Inconsistency evaluation in pairwise comparison using norm-based distances

AbstractThis paper studies the properties of an inconsistency index of a pairwise comparison matrix under the assumption that the index is defined as a norm-induced distance from the nearest consistent matrix. Under additive representation of preferences, it is proved that an inconsistency index defined in this way is a seminorm in the linear space of skew-symmetric matrices and several relevant properties hold. In particular, this linear space can be partitioned into equivalence classes, where each class is an affine subspace and all the matrices in the same class share a common value of the inconsistency index. The paper extends in a more general framework some results due, respectively, to Crawford and to Barzilai. It is also proved that norm-based inconsistency indices satisfy a set of six characterizing properties previously introduced, as well as an upper bound property for group preference aggregation

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

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

User needs elicitation via analytic hierarchy process (AHP). A case study on a Computed Tomography (CT) scanner

Background: The rigorous elicitation of user needs is a crucial step for both medical device design and purchasing. However, user needs elicitation is often based on qualitative methods whose findings can be difficult to integrate into medical decision-making. This paper describes the application of AHP to elicit user needs for a new CT scanner for use in a public hospital. Methods: AHP was used to design a hierarchy of 12 needs for a new CT scanner, grouped into 4 homogenous categories, and to prepare a paper questionnaire to investigate the relative priorities of these. The questionnaire was completed by 5 senior clinicians working in a variety of clinical specialisations and departments in the same Italian public hospital. Results: Although safety and performance were considered the most important issues, user needs changed according to clinical scenario. For elective surgery, the five most important needs were: spatial resolution, processing software, radiation dose, patient monitoring, and contrast medium. For emergency, the top five most important needs were: patient monitoring, radiation dose, contrast medium control, speed run, spatial resolution. Conclusions: AHP effectively supported user need elicitation, helping to develop an analytic and intelligible framework of decision-making. User needs varied according to working scenario (elective versus emergency medicine) more than clinical specialization. This method should be considered by practitioners involved in decisions about new medical technology, whether that be during device design or before deciding whether to allocate budgets for new medical devices according to clinical functions or according to hospital department

On the priority vector associated with a fuzzy preference relation and a multiplicative preference relation.

We propose two straightforward methods for deriving the priority vector associated with a fuzzy preference relation. Then, using transformations between multiplicative preference relations and fuzzy preference relations, we study the relationships between the priority vectors associated with these two types of preference relations.pairwise comparison matrix; fuzzy preference relation; priority vector