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Development of a generalized Choquet integral-based aggregation operator

A multi criteria problem consists of a number of alternatives which are evaluated under a set of predefined, usually conflicting, evaluation criteria. An aggregation phase refers to a function or an aggregation operator which combines the performance values of each alternative in order to produce a...

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Main Authors: Mat Kasim, Maznah, Engku Abu Bakar, Engku Muhammad Nazri
Format: Monograph
Language:English
English
Published: Universiti Utara Malaysia 2012
Subjects:
QA Mathematics
Online Access:http://repo.uum.edu.my/7333/1/Maz.pdf
http://repo.uum.edu.my/7333/4/1.MAZNAH%20MAT%20KASIM.pdf
http://repo.uum.edu.my/7333/
http://lintas.uum.edu.my:8080/elmu/index.jsp?module=webopac-l&action=fullDisplayRetriever.jsp&szMaterialNo=0000784887
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spelling my.uum.repo.73332014-07-06T00:59:05Z http://repo.uum.edu.my/7333/ Development of a generalized Choquet integral-based aggregation operator Mat Kasim, Maznah Engku Abu Bakar, Engku Muhammad Nazri QA Mathematics A multi criteria problem consists of a number of alternatives which are evaluated under a set of predefined, usually conflicting, evaluation criteria. An aggregation phase refers to a function or an aggregation operator which combines the performance values of each alternative in order to produce a single final score. This single final score implies the preference score of the particular alternative which will be helpful for decision makers in selecting, ranking or sorting the alternatives. The available aggregation operators can be grouped into two major classes which are called as additive and non-additive aggregation operators.This study investigated an operator called Choquet aggregation operator which can be called as a generalized operator due to its capability of becoming both types of operators.It is found that the Choquet aggregation operator is of an additive type in a situation where the interactions among the criteria are not considered.Conversely, it is a non additive aggregation operator when the interactions are found and determined prior to its utilization.This research has provided several subjective approaches to calculate these interactions which are also known as fuzzy measures.To elaborate more on its capability, one multi criteria problem in educational sector was identified and solved by this operator. Based on the data of the academic achievement of 33 students of year six on five subjects in a primary school in Perlis, two sets of aggregated final scores were obtained. One set of the final scores was evaluated by the operator after considering the interactions between the criteria which were calculated as λ-fuzzy measures. The other set of the overall scores was obtained by simple weighted average method with the assumption that the subjects were independent but were assigned with subjective weights of importance. These two sets of scores were compared with the scores provided by schools that were determined by simple average method and grade point average (PNGK) method.The overall performance score of students obtained by Choquet non additive aggregation operator was suggested as the main reference for the school to analyze the performance of the students. This is due to the fact that in many practical applications most criteria present interactive characteristics. It is also suggested that, a new grading Choquet-based information system for evaluating students’ performance could be introduced in all level of education. Furthermore, the usage of this aggregation operator could be extended in evaluating performance across other sectors because it can be used in two different settings whether the evaluation criteria are independent or there are interactions or interdependencies between the criteria. Universiti Utara Malaysia 2012 Monograph NonPeerReviewed application/pdf en http://repo.uum.edu.my/7333/1/Maz.pdf application/pdf en http://repo.uum.edu.my/7333/4/1.MAZNAH%20MAT%20KASIM.pdf Mat Kasim, Maznah and Engku Abu Bakar, Engku Muhammad Nazri (2012) Development of a generalized Choquet integral-based aggregation operator. Project Report. Universiti Utara Malaysia. (Submitted) http://lintas.uum.edu.my:8080/elmu/index.jsp?module=webopac-l&action=fullDisplayRetriever.jsp&szMaterialNo=0000784887
institution Universiti Utara Malaysia
building UUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Utara Malaysia
content_source UUM Institutionali Repository
url_provider http://repo.uum.edu.my/
language English
English
topic QA Mathematics
spellingShingle QA Mathematics
Mat Kasim, Maznah
Engku Abu Bakar, Engku Muhammad Nazri
Development of a generalized Choquet integral-based aggregation operator
description A multi criteria problem consists of a number of alternatives which are evaluated under a set of predefined, usually conflicting, evaluation criteria. An aggregation phase refers to a function or an aggregation operator which combines the performance values of each alternative in order to produce a single final score. This single final score implies the preference score of the particular alternative which will be helpful for decision makers in selecting, ranking or sorting the alternatives. The available aggregation operators can be grouped into two major classes which are called as additive and non-additive aggregation operators.This study investigated an operator called Choquet aggregation operator which can be called as a generalized operator due to its capability of becoming both types of operators.It is found that the Choquet aggregation operator is of an additive type in a situation where the interactions among the criteria are not considered.Conversely, it is a non additive aggregation operator when the interactions are found and determined prior to its utilization.This research has provided several subjective approaches to calculate these interactions which are also known as fuzzy measures.To elaborate more on its capability, one multi criteria problem in educational sector was identified and solved by this operator. Based on the data of the academic achievement of 33 students of year six on five subjects in a primary school in Perlis, two sets of aggregated final scores were obtained. One set of the final scores was evaluated by the operator after considering the interactions between the criteria which were calculated as λ-fuzzy measures. The other set of the overall scores was obtained by simple weighted average method with the assumption that the subjects were independent but were assigned with subjective weights of importance. These two sets of scores were compared with the scores provided by schools that were determined by simple average method and grade point average (PNGK) method.The overall performance score of students obtained by Choquet non additive aggregation operator was suggested as the main reference for the school to analyze the performance of the students. This is due to the fact that in many practical applications most criteria present interactive characteristics. It is also suggested that, a new grading Choquet-based information system for evaluating students’ performance could be introduced in all level of education. Furthermore, the usage of this aggregation operator could be extended in evaluating performance across other sectors because it can be used in two different settings whether the evaluation criteria are independent or there are interactions or interdependencies between the criteria.
format Monograph
author Mat Kasim, Maznah
Engku Abu Bakar, Engku Muhammad Nazri
author_facet Mat Kasim, Maznah
Engku Abu Bakar, Engku Muhammad Nazri
author_sort Mat Kasim, Maznah
title Development of a generalized Choquet integral-based aggregation operator
title_short Development of a generalized Choquet integral-based aggregation operator
title_full Development of a generalized Choquet integral-based aggregation operator
title_fullStr Development of a generalized Choquet integral-based aggregation operator
title_full_unstemmed Development of a generalized Choquet integral-based aggregation operator
title_sort development of a generalized choquet integral-based aggregation operator
publisher Universiti Utara Malaysia
publishDate 2012
url http://repo.uum.edu.my/7333/1/Maz.pdf
http://repo.uum.edu.my/7333/4/1.MAZNAH%20MAT%20KASIM.pdf
http://repo.uum.edu.my/7333/
http://lintas.uum.edu.my:8080/elmu/index.jsp?module=webopac-l&action=fullDisplayRetriever.jsp&szMaterialNo=0000784887
_version_ 1644279510554640384
score 13.211869

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