scholarly journals A Recommender System Based on Multi-Criteria Aggregation

2017 ◽  
Vol 9 (4) ◽  
pp. 1-15 ◽  
Author(s):  
Soumana Fomba ◽  
Pascale Zarate ◽  
Marc Kilgour ◽  
Guy Camilleri ◽  
Jacqueline Konate ◽  
...  
Keyword(s):  
Decision Analysis ◽  
Decision Maker ◽  
Recommender System ◽  
Choquet Integral ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Performance Matrix ◽  
Web Platform ◽  
Measures Of Performance

Recommender systems aim to support decision-makers by providing decision advice. We review briefly tools of Multi-Criteria Decision Analysis (MCDA), including aggregation operators, that could be the basis for a recommender system. Then we develop a multi-criteria recommender system, STROMa (SysTem of RecOmmendation Multi-criteria), to support decisions by aggregating measures of performance contained in a performance matrix. The system makes inferences about preferences using a partial order on criteria input by the decision-maker. To determine a total ordering of the alternatives, STROMa uses a multi-criteria aggregation operator, the Choquet integral of a fuzzy measure. Thus, recommendations are calculated using partial preferences provided by the decision maker and updated by the system. An integrated web platform is under development.

Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making

2018 ◽  
Vol 29 (1) ◽  
pp. 393-408 ◽  
Author(s):  
Khaista Rahman ◽  
Saleem Abdullah ◽  
Muhammad Sajjad Ali Khan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Multiple Attribute ◽  
Interval Valued

Abstract In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.

scholarly journals Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1081 ◽  
Author(s):  
Peng ◽  
Tian ◽  
Zhang ◽  
Song ◽  
Wang
Keyword(s):  
Decision Making ◽  
Programming Model ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Preference Information ◽  
Fuzzy Measures ◽  
Correlative Relationship

Single-valued neutrosophic sets (SVNSs), which involve in truth-membership, indeterminacy-membership and falsity-membership, play a significant role in describing the decision-makers’ preference information. In this study, a single-valued neutrosophic multi-criteria decision-making (MCDM) approach is developed based on Shapley fuzzy measures and power aggregation operator that takes a correlative relationship among criteria into account and also simultaneously reduces the effects of abnormal preference information. Firstly, two aggregation operators, namely, generalized weighted single-valued neutrosophic power Shapley Choquet average (GWSVNPSCA) operator and generalized weighted single-valued neutrosophic power Shapley Choquet geometric (GWSVNPSCG) operator, are accordingly defined, and the corresponding properties are discussed as well. Secondly, based on the proposed aggregation operators, an integrated MCDM approach is proposed to effectively solve single-valued neutrosophic problems where the weight information is incompletely known. A programming model is constructed to obtain the optimal Shapley fuzzy measure. Next, the proposed operators are utilized to aggregate the decision-makers’ preference information. Finally, a theoretical example with tourism attraction selection is provided to examine the efficacy of the developed approach, in which the results is found reasonable and credible.

Fuzzy Rationality in Quantitative Decision Analysis

2005 ◽  
Vol 9 (1) ◽  
pp. 65-69 ◽  
Author(s):  
Natalia Nikolova ◽  
◽  
Aleksei Shulus ◽  
Daniela Toneva ◽  
Kiril Tenekedjiev ◽  
...  
Keyword(s):  
Decision Analysis ◽  
Decision Maker ◽  
Decision Makers ◽  
Actual Process ◽  
Subjective Probabilities ◽  
Uncertainty Interval ◽  
The Real ◽  
Elicitation Process ◽  
The One

The paper presents a discussion on fuzzy rationality in the elicitation of subjective probabilities and utilities. In addition to previous research, two functions, measuring the degree of preference of the real decision maker on both sides of the uncertainty interval are introduced, and their relationship with the indifference function, measuring the degree of indifference of the decision maker over gambles, is analyzed and graphically interpreted. A new relation -- hesitation -- is introduced to give a better description of the actual process of subjective elicitation by real decision makers. The influence of the preference-hesitation combination in an elicitation process is presented graphically, and it is argued that the resulting uncertainty interval is much tighter than the one, resulting from the preference-indifference based elicitation.

