scholarly journals Using of Rectangular Stochastic Matrices for the Problem of Evaluating and Ranking Alternatives

2021 ◽  
Vol 4 ◽  
pp. 4-9
Author(s):  
Oleksii Oletsky
Keyword(s):  
Dynamic Equilibrium ◽  
Choice Model ◽  
State Probability ◽  
Pairwise Comparisons ◽  
Stochastic Matrices ◽  
Analytic Hierarchy ◽  
Multi Agent ◽  
Hierarchy Process ◽  
Choice Probabilities

The paper investigates the issue related to a possible generalization of the “state-probability of choice” model so that the generalized model could be applied to the problem of ranking alternatives, either individual or by a group of agents. It is shown that the results obtained before for the problem of multi-agent choice and decision making by majority of votes can be easily transferred to the problem of multi-agent alternatives ranking. On the basis of distributions of importance values for the problem of ranking alternatives, we can move on to similar models for the choice and voting with the help of well-known exponential normalization of rows.So we regard two types of matrices, both of which belonging to the sort of matrices named balanced rectangular stochastic matrices. For such matrices, sums of elements in each row equal 1, and all columns have equal sums of elements. Both types are involved in a two-level procedure regarded in this paper. Firstly a matrix representing all possible distributions of importance among alternatives should be formed, and secondly a “state-probability of choice” matrix should be obtained on its base. For forming a matrix of states, which belongs and the rows of which correspond to possible distributions of importance, applying pairwise comparisons and the Analytic Hierarchy Method is suggested. Parameterized transitive scales with the parameter affecting the spread of importance between the best and the worst alternatives are regarded. For further getting the matrices of choice probabilities, another parameter which reflects the degree of the agent’s decisiveness is also introduced. The role of both parameters is discussed and illustrated with examples in the paper.The results are reported regarding some numerical experiments which illustrate getting distributions of importance on the basis of the Analytic Hierarchy Process and which are connected to gaining the situation of dynamic equilibrium of alternatives, i.e. the situation when alternatives are considered as those of equal value.

scholarly journals A decision support method for evaluating database designs

2012 ◽  
Vol 9 (1) ◽  
pp. 81-106 ◽  
Author(s):  
Erki Eessaar ◽  
Marek Soobik
Keyword(s):  
Decision Support ◽  
Data Model ◽  
Processing System ◽  
Transaction Processing ◽  
Database Management System ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Hierarchy Process ◽  
Decision Support Method

It is possible to produce different database designs based on the same set of requirements to a database. In this paper, we present a decision support method for comparing different database designs and for selecting one of them as the best design. Each data model is an abstract language that can be used to create many different databases. The proposed method is flexible in the sense that it can be used in case of different data models, criteria, and designs. The method is based on the Analytic Hierarchy Process and uses pairwise comparisons. We also present a case study about comparing four designs of SQL databases in case of PostgreSQL? database management system. The results depend on the context where the designs will be used. Hence, we evaluate the designs in case of two different contexts - management of measurements data and an online transaction processing system.

scholarly journals Two Proofs and One Algorithm Related to the Analytic Hierarchy Process

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Miron Pavluš ◽  
Rostislav Tomeš ◽  
Lukáš Malec
Keyword(s):  
Analytic Hierarchy Process ◽  
Pairwise Comparisons ◽  
Problem Solution ◽  
Maximal Eigenvalue ◽  
Analytic Hierarchy ◽  
Solution Vector ◽  
Decision Making Processes ◽  
Hierarchy Process ◽  
Activity Areas

36 years ago, Thomas Saaty introduced a new mathematical methodology, called Analytic Hierarchy Process (AHP), regarding the decision-making processes. The methodology was widely applied by Saaty and by other authors in the different human activity areas, like planning, business, education, healthcare, etc. but, in general, in the area of management. In this paper, we provide two new proofs for well-known statement that the maximal eigenvalue λmax is equal to n for the eigenvector problem Aw=λw, where A is, so-called, the consistent matrix of pairwise comparisons of type n×n (n≥ 2) with the solution vector w that represents the probability components of disjoint events. Moreover, we suggest an algorithm for the determination of the eigenvalue problem solution Aw=nw as well as the corresponding flowchart. The algorithm for arbitrary consistent matrix A can be simply programmed and used.

scholarly journals Urban tourist motivations: why visit Ljubljana?

2017 ◽  
Vol 3 (4) ◽  
pp. 382-398 ◽  
Author(s):  
Sanja Bozic ◽  
James Kennell ◽  
Miroslav D. Vujicic ◽  
Tamara Jovanovic
Keyword(s):  
Capital City ◽  
Structured Interviews ◽  
Pull Factors ◽  
Analytic Hierarchy ◽  
Content Type ◽  
Ahp Model ◽  
Pull Factor ◽  
New Perspective ◽  
Hierarchy Process

Purpose The purpose of this paper is to develop a new perspective on urban tourist motivations by applying the analytic hierarchy process (AHP) model to help to understand how tourists make decisions about which destinations to visit. Design/methodology/approach This study was based on 30 one-hour-long structured interviews with visitors to Ljubljana, the capital city of Slovenia. Respondents were asked to express their preferences between different pull-factor motives for their visit, using Saaty’s scale, and further qualitative data were collected to examine these preferences in more depth. Findings The results of this study indicate that the most relevant criteria and thus predominant factors in motivation for visits to Ljubljana are the Cultural and Nightlife pull factors, while religious and business motives are the lowest ranked factors. The paper argues that the results show the value of applying the AHP model to understand the role of pull factors in urban tourism destination choice. Research limitations/implications As a single-destination case study, it is important that the findings of this research are evaluated against similar studies in other cities. A limitation of this research is the fact that sub motives within major groups of pull-factor motives have not been explored in this study and this should be the subject of future, more detailed research. Originality/value This research shows the value of applying an under-used methodology to understand urban tourist motivations and knowledge gained through applying this method will be of value to destination marketing organisations as well as to researchers conducting future studies.

