represented as nodes and the catalytic relationships are represented by fuzzy edges in the graph. In this paper a non-coordinated FACS of the model is transformed into coordinated FACS. Preliminary analysis of the new graph revealed some relations to left Perron vector of transition matrix for fuzzy graph of FACS. Key-Words: Fuzzy Autocatalytic Set, Fuzzy Graph, Incineration Process, Directed Laplacian for FACS.
Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates the concept of fuzzy, graph ... more Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates the concept of fuzzy, graph and autocatalytic set. It was initially defined and used in the modeling of a clinical waste incineration process which has produced more accurate results than using crisp graph. As it is a newly developed theory, FACS seems to have great potentials in generating new mathematical theories and structures that would enrich the theory itself. With this in mind, we have embarked the study into the Markovian approach. This paper applies the theory of classical Markov chain to the evaluation of steady state of an incineration process. New definition for transition probability matrix of FACS is presented. Two methods for obtaining steady state vector of Markov chain for incineration process are implemented. Our study on FACS with regard to the system led to some relation of a Markov process and Perron-Frobenius Theorem for stochastic matrix.
A number of studies have proposed a method of ranking a smartphone due to the fact that newly sma... more A number of studies have proposed a method of ranking a smartphone due to the fact that newly smartphones in the market are offering more features which could give more benefit to the user and thus become increasingly important as a tool in helping them to make everyday decisions. But most of the studies have exhibited shortcoming associated to level of confidence of decision makers’ in giving a judgement, which significantly influences final ranking result. This study proposes Graph Theory and Matrix Approach (GTMA) on ranking smartphone alternatives that ensures consideration of uncertainty and confidence level upon their judgement towards smartphone selection. A Generalized Triangular Fuzzy Number (GTFN) is used in the calculation of interrelation matrix which leads to give more meaningful value of importance weights of the attributes. Selection index is then calculated to rank the smartphone through fuzzy determinant. A numerical example is provided to illustrate the proposed ap...
In this paper, criteria within the most significant domain of manufacturing in automotive industr... more In this paper, criteria within the most significant domain of manufacturing in automotive industry in Malaysia is analysed and prioritized. This paper aims to propose a multi criteria decision making (MCDM) procedure using concept of fuzzy theory, graph theory and Laplacian matrix approach which is embedded into Graph Theory and Matrix approach (GTMA). The manufacturing domains are ranked using Laplacian energy while the criteria within the most significant domain is prioritized using method of graph drawing whereby the criteria’s is ranked based on the average distance among other criteria in Cartesian coordinate system. The result indicates that cost, quality and service in economic domain are among significant criteria’s that practitioners should give an attention in developing a quality sustainable manufacturing framework so that the industry could sustain for a longer period of time.
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