9 resultados para AHP - Analytic Hierarchy Proces
em Corvinus Research Archive - The institutional repository for the Corvinus University of Budapest
Resumo:
The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. It provides with ratio-scale measurements of the prioirities of elements on the various leveles of a hierarchy. These priorities are obtained through the pairwise comparisons of elements on one level with reference to each element on the immediate higher level. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM), Logarithmic Least Squares Method (LLSM), Weighted Least Squares Method (WLSM) and Chi Squares Method (X2M) are of the tools for computing the priorities of the alternatives. This paper studies a method for generating all the solutions of the LSM problems for 3 3 matrices. We observe non-uniqueness and rank reversals by presenting numerical results.
Resumo:
The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM) are of the possible tools for computing the priorities of the alternatives. A method for generating all the solutions of the LSM problem for 3 3 and 4 4 matrices is discussed in the paper. Our algorithms are based on the theory of resultants.
Resumo:
The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima.
Resumo:
Incomplete pairwise comparison matrix was introduced by Harker in 1987 for the case in which the decision maker does not fill in the whole matrix completely due to, e.g., time limitations. However, incomplete matrices occur in a natural way even if the decision maker provides a completely filled in matrix in the end. In each step of the total n(n1)/2, an incomplete pairwise comparison is given, except for the last one where the matrix turns into complete. Recent results on incomplete matrices make it possible to estimate inconsistency indices CR and CM by the computation of tight lower bounds in each step of the filling in process. Additional information on ordinal inconsistency is also provided. Results can be applied in any decision support system based on pairwise comparison matrices. The decision maker gets an immediate feedback in case of mistypes, possibly causing a high level of inconsistency.
Resumo:
Our research focused on testing various characteristics of pairwise comparison (PC) matrices in controlled experiments. About 270 students have been involved in the test exercises and the final pool contained 450 matrices. Our team conducted experiments with matrices of different size obtained from different types of MADM problems. The matrix elements have been generated by different questioning orders, too. The cases have been divided into 18 subgroups according to the key factors to be analyzed. The testing environment made it possible to analyze the dynamics of inconsistency as the number of elements increased in a given case. Various types of inconsistency indices have been applied. The consequent behavior of the decision maker has also been analyzed in case of incomplete matrices using indicators to measure the deviation from the final ranking of alternatives and from the final score vector.
Resumo:
A pros sszehasonltsok mdszere a tbbszempont dntsi feladatok megoldsnak egy lehetsges eszkze mind a szempontslyok meghatrozsban, mind az alternatvk rtkelsben. A szempontokat pronknt sszehasonltva, fontossgaiknak a dntshoz ltal megtlt arnyait mtrixba rendezve a feladat a slyvektor meghatrozsa gy, hogy annak komponensei valamilyen rtelemben jl illeszkedjenek a dntshoz ltal megadott rtkekhez. A pros sszehasonlts mtrixbl a slyok kiszmtsra leggyakrabban hasznlt sajtvektor mdszer (Analytic Hierarchy Process) mellett szmos tvolsgminimalizl mdszer is ltezik. Ezek egyike a legkisebb ngyzetek mdszere, melynek megoldsa nemlineris, nemkonvex fggvny feltteles optimalizlst jelenti. A cikkben olyan mdszereket mutatunk be a pros sszehasonlts mtrixok legkisebb ngyzetes becslsre, amelyek a clfggvny sszes loklis s globlis minimumhelynek meghatrozsra alkalmasak.
Resumo:
When modeling game situations of incomplete information one usually considers the players hierarchies of beliefs, a source of all sorts of complications. Harsnyi (1967-68)s idea henceforth referred to as the Harsnyi program is that hierarchies of beliefs can be replaced by types. The types constitute the type space. In the purely measurable framework Heifetz and Samet (1998) formalize the concept of type spaces and prove the existence and the uniqueness of a universal type space. Meier (2001) shows that the purely measurable universal type space is complete, i.e., it is a consistent object. With the aim of adding the finishing touch to these results, we will prove in this paper that in the purely measurable framework every hierarchy of beliefs can be represented by a unique element of the complete universal type space.
Resumo:
Egyes alternatvk, forgatknyvek, technolgik stb. fenntarthatsgnak rtkelse definciszeren tbbdimenzis problma. A megfelel alternatva kivlasztsnl ugyanis a dntshozknak egyszerre kell figyelembe vennik krnyezetvdelmi, gazdasgi s trsadalmi szempontokat. Az ilyen dntseket tmogathatjk tbbszempont dntshozatali modellek. A tanulmny ht tbbszempont dntsi mdszertan (MAU, AHP, ELECTRE, PROMETHEE, REGIME, NAIADE s idelis-referencia pont) alkalmazhatsgt vizsglja rszvteli krlmnyek kztt. Az utbbi vek e tmban publiklt esettanulmnyait ttekintve megllapthat, hogy egyik mdszer sem dominlja a tbbit, azok klnbz felttelek mellett eltr sikerrel hasznlhatk. Ennek ellenre a klnbz technikk kombincijval elllthatunk olyan eljrsokat, melyekkel az egyes mdszerek elnyeit mg jobban kiaknzhatjuk. ________ Measuring and comparing the sustainability of certain actions, scenarios, technologies, etc. by definition is a multidimensional problem. Decision makers must consider environmental, economic and social aspects when choosing an alternative course of action. Such decisions can be aided by multi-criteria decision analysis (MCDA). In this paper participatory seven different MCDA methodologies are investigated (MAU, the Analytic Hierarchic Process (AHP), the ELECTRE, PROMETHEE, REGIME, and NAIADE methods and the Ideal and reference point approaches). It is based on a series of reports, in which more than 30 real world case studies focusing on participatory MCDA were reviewed. It is emphasized that there is no best choice from the list of MCDA techniques, but some methods fit certain decision problems more than others. However, with the combination of these methodologies some complementary benefits of the different techniques can be exploited.
Resumo:
A fenntarthatsg rtkelse definciszeren tbbdimenzis problma. A megfelel alternatva, forgatknyv, eljrs stb. kivlasztsakor ugyanis a dntshozknak egyszerre kell figyelembe vennik krnyezetvdelmi, gazdasgi s trsadalmi szempontokat. Az ilyen dntseket altmaszthatjk a tbb szempont dntshozatali modellek. A tanulmny a tbb szempont dntsi eljrsok kzl a legfontosabb htnek az alkalmazhatsgt vizsglja rszvteli krlmnyek kztt. Az utbbi vek e tmban publiklt esettanulmnyainak ttekintsvel megllapthat, hogy egyik mdszer sem uralja a tbbit, azok klnbz felttelek mellett eltr sikerrel hasznlhatk. Ennek ellenre a klnbz mdszerek kombincijval vgrehajthatunk olyan eljrsokat, amelyekkel az egyes mdszerek elnyeit mg jobban kiaknzhatjuk. ________ Measuring and comparing the sustainability of certain actions, scenarios, technologies, etc. is by definition a multidimensional problem. Decision-makers must consider environmental, economic and social aspects when choosing an alternative course of action. Such decisions can be aided by multi-criteria decision analysis (MCDA). This paper investigates seven different MCDA methodologies: MAU, the Analytic Hierarchic Process (AHP), the ELECTRE, PROMETHEE, REGIME, and NAIADE methods, and "Ideal and reference point" approaches). It is based on a series of reports in which over 30 real-world case studies focusing on participatory MCDA were reviewed. It is stressed, however, that there is no "best" choice in the list of MCDA techniques. Some methods fit certain decision problems better than others. Nonetheless, some complementary benefits of the different techniques can be exploited by combining these methodologies.
