Soft consensus model for the group fuzzy AHP decision making

The fuzzy analytic hierarchy process (AHP) is an extension to the classical AHP that enables dealing with the impreciseness and vagueness of judgments. It has been frequently used for handling complex decision making problems that demand a group rather than a single decision maker. Group decision making aggregates the judgments of individuals into a joint decision. Although consensus is the desired result in group decision making, it is difficult to achieve due to the diversity of opinions, knowledge and experiences of the decision makers. Therefore, the concept of soft consensus can be applied. We propose a new soft consensus based model for fuzzy AHP group decision making. The judgments in the model are presented as triangular fuzzy numbers. The closeness between judgments of two decision makers is measured by the individual fuzzy consensus index which in turn is based on the compatibility index from classical AHP. In each iteration, two decision makers with the most dissimilar opinions are identified and their judgments are adapted. The process is repeated until the desired consensus level is reached. The model can also take into account the weights of importance of individual decision makers. A fuzzy extension of the geometric mean method is employed for deriving fuzzy weights from a group fuzzy pairwise comparison matrix. The application of the model is provided in an example from the literature

The state of the art development of AHP (1979-2017): a literature review with a social network analysis

Although many papers describe the evolution of the analytic hierarchy process (AHP), most adopt a subjective approach. This paper examines the pattern of development of the AHP research field using social network analysis and scientometrics, and identifies its intellectual structure. The objectives are: (i) to trace the pattern of development of AHP research; (ii) to identify the patterns of collaboration among authors; (iii) to identify the most important papers underpinning the development of AHP; and (iv) to discover recent areas of interest. We analyse two types of networks: social networks, that is, co-authorship networks, and cognitive mapping or the network of disciplines affected by AHP. Our analyses are based on 8441 papers published between 1979 and 2017, retrieved from the ISI Web of Science database. To provide a longitudinal perspective on the pattern of evolution of AHP, we analyse these two types of networks during the three periods 1979–1990, 1991–2001 and 2002–2017. We provide some basic statistics on AHP journals and researchers, review the main topics and applications of integrated AHPs and provide direction for future research by highlighting some open questions

A hierarchical integration method under social constraints to maximize satisfaction in multiple criteria group decision making systems

Aggregating multiple opinions or assessments in a decision has always been a challenging field topic for researchers. Over the last decade, different approaches, mainly based on weighting data sources or decision-makers (DMs), have been proposed to resolve this issue, although social choice theory, focused on frameworks to combine individual opinions, is generally overlooked. To resolve this situation, a novel methodology is developed in this paper based on social choice theory and statistical mathematics. This method innovates by dividing the assessment into components which provides a multiple assessment analysis, assigning weights to each source regarding their position compared to the group for each considered criteria. This multiple-weighting process maximises individual and group satisfaction. Furthermore, the method makes it possible to manage previously assigned influence. An example is given to illustrate the proposed methodology. Additionally, sensitivity analysis is performed and comparisons with other methods are made. Finally, conclusions are presented.The first author acknowledges support from the Spanish Ministry of Education, Culture and Sports [grant number FPU18/01471]. The second and third author wish to recognise their support from the Serra Hunter programme. Finally, this work was supported by the Catalan agency AGAUR through its research group support program (2017SGR00227). This research is part of the R&D project IAQ4EDU, reference no. PID2020-117366RB-I00, funded by MCIN/AEI/10.13039/501100011033.Peer ReviewedPostprint (published version