# Author: i.palomares

## Back-to-Basics: Group Decision Making

Supporting collective decisions made by groups of experts or stakeholders with their own different opinions, and supporting recommendations for groups of users that *satisfy* them all, constitute some of the fundamental research interests in our team. But, what are the principles and basic ideas underlying **Group Decision Making**?

In this post, we attempt to answer this question by introducing a brief introduction to the topic. The following content extends my originally written overview* *in the AFRYCA website back in 2014, whose software suite I founded as part of my PhD thesis:

A **Group Decision Making (GDM)** problem is a decision situation where:

- There exists a group
*m*of individuals or*experts, E = {e*, who each have their own attitudes and knowledge. Consider for example_{1}, … ,e_{m}}*E={Binyamin, Ercan, Hugo, Ivan, James}*as a group of five experts. Intuitively,*m*should be equal or higher than 2, since a group should have at least two members 🙂 - There is a decision problem consisting of
*n alternatives*or possible solutions to the problem,*X = {x*(again, at least two). Say, for instance, that our five friends in group_{1}, … ,x_{n}}*E*want to choose a destination for a research group away day, among four possible options in England:*X = {Costwolds, Cambridge, Oxford, Cheddar*}.*

##### (*Note: Cheddar is a beautiful place in southwest England, not necessarily the cheese!)

- The experts try to achieve a common solution, i.e. a final decision on selecting one of the four possible destinations.

Each expert *e _{i}* ,

*with i=1,…m*, expresses his/her opinions or

*preferences*over the

*n*alternatives in

*X,*in other words, they provide judgment information indicating to what extent they support – or don’t support – each of the available options. For this, each participant supplies a

*preference structure*. Some examples of preference structures widely used in scientific literature related to GDM, are:

**Preference orderings**: A ranking established by each individual, establishing their ordering of alternatives from the most to the least preferred one. For instance, Ivan may provide the following preference ordering according to which Oxford is his most preferred place and Cheddar is his least preferred one. (Please note, this is merely and example and Ivan absolutely likes all four destinations! 😉 ):

*Oxford > Costwolds > Cambridge > Cheddar*

**Utility vectors**: Despite being the most intuitive preference format to be provided by humans, preference ordering are also the least informative ones: they allow to express that Cambridge is preferred over Cheddar, but they do not allow to indicate how strongly Cambridge is preferred over Cheddar (a lot more? just slightly?). A suitable structure to indicate*degrees*of preference or likeness on each alternative are preference vectors. The following example shows a preference vector over*X = {Costwolds, Cambridge, Oxford, Cheddar}*with assessments in the [0,1], such that the higher the value of the assessment, the more preferred the alternative is. In this case, the fourth alternative in*X*(Cheddar) is the most preferred one, whereas the second alternative (Cambridge) is the least preferred one:

[0.6 **0.4** 0.7 **0.8**]

**Fuzzy preference relations**: Represented as an*nxn*square matrix, where each element located at the row*l*and column*k*– excluding those in the main diagonal of the matrix – is called assessment and represents the degree to which the*l*th alternative is preferred against the the*k*th alternative in*X*. Assessments therefore describe “pairwise” comparative judgments among alternatives. For instance, assuming we use the [0,1] interval to assess pairs of alternatives, an intermediate value of 0.5 indicates**indifference**between two alternatives (see 0.5 for indifference between Costwolds and Cheddar), a value higher than 0.5 indicates preference towards the first alternative in the pair (see 0.8 for strong preference on Cambridge with respect to Oxford) and, conversely, a value lower than 0.5 indicates that the first alternative in the pair is less preferred than the second one (see 0.4 for weak preference*against*Cheddar with respect to Cambridge).

