Application of Choquet Integral-Fuzzy Measures for Aggregating Customers’ Satisfaction

Abdullah, Lazim; Awang, Noor Azzah; Othman, Muhamad Fauzi

doi:10.1155/2021/2319004

Cited by 6 publications

(7 citation statements)

References 30 publications

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“…Usually, the problem of evaluation of employees is performed using the weighted arithmetic mean (see [18][19][20][21]).…”

Section: Application Of the Discrete Choquet Integral For Personnel S...mentioning

confidence: 99%

“…The major goals of the study conducted in [20] are to determine the most important customer satisfaction criterion and to determine which fast-food restaurant is preferred over the other, from the perception of consumers' satisfaction, using the Choquet integral.…”

Section: Introductionmentioning

confidence: 99%

“…Choquet integral research has been applied to various management problems (see [20,28,29]). In this study, a decision support tool using an integrated Choquet integral is applied for a postal company to support personnel selection.…”

Section: Introductionmentioning

confidence: 99%

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Application of the Choquet Integral: A Case Study on a Personnel Selection Problem

et al. 2022

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Personnel selection plays a decisive role in human resource management since it determines the input quality of personnel. One approach, fuzzy decision-making methods, has become popular in decision making for personnel selection, considering those methods provide a wide range of tools for dealing with uncertainty. Choquet integral is an aggregation operator, frequently used to unite interrelated information. Choquet integral, with respect to fuzzy, allows consideration of the phenomenon of dependence between criteria. In this paper, personnel selection was performed using the Choquet integral, based on a fuzzy measure. The problem of the evaluation of employees is performed with respect to the personal characteristics of the employees, task performance, employee–employee relationship approaches, and effectiveness of communication.

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“…Usually, the problem of evaluation of employees is performed using the weighted arithmetic mean (see [18][19][20][21]).…”

Section: Application Of the Discrete Choquet Integral For Personnel S...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of the Choquet Integral: A Case Study on a Personnel Selection Problem

et al. 2022

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“…Often in the expert knowledge-based models of complex processes or events, researchers use nonadditive but monotone estimators instead of additive ones [1][2][3][4][5][6][7][8]. This…”

Section: Introductionmentioning

confidence: 99%

“…In [35], a new visualization scheme for a better understanding of the inner workings of a fuzzy measure was given. In [1], a joint Choquet integral-fuzzy measures (CI-FM) operator that utilizes the interactions between elements of information was studied. In [36], the authors, for identification of a fuzzy measure (capacity), used a hesitant fuzzy linguistic term set in describing the interactivity between attributes.…”

Section: Introductionmentioning

confidence: 99%

Connections between Campos-Bolanos and Murofushi–Sugeno Representations of a Fuzzy Measure

Sirbiladze

Manjafarashvili

2022

Mathematics

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Nonadditivity of a fuzzy measure, as an indicator of defectiveness, makes a fuzzy mea-sure less useful in applications compared to additive, probabilistic measures. In order to neutralize this indicator of defectiveness to some degree, it is important to study the representations of fuzzy measures, including, in particular, additive, probabilistic representations. In this paper, we discuss a couple of probability representations of a fuzzy measure: the Campos-Bolanos representation (CBR) and the Murofushi–Sugeno representation (MSR). The CBR is mainly represented by the Associated Probability Class (APC). The APC is well studied and the aspects of its use can be found in many interesting studies. This is especially true for the environment of interactive attributes in their identification and multi-attribute group decision-making (MAGDM) models, related to the attributes’ Shapley values and interaction indexes. The MSR is a less-used tool in practice today. The main motivation of the research presented here was to explore the connections between these two representations, which will help increase the usability of the MSR in practice in the future. In the MSR, we constructed the nonequivalent representation class (NERC) of a fuzzy measure. This probabilistic new representation is somewhat similar to the APC in the CBR environment. The proposition on the existence of the MSR induced by the CBR was proven. The presented formula of the APC by the NERC was obtained. The duality property of fuzzy measures for the CBR is well studied with respect to fuzzy measures—Choquet second-order dual capacities. Significant properties were proven for the representation of a monotone expectation (ME) under the NERC conditions: as is known, the necessary and sufficient conditions for the existence of the second-order Choquet dual capacities are proven in the terms of the APC of a CBR and ME. After establishing the links between the APC of a CBR and the NERC of a MSR, we proved the same in the case of the MSR. A recursive connection formula between the interaction indexes, Shapley values, and the probability distribution of the NERC of a two-order additive fuzzy measure was obtained in the environment of a general MAGDM. A new distance concept was introduced for all fuzzy measures’ classes defined in finite sets in terms of the NERC. The distance between two fuzzy measures was defined as the distance between their NERCs. This distance is equivalent to the distance defined on the same class under the conditions of the APC of a CBR. The correctness proposition on the extension of the distance between fuzzy measures for the NERC was preserved: distances between any two fuzzy measures and between their dual fuzzy measures also coincided in the CBR as the MSR. After parameterization, the calculation formula of the new distance was obtained. An illustrative example was considered in order to easily present the obtained results. The connection schemes between the CBR and MSR and the sequential scheme of key facts and results obtained are presented at the end of this work.

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[Retracted] Preorder of Factors Affecting Oil Prices: Fuzzy PROMETHEE Approach

Abdullah

Harun

Mahali

et al. 2022

Journal of Mathematics

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Oil is a highly demanded worldwide product as oil prices can have a major economic and social impact. There are many factors affecting oil prices, but little is known about which factor mostly influenced oil prices. To understand what caused the fluctuation of oil prices, the investigation leading up to the identification of the factors must be constructed. Thus, this paper attempts to explore the factors that might have contributed to oil prices and analyze them using the fuzzy preference ranking organization method for enrichment evaluation (PROMETHEE) method. In particular, the objective of this study is to rank the influential factors affecting oil prices with the consideration of a few criteria. The fuzzy PROMETHEE model comprises four criteria and five factors as the input information. A group of four experts are invited to provide an evaluation on scales of 1 to 5 of the importance of factors with respect to criteria. In computation, the evaluations are treated as triangular fuzzy numbers in which the uncertainty in data is dealt with amicably. This approach combines the advantages of transformation equation and nonarithmetic mean of the defuzzification method that transforms triangular fuzzy numbers into crisp numbers. The results indicate that “supply and demand” is the most influential factor in determining oil prices. Comparative analysis and future research directions are also discussed at the end of this paper.

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Application of Choquet Integral-Fuzzy Measures for Aggregating Customers’ Satisfaction

Cited by 6 publications

References 30 publications

Application of the Choquet Integral: A Case Study on a Personnel Selection Problem

Application of the Choquet Integral: A Case Study on a Personnel Selection Problem

Connections between Campos-Bolanos and Murofushi–Sugeno Representations of a Fuzzy Measure

[Retracted] Preorder of Factors Affecting Oil Prices: Fuzzy PROMETHEE Approach

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