Aggregating membership values by a Choquet-fuzzy-integral based operator

doi:10.1016/S0165-0114(98)00145-6

Fuzzy Sets and Systems

Volume 114, Issue 3, 16 September 2000, Pages 367-375

https://doi.org/10.1016/S0165-0114(98)00145-6 Get rights and content

Abstract

A new type of aggregator, the Choquet-fuzzy-integral based operator, is introduced and applied in aggregation of membership values. In this paper, we generalized the definition of the fuzzy integral as a tool for membership aggregation. The generalization involves replacing the max (or min) operator in information integration with a Choquet-fuzzy-integral based aggregator, resulting in increased flexibility. The characteristics of the Choquet fuzzy integral are studied and a two-phase aggregating process is proposed. Also, we demonstrate a good classification result using the proposed aggregator to integrate the memberships of several clusters in a complex unconstrained handwritten digit recognition domain.

References (35)

D. Dubois et al.
A review of fuzzy sets aggregation connectives
Inform. Sci.
(1985)
M. Friedman et al.
Numerical methods for calculating the fuzzy integral
Fuzzy Sets and Systems
(1996)
J. Keller et al.
Advances in fuzzy integration for pattern recognition
Fuzzy Sets and Systems
(1994)
R. Krishnapuram et al.
Fuzzy-connective-based hierarchical aggregation networks for decision making
Fuzzy Sets and Systems
(1992)
R. Kruse
Fuzzy integrals and conditional fuzzy measures
Fuzzy Sets and Systems
(1983)
T. Murofushi et al.
An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure
Fuzzy Sets and Systems
(1989)
T. Murofushi et al.
Some quantities represented by the Choquet integral
Fuzzy Sets and Systems
(1993)
W. Pedrycz
Fuzzy neural networks and neurocomputations
Fuzzy Sets and Systems
(1993)
A.L. Ralescu et al.
Extensions of fuzzy aggregation
Fuzzy Sets and Systems
(1997)
M. Sugeno et al.
Pseudo-additive measures and integrals
J. Math. Anal. Appl.
(1987)

Z. Wang et al.

Monotone set functions defined by Choquet integral

Fuzzy Sets and Systems

(1996)

H.-J. Zimmermann et al.

Quantifying vagueness in decision models

European J. Oper. Res.

(1985)

F.-H. Cheng et al.

Research on Chinese OCR in Taiwan

Int. J. Pattern Recognition Artif. Intell.

(1991)

J.-H. Chiang, An automated numeral reading system for VISA card application forms, Computers in Industry (1998), to...

J.-H. Chiang et al.

Hybrid fuzzy-neural systems in handwritten word recognition

IEEE Trans. Fuzzy Systems

(1997)

J.-H. Chiang et al.

Recognition of handprinted numerals in VISA card application forms

Mach. Vision Appl.

(1997)

G. Choquet

Theory of capacities

Ann. Inst. Fourier

(1953)

Cited by (60)