Cost. | Camb. | Oxf. | Ched. | |

Cost. | – | 0.4 | 0.6 | 0.5 |

Camb. | 0.6 | – | 0.8 |
0.6 |

Oxf. | 0.4 | 0.2 | – | 0.4 |

Ched. | 0.5 | 0.4 |
0.6 |
– |

**Decision matrices**: In some GDM problems, each alternative needs to be assessed in terms of multiple criteria,*C = {c*. Consider for instance the following scenario in medical treatment decision-making:_{1}, … ,c_{q}}

##### A group of clinicians with expertise in making treatment decisions for patients with complex health needs, need to prioritise possible treatment options (

*alternatives*) for patients with multiple diagnosis, symptoms and risk factors, by evaluating each treatment in terms of safety, cost and efficiency level (*criteria).***(Acknowledgements: Dr Rachel Denholm, Population Health Sciences, University of Bristol Medical School)**In these contexts, we would define the decision framework as a

*Multi-Criteria Group Decision Making*problem, in which case decision matrices would be the best approach to express preferential of judgement information by participating experts. Each element in a decision matrix is an assessment on a specific alternative (row) in terms of a specific criterion (column). For instance, the following decision matrix indicating that Treatment 3 is the safest but least efficient one:

Safety | Cost | Efficiency | |

Treat1 | 0.7 | 0.4 | 0.5 |

Treat2 | 0.6 | 0.5 | 0.9 |

Treat3 | 0.9 |
0.4 | 0.2 |

Treat4 | 0.5 | 0.6 | 0.5 |

GDM problems are usually defined in environments of uncertainty, in which the information regarding the problem is vague and imprecise. These situations are also known as GDM problems under fuzzy contexts. Some information domains for expressing preferences, that have been frequently utilized by experts to deal with uncertainty, are: numerical, interval-valued or linguistic information. This post has shown examples of preference modelling with numerical information between 0 and 1, but other approaches exist to allow participants to assess decision information both quantitatively and qualitatively.

The solution for a GDM problem has been classically determined by applying an **alternative selection** process, which is composted of two phases:

*Aggregation phase*: Experts’ preferences are combined at assessment level, by using an aggregation operator. How to aggregate individual opinions into a representative opinion, constitutes a key and very widely investigated question across the decision making and information fusion research communities.*Exploitation phase*: Once a group preference has been obtained, an alternative or subset of alternatives is obtained as the solution for the GDM problem, by applying a selection criterion (e.g. dominance or non-dominance degrees).

Interested in delving deeper into Group Decision Making and its extended lines of research (consensus building, large-group decision making)? Then we suggest you taking a look at the newly published book **Large Group Decision Making: Creating Decision Support Approaches at Scale,** which includes a detailed overview on Group Decision Making and Consensus Decision Making in Chapter 2!

Thank you for reading 🙂

## From Tokyo to Bristol: DSRS welcomes James Neve!

Today we were delighted to welcome **Mr ****James Neve** on board, who has been awarded with a prestigious DTP scholarship (Doctoral Training Partnership) by the *Engineering and Physical Sciences Research Council *(EPSRC) to start his PhD studies at the University of Bristol. Under the supervision of Ivan Palomares Carrascosa, James will concentrate his research on **Reciprocal Recommender Systems**: *recsys* *approaches to recommend users to each other instead of recommending items to users*. Online dating is one of the several related application domains of reciprocal recommendation approaches (along with making friends, job recruitment, etc.), which James investigated and worked on as part of his previous role of Principal R&D Engineer in **Eureka Inc. Tokyo, **Japan. The Japanese dating application *Pairs, *along as an underlying system to detect dubious users in such applications, are part of his pre-PhD work, which he will continue to actively investigate within the frame of a very interesting PhD project!

It is noteworthy that, prior to his official PhD start date, James has already recently participated in the IEEE SMC 2018 conference held in Miyazaki, Japan, where he presented his latest developments and research findings as an accepted full paper.

Here are some pictures of this participation in the IEEE SMC 2018 conference two weeks ago.

And here is our new @DSRS_uob member James Neve in action! presenting "Arikui: A Dubious User Detection System in Online Dating in Japan" @BristolUni @UoB_Engineering #ieeesmc2018 pic.twitter.com/A6Rk3gNrt4

— Decision Support and Recommender Systems (Bristol) (@DSRS_uob) October 9, 2018

And finally, the traditional “growing family picture” with our new DSRS team mate!