scholarly journals Note on the Choquet Integral as an Interval-Valued Aggregation Operators and Their Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Lee-Chae Jang
Keyword(s):  
Choquet Integral ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Discrete Interval ◽  
Interval Valued

The concept of an interval-valued capacity is motivated by the goal to generalize a capacity, and it can be used for representing an uncertain capacity. In this paper, we define the discrete interval-valued capacities, a measure of the entropy of a discrete interval-valued capacity, and, Choquet integral with respect to a discrete interval-valued capacity. In particular, we discuss the Choquet integral as an interval-valued aggregation operator and discuss an application of them.

scholarly journals Bonferroni Prioritized Aggregation Operators Applied to Government Transparency

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 24 ◽  
Author(s):  
Luis A. Perez-Arellano ◽  
Fabio Blanco-Mesa ◽  
Ernesto Leon-Castro ◽  
Victor Alfaro-Garcia
Keyword(s):  
Main Idea ◽  
Weighted Average ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Bonferroni Mean ◽  
Different Types ◽  
Ordered Weighted Average ◽  
Types Of Information ◽  
Prioritized Aggregation Operators

This article applies the Bonferroni prioritized induced heavy ordered weighted average (OWA) to analyze a series of data and focuses on the Bonferroni average and heavy induced prioritized aggregation operators. The objective of the present work is to present a new aggregation operator that combines the heavy induced prioritized Bonferroni and its formulations and represents the Bonferroni mean with variables that induce an order with vectors that are greater than one. This work develops some extensions using prioritization. The main advantage is that different types of information provided by a group of decision makers to compare real situations are included in this formulation. Finally, an example using the operators to calculate the transparency of the websites of the 32 states of Mexico was performed. The main idea was to visualize how the ranking can change depending on the importance of the five components of the methodology. The main results show that it is possible to detect some important changes depending on the operator and the experts considered.

Suitable Aggregation Models Based on Risk Preferences for Supplier Selection and Order Allocation Problem

2018 ◽  
Vol 22 (1) ◽  
pp. 5-16 ◽  
Author(s):  
Sirin Suprasongsin ◽  
Pisal Yenradee ◽  
Van-Nam Huynh ◽  
Chayakrit Charoensiriwath ◽  
◽  
...  
Keyword(s):  
Risk Taking ◽  
Supplier Selection ◽  
Selection Criteria ◽  
Risk Preferences ◽  
Statistical Technique ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Multiple Objective Linear Programming ◽  
Order Allocation

In this paper, we propose (a) fuzzy multiple objective linear programming models for the Supplier Selection and Order Allocation (SSOA) problem under fuzzy demand and volume/quantity discount environments, and (b) an analysis of how to select the suitable aggregation operator based on the risk preferences of decision makers. The aggregation operators under consideration are additive, maximin, and augmented operators while the risk preferences are classified as risk-averse, risk-taking, and risk-neutral ones. The suitabilities of aggregation operators and risk preferences of decision makers are analyzed by a statistical technique, considering the average and the lowest satisfaction levels of the supplier selection criteria, based on numerical examples. Analysis results reveal that decision makers with different risk preferences will prefer only some aggregation operators and models. Moreover, a particular aggregation operator and model may generate a dominated solution for some situations. Thus, it should be applied with caution.