scholarly journals Assessing the Contribution of Urban Freight Terminals in Last Mile Operations

2016 ◽  
Vol 17 (3) ◽  
pp. 231-241 ◽  
Author(s):  
Eftihia Nathanail ◽  
Michael Gogas ◽  
Giannis Adamos
Keyword(s):  
Performance Indicator ◽  
Evaluation Framework ◽  
Analytic Hierarchy ◽  
Urban Freight ◽  
Multi Criteria Evaluation ◽  
Last Mile ◽  
Multi Stakeholder ◽  
Hierarchy Process ◽  
Freight Terminals

Abstract This paper introduces a multi-stakeholder multi-criteria evaluation framework, which can be used for the assessment of the last mile distribution performance of urban freight terminals. To this end, a comparative analysis is conducted addressing two Greek urban intermodal freight terminals located at the port of Thessaloniki (ThPA) and Kuehne+Nagel (K+N)’s premises. The assessment of the terminals’ performance relies on a tailored multi-criteria Key Performance Indicator (KPI)-based evaluation framework, whereas the selection and significance of the incorporated criteria and KPIs is predetermined by the relevant responsible stakeholders, who imposed their viewpoint through an analytic hierarchy process. Results showed that ThPA was ranked first according to its performance pertaining to the role of an intermodal interchange; still, K+N’s performance index was only 8.5% lower than ThPA’s, while in specific KPIs it seems that it performs in a better way.

A Study on the Agent-Based Vehicles Dispatching Optimization at Container Terminals

2012 ◽  
Vol 241-244 ◽  
pp. 1745-1750
Author(s):  
Nan Nan Yan ◽  
Di Zheng
Keyword(s):  
Decision Support ◽  
Analytic Hierarchy Process ◽  
Container Terminal ◽  
Container Terminals ◽  
Analytic Hierarchy ◽  
Agent Based ◽  
Agent Model ◽  
Contract Net ◽  
Multi Agent ◽  
Hierarchy Process

This paper mainly concentrated on the method of improving the dispatching trucks working at a container terminal and built the multi-agent model for the dispatching job. The contract net protocol was taken as the communication ones among agents, and the analytic hierarchy process was also applied for the decision support for container trucks dispatching.

FARSJUM, A FUZZY SYSTEM FOR RANKING SPARSE JUDGMENT MATRICES: A CASE STUDY IN SOCCER TOURNAMENTS

2007 ◽  
Vol 15 (01) ◽  
pp. 115-129 ◽  
Author(s):  
M. R. GHOLAMIAN ◽  
S. M. T. FATEMI GHOMI ◽  
M. GHAZANFARI
Keyword(s):  
Pairwise Comparison ◽  
Major Constituent ◽  
Pairwise Comparisons ◽  
Ahp Method ◽  
World Cup ◽  
Analytic Hierarchy ◽  
Rank Reversal ◽  
Judgment Matrix ◽  
Hierarchy Process

The establishment of the priorities from pairwise comparison matrices is the major constituent of the Analytic Hierarchy Process (AHP). However, the number of pairwise comparisons necessary in real problems often becomes overwhelming. In such cases, generally the experts are not able to answer all questions and consequently sparse judgment matrix is generated which caused "equal ranks" and "rank reversal" based on AHP method. In this paper, a new ranking system (FARSJUM) is developed for such sparse judgment matrix. The system is constructed on fuzzy rules and fuzzy reasoning methods. The numerical example of world cup soccer tournament is brought to clarify the performance of the developed system comparing with AHP method in ranking the sparse judgment matrices.

scholarly journals Report on an Analytic Network Process (ANP) Model to Estimate the Benefits, Opportunities, Costs, and Risks (BOCR) that Gun Policies and Violence Prevention Interventions have on Legal Users of Firearms

2021 ◽  
Vol 13 (2) ◽  
Author(s):  
Luis G Vargas ◽  
Amos N. Guiora ◽  
Marcel C. Minutolo
Keyword(s):  
Violence Prevention ◽  
Analytic Network Process ◽  
Federal Agencies ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Prevention Interventions ◽  
Network Process ◽  
Zero Sum ◽  
The Impact ◽  
Hierarchy Process

Balancing public good with individual rights is a difficult task; gun policies attempt to do just this. To ensure public safety, local, state, and federal agencies piece together policies that each entity believes will meet the needs of public welfare. When legislating new gun policies, the impact the policies have on gun owners are perceived as a zero-sum game; some groups are perceived to gain while others think they are losing, but the reality is much more nuanced.    The reason the impact of these policies on all lawful gun owners has been considered a zero-sum game is largely because to date there has been no research measuring the impact. Further, there have been no attempts to quantify the impact that the policies have on lawful gun owners. The sole argument that has been made is about constitutionality.   In this paper, we develop an approach based on the Analytic Hierarchy Process (AHP). The approach allows us to develop criteria for evaluating the impact of these policies on lawful gun owners and generate priorities for the criteria from pairwise comparisons. Criteria are compared in pairs, thus the term pairwise comparisons.  This allows us to score, as with a scorecard model, gun policies for various types of gun owners with respect to the criteria according to the Benefits, Opportunities, Costs, and Risks, thereby determining the impact of each policy.

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