scholarly journals An Alternate Unsupervised Technique Based on Distance Correlation and Shannon Entropy to Estimate λ0-Fuzzy Measure

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1708
Author(s):  
Anath Rau Krishnan ◽  
Maznah Mat Kasim ◽  
Rizal Hamid
Keyword(s):  
Shannon Entropy ◽  
Additional Data ◽  
Choquet Integral ◽  
Fuzzy Measure ◽  
Decision Makers ◽  
Distance Correlation ◽  
Decision Attributes ◽  
Multi Attribute Decision Making ◽  
Correlation Measures ◽  
Similar Evaluation

λ0-measure is a special type of fuzzy measure. In the context of multi-attribute decision making (MADM), the measure can be used together with Choquet integral to model the interdependencies that usually present between the decision attributes. Unfortunately, the range of techniques available to estimate λ0-measure values is too limited i.e., only four techniques are available to this date. Besides, the review on literature shows that each of these existing techniques either requires some initial data from the decision-makers or misrepresents the actual interdependencies held by the attributes. Thus, an alternate unsupervised technique is needed for the estimation of λ0-measure values. This study has developed such a technique by integrating the idea of distance correlation and Shannon entropy. In this technique, the two inputs required to estimate λ0-measure values, namely, the interdependence degrees and fuzzy densities are determined by utilizing the distance correlation measures and entropy weights, respectively. An evaluation to rank the websites owned by five different hospitals located in Sabah, Malaysia, was conducted to illustrate the usage of the technique. A similar evaluation was also performed with a few selected MADM techniques for comparison purposes, where the proposed technique is found to have produced the most consistent ranking. From the literature perspective, this study has contributed an alternate unsupervised technique that can estimate λ0-measure values without necessitating any additional data from the decision-makers, and at the same time can better capture the interdependencies held by the attributes.

Additive Intuitionistic Fuzzy Aggregation Operators Based on Fuzzy Measure

2016 ◽  
Vol 24 (01) ◽  
pp. 1-12 ◽  
Author(s):  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Probability Measure ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Fuzzy Measure ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Aggregation ◽  
The World ◽  
Multi Attribute Decision Making

Intuitionistic fuzzy sets can describe the uncertainty and complexity of the world flexibly, so it has been widely used in multi-attribute decision making. Traditional intuitionistic fuzzy aggregation operators are usually based on the probability measure, namely, they consider that the attributes of objects are independent. But in actual situations, it is difficult to ensure the independence of attributes, so these operators are unsuitable in such situations. Fuzzy measure is able to depict the relationships among the attributes more comprehensively, so it can complement the traditional probability measure in dealing with the multi-attribute decision making problems. In this paper, we first analyze the existing intuitionistic fuzzy operators based on fuzzy measure, then introduce two novel additive intuitionistic fuzzy aggregation operators based on the Shapley value and the Choquet integral, respectively, and show their advantages over other ones.

scholarly journals Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2337
Author(s):  
Gia Sirbiladze
Keyword(s):  
Choquet Integral ◽  
Pair Interaction ◽  
Small Degree ◽  
Aggregation Operators ◽  
Fuzzy Measure ◽  
Weighted Averaging ◽  
Location Selection ◽  
Multi Attribute Decision Making ◽  
The Difference ◽  
Pair Interactions

In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms (Tp,Spq) and (Tmin,Smax) are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes.

New Fuzzy Aggregation Operators Based on the Finite Choquet Integral — Application in the MADM Problem

2016 ◽  
Vol 15 (03) ◽  
pp. 517-551 ◽  
Author(s):  
Gia Sirbiladze
Keyword(s):  
Decision Making ◽  
Choquet Integral ◽  
Aggregation Operators ◽  
Fuzzy Measure ◽  
Weighted Averaging ◽  
Positive Real ◽  
Information Measures ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
States Of Nature

In this paper, new generalizations of the probabilistic averaging operator — Associated Fuzzy Probabilistic Averaging (As-PA and As-FPA) and Immediate Probabilistic Fuzzy Ordered Weighted Averaging (As-IP-OWA and As-IP-FOWA) operators are presented in the environment of fuzzy uncertainty. An uncertainty is presented by associated probabilities of a fuzzy measure. Expert’s evaluations as arguments of the aggregation operators are described by a variable, values of which are compatibility levels on the states of nature defined in positive real or triangular fuzzy numbers (TFNs). Two propositions on the As-FPA operator are proved: (1) The As-FPA operator for the fuzzy measure — capacity of order two coincides with the finite Choquet Averaging (CA) Operator; (2) the As-FPA operator coincides with the FPA operator when a probability measure is used in the role of a fuzzy measure. Analogous propositions for the As-IP-FOWA operator are proved. Some propositions on the connection of the As-FPA and As-IP-FOWA operators are also proved. Information measures — Orness and Divergence for the constructed operators are defined. Some propositions on the connections of these parameters with the corresponding parameters of the finite CA Operator are proved. Two illustrative examples on the applicability of the As-FPA and As-IP-FOWA operators are presented: (1) Several variants of the As-FPA and As-IP-FOWA operators are used for comparison of decision-making results for the problems regarding the fiscal policy of a country; (2) The As-FPA operator is used in the Multi-attribute decision-making (MADM) problem of choosing the best version of the students’ project.

scholarly journals Generalized Fuzzy Soft Power Bonferroni Mean Operators and Their Application in Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 810
Author(s):  
Zitai Xu ◽  
Chunfang Chen ◽  
Yutao Yang
Keyword(s):  
Decision Making ◽  
Soft Power ◽  
Original Data ◽  
Decision Makers ◽  
Decision Making Process ◽  
Software Selection ◽  
Decision Method ◽  
Bonferroni Mean ◽  
Special Cases ◽  
Multi Attribute Decision Making

