Consistency based completion approaches of incomplete preference relations in uncertain decision contexts.

Uncertainty, hesitation and vagueness are inherent to human beings when articulating opinions and preferences. Therefore in decision making situations it might well be the case that experts are unable to express their opinions in an accurate way. Under these circumstances, various families of preference relations (PRs) have been proposed (linguistic, intuitionistic and interval fuzzy PRs) to allow the experts to manifest some degree of hesitation when enunciating their opinions. An extreme case of uncertainty happens when an expert is unable to differentiate the degree up to which one preference is preferred to another. Henceforth, incomplete preference relations are possible. It is worth to bear in mind that incomplete information does not mean low quality information, on the contrary, in many occasions experts might prefer no to provide information in other to keep consistency. Consequently mechanism to deal with incomplete information in decision making are necessary. This contribution presents the main consistency based completion approaches to estimate incomplete preference values in linguistic, intuitionistic and interval fuzzy PRs

Dealing with Incomplete Information in Linguistic Group Decision Making by Means of Interval Type-2 Fuzzy Sets

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Nowadays in the social network based decision making processes, as the ones involved in e-commerce and e-democracy, multiple users with di erent backgrounds may take part and diverse alternatives might be involved. This diversity enriches the process but at the same time increases the uncertainty in the opinions. This uncertainty can be considered from two di erent perspectives: (i) the uncertainty in the meaning of the words given as preferences, that is motivated by the heterogeneity of the decision makers, (ii) the uncertainty inherent to any decision making process that may lead to an expert not being able to provide all their judgments. The main objective of this contribution is to address these two type of uncertainty. To do so the following approaches are proposed: Firstly, in order to capture, process and keep the uncertainty in the meaning of the linguistic assumption the Interval Type 2 Fuzzy Sets are introduced as a way to model the experts linguistic judgments. Secondly, a measure of the coherence of the information provided by each decision maker is proposed. Finally, a consistency based completion approach is introduced to deal with the uncertainty presented in the expert judgments. The proposed approach is tested in an e-democracy decision making scenario

Valuing health states: is the MACBETH approach useful for valuing EQ-5D-3L health states?

Background Quality Adjusted Life Years (QALYs) are a key outcome measure widely used within health technology assessment and health service research studies. QALYs combine quantity and quality of life, with quality of life calculations relying on the value of distinct health states. Such health states’ values capture the preferences of a population and have been typically built through numerical elicitation methods. Evidence points to these value scores being influenced by methods in use and individuals reporting cognitive difficulties in eliciting their preferences. Evidence from other areas has further suggested that individuals may prefer using distinct elicitation techniques and that this preference can be influenced by their numeracy. In this study we explore the use of the MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) non-numerical preference elicitation approach for health states’ evaluation. Methods A new protocol for preference elicitation based on MACBETH (only requiring qualitative judgments) was developed and tested within a web survey format. A sample of the Portuguese general population (n=243) valued 25 EQ-5D-3L health states with the MACBETH protocol and with a variant of the time trade-off (TTO) protocol, for comparison purposes and for understanding respondents’ preference for distinct protocols and differences in inconsistent evaluations. Respondents answered to a short numeracy test, and basic socio-economic information collected. Results Results show that the mean values derived from MACBETH and the TTO variant are strongly correlated; however, there are substantial differences for several health states’ values. Large and similar numbers of logical inconsistencies were found in respondents’ answers with both methods. Participants with higher levels of numeracy according to the test preferred expressing value judgments with MACBETH, while participants with lower levels were mostly indifferent to both methods. Higher correlations between MACBETH and TTO variant evaluations were observed for individuals with higher numeracy. Conclusion Results suggest that it is worth researching the use of non-numerical preference elicitation methods. Numeracy tests more appropriate for preference elicitation when no explicit considerations of uncertainty are made need to be explored and used. Further behavioural research is needed to fully understand the potential for using these methods in distinct settings (e.g. in different evaluation contexts and in face-to-face and non-face-to-face environments), as well as to explore the effect of literacy on assessments and on respondents’ preferences.UID/MULTI/4066/2016info:eu-repo/semantics/publishedVersio

Neutrosophic Completion Technique for Incomplete Higher-Order AHP Comparison Matrices

[EN] After the recent establishment of the Sustainable Development Goals and the Agenda 2030, the sustainable design of products in general and infrastructures in particular emerge as a challenging field for the development and application of multicriteria decision-making tools. Sustainability-related decision problems usually involve, by definition, a wide variety in number and nature of conflicting criteria, thus pushing the limits of conventional multicriteria decision-making tools practices. The greater the number of criteria and the more complex the relations existing between them in a decisional problem, the less accurate and certain are the judgments required by usual methods, such as the analytic hierarchy process (AHP). The present paper proposes a neutrosophic AHP completion methodology to reduce the number of judgments required to be emitted by the decision maker. This increases the consistency of their responses, while accounting for uncertainties associated to the fuzziness of human thinking. The method is applied to a sustainable-design problem, resulting in weight estimations that allow for a reduction of up to 22% of the conventionally required comparisons, with an average accuracy below 10% between estimates and the weights resulting from a conventionally completed AHP matrix, and a root mean standard error below 15%.The authors acknowledge the financial support of the Spanish Ministry of Economy and Business, along with FEDER funding (DIMALIFE Project: BIA2017-85098-R).Navarro, IJ.; Martí Albiñana, JV.; Yepes, V. (2021). Neutrosophic Completion Technique for Incomplete Higher-Order AHP Comparison Matrices. Mathematics. 9(5):1-19. https://doi.org/10.3390/math905049611995Worrell, E., Price, L., Martin, N., Hendriks, C., & Meida, L. O. (2001). CARBON DIOXIDE EMISSIONS FROM THE GLOBAL CEMENT INDUSTRY. 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