On behalf of Ercan, Binyamin and Ivan, welcome on board James 🙂

## Talk slides available – IEEE SMC 2018

The slides of the talk delivered by Ivan Palomares at IEEE SMC 2018 are now available in slideshare:

## DSRS members attend ACM Recsys 2018 in Vancouver

It has been a hectic yet very enjoyable week for **Ercan Ezin** and **Ivan Palomares** who attended the 12th International ACM Conference on Recommender Systems (ACM Recsys 2018) in Vancouver, Canada.

Conference website: https://recsys.acm.org/recsys18/

For the conference program please check out the link here.

Conference venue and Vancouver were astonishing with the service and nature visible from any location of the lovely city.Besides attending exciting tutorials and sessions in the main conference, we presented our preliminary work in collaboration with our – almost graduating! – MSc student Eunchong Kim! Our paper, **‘Fitness that Fits: a prototype model for workout video recommendation’** has been disseminated in the co-located workshop on Health Recommender Systems. Thanks to all the workshop organisers, in particular to *Christoph Trattner*, *He*l*ma Torkamaan* and *Hanna Schaefer*, whom we had the honour to meet in the workshop, as well as ACM-Recsys programme chair *Xavier Amatriain*** **(thanks for your valuable feedback on our work!). We were also pleased to meet and network with many other leading experts in health technologies and the recsys community in general!

Here are some photos from the conference and exciting natural parks located not far away from the city centre.

Conference

Sightseeing

Videos

Greetings from Vancouver Intl Airport. Next stop: Miyazaki (Japan) for IEEE SMC 2018 along with our newest arrival **James Neve!**

Ivan P., Ercan E. 🙂

## Welcome to our third team mate

Dr. Binyamin bin Yusoff, Lecturer in Mathematics from *Universiti Malaysia Terengannu* (UMT, Malaysia) started his long-term stay with us as a visiting lecturer with the DSRS group.

With a broad expertise in computational mathematics, and specialization in fuzzy mathematics, decision sciences and optimization, aggregation operators and applied financial economics, Binyamin will initiate collaborative and multidisciplinary research with UoB, hosted by Iván Palomares Carrascosa (Computer Science Dept.). Please contact us if you are interested to know more about his research and our collaborations.

Here is a summary of Binyamin’s research contributions, achievements and interests:

*“My research interests are concerned with decision analysis under uncertainty and soft aggregation processes – broadly falling into the area of computational mathematics. My major foci are: i) fuzzy set theory and higher order fuzzy sets such as intuitionistic fuzzy set, type-2 fuzzy set, hesitant fuzzy set, neutrosophic set, bipolar fuzzy set, conflicting bifuzzy set and imprecise probability theory such as Dempster-Shafer theory of evidence; ii) decision analysis models under multidimensional aspect such as additive and multiplicative preference relation models, outranking relation models, cardinal-based decision models; iii) aggregation operators for information fusion involving dependency and independency among data or arguments. The classical arithmetic means and ordered weighted average are among the independency type of aggregation operators. This also holds for the weighted and the generalized versions of these operators. Moreover, dependency type of aggregation operators is based on fuzzy measure such as choquet integral and sugeno integral. The integration of the above-mentioned techniques can produce more sophisticated decision-making models that deal with complex decision analysis of real-world problem. Current research interest is on the inclusion of human perception in decision analysis, including the consideration of human behaviour or preference between two extreme cases; pessimistic to optimistic points of view. My current contribution is on the integration of soft aggregation processes based on majority concept for the multi-expert decision making models. Ordered weighted average and its variants as well as the concept of fuzzy set theory play their role in expanding and generalizing the classical models. Recently, the developed models have been applied and tested in the financial analysis domain.”*

Wishing Binyamin all the very best during his time with us at Bristol!

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