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Application of the MCDM Technique for an Astute Decision-Making Process in the Renewable Energy Sector
Published in Rahul Sindhwani, Punj Lata Singh, Bhawna Kumar, Varinder Kumar Mittal, J. Paulo Davim, Multi-Criteria Decision Modelling, 2021
Eshan Bajal, Alakananda Chakraborty, Muskan Jindal, Shilpi Sharma
These methods can be broadly described as comparison-based approaches, i.e. AHP and ANP, methods based on distance approaches, i.e. TOPSIS and VIKOR, while outranking approaches are ELECTRE, PROMETHEE, and DEMATEL. Miscellaneous approaches include Choquet Integral. For comprehending weight calculations for criteria, two popularly used methods are the Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP), which have various advantages on the grounds of monetary funds, risk evaluation, and scope. The disadvantage of the two methods is mainly in calculating the consistency ratio that quantizes or validates if the comparison performed is authentic, but these methods can also be implemented when an alternative analysis is done, as its efficacy is proven in this area. On the contrary, the methods using grade available alternatives based on their proximity for the best ideal case solution (by utilizing any germane method) are the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Vlse Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR). Some MCDM methodologies are implemented with the aim of developing an alternatives triage, i.e. prioritizing them by their intermittent ranking relations, their primordial aim to draw a comparison between alternatives and create a prioritized list. Approaches like the decision-making trial and evaluation laboratory (DEMATEL) are specifically used to analyze and rank intermittent relationships among the deliberated attributes to winnow the attributes selected for application of further analysis. Deliberating various methods of MCDM, one cannot declare which method is universally preferable, as each has its merits and demerits. One method can be preferred over another considering a specific scenario and deliberated attributes or model used.
Traditional MADM and New Hybrid MADM for Problem Solving
Published in Gwo-Hshiung Tzeng, Kao-Yi Shen, New Concepts and Trends of Hybrid Multiple Criteria Decision Making, 2017
The fuzzy integral technique was proposed by Gustave Choquet (1953), and is hence also called the Choquet integral. Later, Michio Sugeno (1974) introduced the idea of the fuzzy measure, to be integrated with fuzzy integrals for modeling the imprecise synergy effect among variables. How to adopt fuzzy integrals for MADM research is introduced here, and the details of fuzzy measures and fuzzy integrals can be found in Dubois and Parade (1980) and Grabisch (1995). The required steps for adopting fuzzy integrals in MADM problems can be summarized as follows.
Mechatronic Design Quotient (MDQ)
Published in C.W. de Silva, Mechatronic Systems, 2007
There are two nonlinear fuzzy integrals, Choquet and Sugeno integrals, which have been successfully used in literature for aggregation of criteria [9,10]. In particular, Choquet integral fits intuitive requirements for decision making in the case of interacting criteria [10–12].
A note on the approximation of Shenoy's expectation operator using probabilistic transforms
Published in International Journal of General Systems, 2020
R. Jiroušek, V. Kratochvíl, J. Rauh
Similarly to a probability measure on , basic assignment (or any other above-introduced alternative function) expresses knowledge about chances that occurs. Therefore, knowing a real-valued utility function2, one should be able to compute the expected value of this utility under the knowledge represented by a basic assignment m. It has been proposed to compute such an expected value with the help of the Choquet integral (1954), which is known to have some advantageous properties, especially for superadditive and subadditive capacities (Gilboa and Schmeidler 1994). In particular, for getting the respective upper and lower limits, one can use the Choquet integral of the utility function with respect to the corresponding plausibility and belief functions (Coletti, Petturiti, and Vantaggi 2019). To compute the Choquet integral of utility function u with respect to the belief function, consider the set of all values of the considered utility function u and order them, so that and . Then where for (). For its application to decision-making, see, e.g. Smets (1981) and Coletti, Petturiti, and Vantaggi (2015). Its main disadvantage is that the Choquet integral is not linear in its integrand.
Multi-criteria classification of reward collaboration proposals
Published in IISE Transactions, 2023
Annibal Parracho Sant’Anna, Luiz Octávio Gavião, Tiago Lezan Sant’Anna
Beginning with the transformation of attribute measures into probabilities of preference, CPP enables the consideration of the interaction between the criteria. This allows for the inclusion of a broad range of criteria. It also enables consideration of the social interest in selecting the solution that maximizes the satisfaction of all stakeholders through the use of a Choquet integral (Choquet, 1953), which combines the probabilities of optimization according to all criteria while accounting for their interaction.
An interval-valued 2-tuple linguistic group decision-making model based on the Choquet integral operator
Published in International Journal of Systems Science, 2018
Bingsheng Liu, Meiqing Fu, Shuibo Zhang, Bin Xue, Qi Zhou, Shiruo Zhang
Since Yager (Yager, 1988) proposed the ordered weighted averaging operator, the following operators have been proposed: the linguistic averaging operator (Xu, 2006b), the linguistic hybrid averaging operator (Xu, 2006a), the uncertain linguistic weighted averaging operator (Xu, 2004), the 2-tuple arithmetic mean operator (Xu, 2008), the 2-tuple weighted average operator (Xu, 2010) and the hesitant interval-valued fuzzy ordered weighted geometric operator (Wei, Zhao, & Lin, 2013). These operators were constructed under the assumption that the attributes are independent, without any interactive influence or crossover. However, in practical situations, such attributes are usually correlative and dependent (Xu, 2010). To improve decision quality, scholars have adopted the analytic network process (ANP), decision-making trial and evaluation laboratory (DEMATEL) and the Choquet integral to handle correlated decision attributes (e.g. Malviya & Kant, 2016; Meng, Zhang, & Cheng, 2013; Ossadnik, Schinke, & Kaspar, 2016; Ozcan & Tuysuz, 2016; Uygun & Dede, 2016; Vinodh, Balagi, & Patil, 2016; Wu, Chen, Nie, & Zhang, 2013; Yang & Chen, 2012). Due to that, the decision-maker's preference for attributes in MAGDM problems is highly uncertain, the solution of calculating attribute weights is also highly uncertain. Compared with ANP and DEMATEL, Choquet integral is often used to analyse some of the practical problems with high uncertainties that cannot be described by probability measure and mathematical expectation (Qin, Liu, & Pedrycz, 2016; Tan & Chen, 2013). It is a nonlinear integration operator which can deal with the interrelation of attributes and has been widely applied in the fuzzy MAGDM problems (Aggarwal, 2017; Angilella, Greco, & Matarazzo, 2010; Ling et al., 2015; Zhang, Ju, & Liu, 2017). The main advantage of Choquet integral is that it not only can deal with the interactions of multi-attributes (any attribute sets), but also describes the complex and nonlinear interactions, ranging from redundancy to synergy (Branke, Corrente, Greco, Słowiński, & Zielniewicz, 2016; Liginlal & Ow, 2005). Therefore, we adopt Choquet integral to aggregate DMs’ assessment information and address the interactions of attributes.