INDUCED QUASI-ARITHMETIC UNCERTAIN LINGUISTIC AGGREGATION OPERATOR

2013 ◽  
Vol 21 (01) ◽  
pp. 55-77 ◽  
Author(s):  
WEI YANG
Keyword(s):  
Supplier Selection ◽  
Choquet Integral ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Selection Problems ◽  
New Methods ◽  
Dempster Shafer Theory ◽  
Special Cases ◽  
Shafer Theory ◽  
Theory Of Evidence

Induced quasi-arithmetic aggregation operators are considered to aggregate uncertain linguistic information by using order inducing variables. We introduce the induced correlative uncertain linguistic aggregation operator with Choquet integral and we also present the induced uncertain linguistic aggregation operator by using the Dempster-Shafer theory of evidence. The special cases of the new proposed operators are investigated. Many existing linguistic aggregation operators are special cases of our new operators and more new uncertain linguistic aggregation operators can be derived from them. Decision making methods based on the new aggregation operators are proposed and architecture material supplier selection problems are presented to illustrate the feasibility and efficiency of the new methods.

scholarly journals Picture Fuzzy Interaction Partitioned Heronian Aggregation Operators for Hotel Selection

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 3 ◽  
Author(s):  
Suizhi Luo ◽  
Lining Xing
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Sensitivity Analyses ◽  
Special Cases ◽  
Different Parts

Picture fuzzy numbers (PFNs), as the generalization of fuzzy sets, are good at fully expressing decision makers’ opinions with four membership degrees. Since aggregation operators are simple but powerful tools, this study aims to explore some aggregation operators with PFNs to solve practical decision-making problems. First, new operational rules, the interaction operations of PFNs, are defined to overcome the drawbacks of existing operations. Considering that interrelationships may exist only in part of criteria, rather than all of the criteria in reality, the partitioned Heronian aggregation operator is modified with PFNs to deal with this condition. Then, desirable properties are proved and several special cases are discussed. New decision-making methods with these presented aggregation operators are suggested to process hotel selection issues. Last, their practicability and merits are certified by sensitivity analyses and comparison analyses with other existing approaches. The results indicate that our methods are feasible to address such situations where criteria interact in the same part, but are independent from each other at different parts.

Hybrid method for assessing marketable fashion designs: diamond pairwise comparison combined with the Choquet integral

2017 ◽  
Vol 88 (13) ◽  
pp. 1531-1542
Author(s):  
Shi-Woei Lin ◽  
Mohammad Adam Jerusalem
Keyword(s):  
Decision Analysis ◽  
Hybrid Method ◽  
Integral Method ◽  
Choquet Integral ◽  
Pairwise Comparison ◽  
Comparison Method ◽  
Decision Makers ◽  
Fashion Design ◽  
Multiple Attribute

Various multiple-attribute decision analysis approaches have been developed to choose the best fashion design among alternatives, but none of them consider interdependence among their criteria. This study combined the diamond pairwise comparison method to elicit the weights and interaction degrees of a set of criteria and the Choquet integral method for aggregating the evaluation to identify the best design based on the decision-makers’ preferences and prospects. The criteria were determined from input by 10 experts in diverse areas related to fashion design. By implementing the hybrid method in a case example, the efficacy of the proposed approach for evaluating fashion designs is demonstrated.

The ordered weighted government transparency average: Colombia case

2020 ◽  
pp. 1-13 ◽  
Author(s):  
Luis A. Perez-Arellano ◽  
Ernesto Leon-Castro ◽  
Fabio Blanco-Mesa ◽  
Gina Fonseca-Cifuentes
Keyword(s):  
Decision Maker ◽  
Weighted Average ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Mathematical Application ◽  
Government Transparency ◽  
Weight Factors ◽  
Ordered Weighted Average ◽  
Level Of Importance

The main aim of this paper is to propose a new aggregation operator to improve the evaluation of the transparency index. This new operator is called the prioritized induced ordered weighted average weighted average (PIOWAWA) operator. The main characteristics of the PIOWAWA operator are that it allows considering the degree of importance, reordering and weight factors given to the information in the same formulation by the decision maker. A mathematical application is performed using a Colombia transparency case. The findings highlight that according to the operator used, there are significant changes in the ranking. The main implications are given by using these aggregation operators for the generation of scenarios by considering the changes in the allocation of weights, the level of importance and the ordering of information simultaneously.

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