Using a hybrid method to evaluate service innovation in the hotel industry
2015, Applied Soft Computing Journal
Citation Excerpt :
Many studies have applied a Choquet integral in different situations. Chiang [41] demonstrated acceptable classification results using the proposed aggregator to integrate the memberships of several clusters in a complex unconstrained handwritten digit recognition domain. Chen and Tzeng [42] demonstrated that a suitable traffic assignment model can be a powerful tool for describing the characteristics of traffic behavior within a road network; the results explain more interactivity and uncertainty in traffic among links compared with a traditional model.
This study develops a hybrid method to improve selection decision making in service innovation. Because criteria for customer perceptions tend to be vague and conflicting, the process of evaluating perceptions (qualitative scale) and operational data (quantitative scale) should be combined. This study proposes the concomitant evaluation of qualitative and quantitative scales using a hybrid approach that combines fuzzy set theory, a discrete multi-criteria method based on prospect theory (known as TODIM in Portuguese) and the non-addictive Choquet integral. The study assumes that the criteria possess interdependent relationships. The advantages of the proposed hybrid approach, which exhibits a hierarchical structure, have been demonstrated throughout the hot spring hotel industry. The proposed method demonstrates that it can be extremely useful for recommending operational alternatives because it clearly identifies the main criteria of the expressed alternatives. The results indicate that the approach easily and effectively accommodates criteria with gain and loss functions and can help practitioners improve their performance and reduce overall service innovation risks.
RGB color image encryption based on Choquet fuzzy integral
2014, Journal of Systems and Software
In recent years, one can see an increasing interest in the security of digital images. This research presents a new RGB color image encryption using keystream generator based on Choquet fuzzy integral (CFI). The properties of the dynamical keystream generator with mathematical analysis are presented in this work. In the proposed method, the CFI is first used to generate pseudo-random keystreams. Then, each of the color pixels is decomposed into three gray-level components. The output of the CFI is used to randomly shift the bits of three gray-level components. Finally, three components of RGB color pixels and the generated keystream are coupled to encrypt the permuted components. Performance aspects of the proposed algorithm such as the entropy analysis, differential analysis, statistical analysis, cipher random analysis, and cipher sensitivity analysis are introduced to evaluate the security of the new scheme. The experimental results reveal the fact that the proposed algorithm is suitable for practical use in protecting the security of digital image information distributed via the Internet.
A quality evaluation model for the design quality of online shopping websites
2013, Electronic Commerce Research and Applications
Citation Excerpt :
Fuzzy triangular numbers has been adopted into DEMATEL procedure for linguistic assessments instead of numerical values (Mohamadnejad et al. 2011). The Choquet and Sugeno integrals are used as aggregation operators (Choquet 1954; Murofushi and Sugeno 1989; Chiang 2000; Tsai and Lu 2006; Beliakov et al. 2007; Grabisch et al. 2009; Tan and Chen 2011). There are similiarities and slightly differences between the Choquet and Sugeno integrals since bothinvolve the same formal model and take into account interactions between design parameters (de Campos and Jorge 1992; Torra and Narukawa 2007; Grabisch and Labreuche 2008).
Design quality of websites is known to have a positive impact on user attention. Although there are lots of papers that investigate design qualities of websites in the literature, none of them takes into account interactions among design characteristics. The main objective of this study is to evaluate the perceived design quality of websites while considering the interactions among design characteristics. For this purpose, a new approach named the quality evaluation model (QuEM), which includes fuzzy set theory, the decision-making trial and evaluation laboratory method (DEMATEL), and generalized Choquet integral techniques, is proposed. The critical design characteristics of websites are determined based on interactions among them by using DEMATEL. Then, the degrees of importance are utilized in the generalized Choquet integral to evaluate the perceived design quality of website designs. Fuzzy set theory is utilized to cope with ambiguity in the linguistic evaluation of the different design characteristics and supports the analysis of the collected data. Finally, the proposed method is applied for the evaluation of the quality of the most used shopping websites in Turkey.
Membership-value-based homogenization for a descriptive multifactor multivariate data analysis. Example featuring quantitative and qualitative time variables in car driving
2010, International Journal of Information Technology and Decision Making
Age invariant face recognition using discriminative tensor subspace learning with fuzzy based classification
2023, Expert Systems
Choquet Integral-Based Aggregation for the Analysis of Anomalies Occurrence in Sustainable Transportation Systems
2023, IEEE Transactions on Fuzzy Systems

View all citing articles on Scopus

View full text

Aggregating membership values by a Choquet-fuzzy-integral based operator

Abstract

Inform. Sci.

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

J. Math. Anal. Appl.

Fuzzy Sets and Systems

European J. Oper. Res.

Research on Chinese OCR in Taiwan

Int. J. Pattern Recognition Artif. Intell.

Hybrid fuzzy-neural systems in handwritten word recognition

IEEE Trans. Fuzzy Systems

Recognition of handprinted numerals in VISA card application forms

Mach. Vision Appl.

Theory of capacities

Ann. Inst. Fourier