In decision-making process, decision-makers may make different decisions because of their different experiences and knowledge. The abnormal preference value given by the biased decision-maker (the value that is too large or too small in the original data) may affect the decision result. To make the decision fair and objective, this paper combines the advantages of the power average (PA) operator and the Bonferroni mean (BM) operator to define the generalized fuzzy soft power Bonferroni mean (GFSPBM) operator and the generalized fuzzy soft weighted power Bonferroni mean (GFSWPBM) operator. The new operator not only considers the overall balance between data and information but also considers the possible interrelationships between attributes. The excellent properties and special cases of these ensemble operators are studied. On this basis, the idea of the bidirectional projection method based on the GFSWPBM operator is introduced, and a multi-attribute decision-making method, with a correlation between attributes, is proposed. The decision method proposed in this paper is applied to a software selection problem and compared to the existing methods to verify the effectiveness and feasibility of the proposed method.

Forecasting stock market price by using fuzzified Choquet integral based fuzzy measures with genetic algorithm for parameter optimization

2020 ◽  
Vol 54 (2) ◽  
pp. 597-614
Author(s):  
Shanoli Samui Pal ◽  
Samarjit Kar
Keyword(s):  
Genetic Algorithm ◽  
Time Series ◽  
Linear Regression ◽  
Regression Model ◽  
Choquet Integral ◽  
Time Series Forecasting ◽  
Fuzzy Measure ◽  
Model Parameters ◽  
Forecasting Models ◽  
Non Linear

In this paper, fuzzified Choquet integral and fuzzy-valued integrand with respect to separate measures like fuzzy measure, signed fuzzy measure and intuitionistic fuzzy measure are used to develop regression model for forecasting. Fuzzified Choquet integral is used to build a regression model for forecasting time series with multiple attributes as predictor attributes. Linear regression based forecasting models are suffering from low accuracy and unable to approximate the non-linearity in time series. Whereas Choquet integral can be used as a general non-linear regression model with respect to non classical measures. In the Choquet integral based regression model parameters are optimized by using a real coded genetic algorithm (GA). In these forecasting models, fuzzified integrands denote the participation of an individual attribute or a group of attributes to predict the current situation. Here, more generalized Choquet integral, i.e., fuzzified Choquet integral is used in case of non-linear time series forecasting models. Three different real stock exchange data are used to predict the time series forecasting model. It is observed that the accuracy of prediction models highly depends on the non-linearity of the time series.

scholarly journals Multi-attribute Decision-making is Best Characterized by an Attribute-Wise Reinforcement Learning Model

2017 ◽  
Author(s):  
Shaoming Wang ◽  
Bob Rehder
Keyword(s):  
Computational Models ◽  
Theoretical Models ◽  
Decision Makers ◽  
Common Finding ◽  
Cue Competition ◽  
Recency Effects ◽  
Multiple Attribute ◽  
Multi Attribute Decision Making ◽  
The Common ◽  
Alternative Choice

AbstractChoice alternatives often consist of multiple attributes that vary in how successfully they predict reward. Some standard theoretical models assert that decision makers evaluate choices either by weighting those attribute optimally in light of previous experience (so-called rational models), or adopting heuristics that use attributes suboptimally but in a manner that yields reasonable performance at minimal cost (e.g., the take-the-best heuristic). However, these models ignore both the possibility that decision makers might learn to associate reward with whole stimuli (a particular combination of attributes) rather than individual attributes and the common finding that decisions can be overly influenced by recent experiences and exhibit cue competition effects. Participants completed a two-alternative choice task where each stimulus consisted of three binary attributes that were predictive of reward, albeit with different degrees of reliability. Their choices revealed that, rather than using only the “best” attribute, they made use of all attributes but in manner that reflected the classic cue competition effect known as overshadowing. The time needed to make decisions increased as the number of relevant attributes increased, suggesting that reward was associated with attributes rather than whole stimuli. Fitting a family of computational models formed by crossing attribute use (optimal vs. only the best), representation (attribute vs. whole stimuli), and recency (biased or not), revealed that models that performed better when they made use of all information, represented attributes, and incorporated recency effects and cue competition. We also discuss the need to incorporate selective attention and hypothesis-testing like processes to account for results with multiple-attribute stimuli.

scholarly journals Neural Representation and Learning of Hierarchical 2-additive Choquet Integrals

2020 ◽  
Author(s):  
Roman Bresson ◽  
Johanne Cohen ◽  
Eyke Hüllermeier ◽  
Christophe Labreuche ◽  
Michèle Sebag
Keyword(s):  
Real World ◽  
Choquet Integral ◽  
Marginal Utility ◽  
Decision Makers ◽  
Neural Representation ◽  
Automatic Identification ◽  
Neural Architecture ◽  
Real World Applications ◽  
Choquet Integrals ◽  
The Cost

Multi-Criteria Decision Making (MCDM) aims at modelling expert preferences and assisting decision makers in identifying options best accommodating expert criteria. An instance of MCDM model, the Choquet integral is widely used in real-world applications, due to its ability to capture interactions between criteria while retaining interpretability. Aimed at a better scalability and modularity, hierarchical Choquet integrals involve intermediate aggregations of the interacting criteria, at the cost of a more complex elicitation. The paper presents a machine learning-based approach for the automatic identification of hierarchical MCDM models, composed of 2-additive Choquet integral aggregators and of marginal utility functions on the raw features from data reflecting expert preferences. The proposed NEUR-HCI framework relies on a specific neural architecture, enforcing by design the Choquet model constraints and supporting its end-to-end training. The empirical validation of NEUR-HCI on real-world and artificial benchmarks demonstrates the merits of the approach compared to state-of-art baselines.

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