New optimization based method for estimating priority weights

Abstract

Abstract. The estimation of priority vectors from pairwise comparison matrices is a core of the Analytic Hierarchy Process. Perhaps the most popular approach for deriving the priority weights is the right eigenvalue method (EM). Despite its popularity, various shortcomings of the EM have been described in literature. In this paper a new method for deriving priority vectors is proposed. This method makes use of the idea underlying the EM but in difference to the latter, the new one is optimization based. Important features of this new technique are studied via computer simulations and illustrated by some numerical examples.

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

“…As summarised in Table 3, a number of complex issues have been identified in recent years, and addressed by researchers proposing different AHP approaches. Among these crucial open problems, we would highlight: (i) issues connected to the mathematical theory of PCMs such as the consistency of decision-maker's judgements (Kazibudzki 2016;Kazibudzki and Grzybowski 2013); (ii) the introduction of new prioritisation methods to deal with nonreciprocal PCMs (Grzybowski 2013); (iii) problems related to group decisions (Dong and Cooper 2016;Grošelj et al 2015;Srdjevic et al 2013); problems of consistency indices (Li, Wang, and Tong 2016) and inconsistency indices in PCM Fedrizzi 2014, 2015;Siraj, Mikhailov, and Keane 2015). Some of these issues are closely intertwined and lead on from one another.…”

“…To overcome this, they developed a hesitant multiplicative programming method as a new prioritisation method to derive ratioscale priorities from hesitant judgments. Another advancement was proposed by Grzybowski (2013) and constitutes a new prioritisation method based on the original eigenvalue method, but optimisation-based. The new method provides a tool to deal with nonreciprocal PCMs.…”

Redefinition of triad's inconsistency and its impact on the consistency measurement of pairwise comparison matrix

“…Furthermore, since the publication of [7] a few other procedures were introduced to the literature along with their consistency measures concepts, i.e. : the procedure based on the goal programming approach [8], and a few based on constrained optimization models [9,10]. However, there is a consistency index that is not connected with any prioritization procedure, and this index was devised by Koczkodaj [11], which attracts our special attention.…”