Priority vector and consistency

2014 ◽  
pp. 17-31 ◽  
Author(s):  
Matteo Brunelli
Keyword(s):  
Priority Vector

Expected consistency-based model and multiplicative DEA cross-efficiency for group decision-making with incomplete distribution linguistic preference relations

2021 ◽  
pp. 1-21
Author(s):  
Jinpei Liu ◽  
Longlong Shao ◽  
Ligang Zhou ◽  
Feifei Jin
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Optimization Model ◽  
Group Decision ◽  
Preference Relation ◽  
Preference Relations ◽  
Priority Vector ◽  
Linguistic Preference Relation ◽  
Multiplicative Preference Relations ◽  
High Consistency

Faced with complex decision problems, Distribution linguistic preference relation (DLPR) is an effective way for decision-makers (DMs) to express preference information. However, due to the complexity of the decision-making environment, DMs may not be able to provide complete linguistic distribution for all linguistic terms in DLPRs, which results in incomplete DLPRs. Therefore, in order to solve group decision-making (GDM) with incomplete DLPRs, this paper proposes expected consistency-based model and multiplicative DEA cross-efficiency. For a given incomplete DLPRs, we first propose an optimization model to obtain complete DLPR. This optimization model can evaluate the missing linguistic distribution and ensure that the obtained DLPR has a high consistency level. And then, we develop a transformation function that can transform DLPRs into multiplicative preference relations (MPRs). Furthermore, we design an improved multiplicative DEA model to obtain the priority vector of MPR for ranking all alternatives. Finally, a numerical example is provided to show the rationality and applicability of the proposed GDM method.

scholarly journals A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 554
Author(s):  
Jiří Mazurek ◽  
Radomír Perzina ◽  
Jaroslav Ramík ◽  
David Bartl
Keyword(s):  
Research Method ◽  
Geometric Mean ◽  
Pairwise Comparisons ◽  
Numerical Comparison ◽  
Priority Vector ◽  
Eigenvalue Method ◽  
Fundamental Scale ◽  
Matrix Vector ◽  
Best Worst Method ◽  
Order Violation

In this paper, we compare three methods for deriving a priority vector in the theoretical framework of pairwise comparisons—the Geometric Mean Method (GMM), Eigenvalue Method (EVM) and Best–Worst Method (BWM)—with respect to two features: sensitivity and order violation. As the research method, we apply One-Factor-At-a-Time (OFAT) sensitivity analysis via Monte Carlo simulations; the number of compared objects ranges from 3 to 8, and the comparison scale coincides with Saaty’s fundamental scale from 1 to 9 with reciprocals. Our findings suggest that the BWM is, on average, significantly more sensitive statistically (and thus less robust) and more susceptible to order violation than the GMM and EVM for every examined matrix (vector) size, even after adjustment for the different numbers of pairwise comparisons required by each method. On the other hand, differences in sensitivity and order violation between the GMM and EMM were found to be mostly statistically insignificant.

How to Evaluate the Economic Value Added of Innovative Interface Technologies in a Booming Cyber Commerce Environment

2011 ◽  
Vol 467-469 ◽  
pp. 1006-1011
Author(s):  
Ming Yuan Hsieh ◽  
Chung Hsing Huang ◽  
Wen Ming Wu
Keyword(s):  
Factor Analysis ◽  
Customer Service ◽  
Economic Value ◽  
Value Added ◽  
Business Environment ◽  
Economic Value Added ◽  
Social Community ◽  
Priority Vector ◽  
Network Process ◽  
Four Levels

Beginning in the 21st century, e-business enterprises need to take vigorous tactics in facing greater challenges in a booming cyber commerce era. In today’s e-business environment, innovative interface technologies change with each passing day, customers’ (users’) satisfaction are more and more discerning, and market demands can fluctuate unpredictably. While facing constant changes in the lower-profit and high customer-service cyber commerce environment, it is important to know how to break through the current Information Technology (IT) industrial situation, maintain the enterprises’ owned advantage and continuously make a profit under a booming transition. In this research, nineteen sub-criteria are categorized into five factors (criteria) by the measurement of factor analysis. Three basic types of innovative business websites (portals, cyber commerce and social community) in an e-business environment are then evaluated by nineteen assessable criteria of five characteristics of innovation interface technology through the use of the Analytical Network Process (ANP) approach. The specific feature of the ANP model is to establish a pairwise comparative matrix and furthermore, to calculate the priority vector weights (eigenvector) of each assessable characteristic, criteria and sub-criteria. The factor analysis can utilize more measure matrix to benefit the deviation of ANP approach due to less data from expert’s opinions. Additionally, in the content, the analytical hierarchical relations are definitely expressed in four levels among each characteristic of innovative interface technology (IIT), criterion and sub-criteria. Moreover, based on the empirical analysis, the enterprises are able to choose the best potential business website with highest economic value added (EVA) through this research in order to maximize financial profits and benefits from an innovative perspective. Finally, some suggestions for managers and researchers are inductively formed to further determine the best development of innovative interface technologies in a thriving cyber commerce environment.

JUDGMENT NUMBER REDUCTION: AN ISSUE IN THE ANALYTIC HIERARCHY PROCESS

2010 ◽  
Vol 09 (01) ◽  
pp. 175-189 ◽  
Author(s):  
LONG-TING WU ◽  
XIA CUI ◽  
RU-WEI DAI
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Pairwise Comparison ◽  
Random Variable ◽  
Analytic Hierarchy ◽  
Priority Vector ◽  
Judgment Error ◽  
Scale Error ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The Analytic Hierarchy Process (AHP) uses pairwise comparison to evaluate alternatives' advantages to a certain criterion. For decision-making problem with many different criteria and alternatives, pairwise comparison causes a prolonged decision-making period and rises fatigue in decision-makers' mentality. A question of practical value is if there exists a way to reduce judgment number and what influence the reduction will have on the overall evaluation of alternative ratings. To answer this question, we introduce scale error and judgment error into AHP judgment matrix. By expanding the scales defined in the AHP, scale error is eliminated. Taking judgment error as random variable, a new estimator to calculate priority vector is presented. In the end, an example is proved to show lowering judgment number will increase the probability of larger errors appearing in priority vector computation.

scholarly journals AHP PRIORITIES AND MARKOV-CHAPMAN-KOLMOGOROV STEADY-STATES PROBABILITIES

2015 ◽  
Vol 7 (2) ◽  
Author(s):  
Stan Lipovetsky
Keyword(s):  
Steady State ◽  
General Solution ◽  
Stochastic Modeling ◽  
Pairwise Comparison ◽  
System Of Equations ◽  
Pairwise Comparison Matrix ◽  
Pair Comparison ◽  
Priority Vector ◽  
Discrete States ◽  
Steady State Probabilities

<div class="MsoTitle" style="margin: 12pt 0in 15pt;"><p>An AHP matrix of the quotients of the pair comparison priorities is transformed to a matrix of shares of the preferences which can be used in Markov stochastic modeling via the Chapman-Kolmogorov system of equations for the discrete states. It yields a general solution and the steady-state probabilities. The AHP priority vector can be interpreted as these probabilities belonging to the discrete states corresponding to the compared items. The results of stochastic modeling correspond to robust estimations of priority vectors not prone to influence of possible errors among the elements of a pairwise comparison matrix.</p></div><div class="MsoTitle" style="margin: 12pt 0in 15pt;"> </div>

Comparative analysis of the evolution of scientific and pedagogical knowledge in the field of education of the culture of piano performance and intonation

2020 ◽  
pp. 147-156
Author(s):  
Anastasiya Y. Maryatch
Keyword(s):  
Comparative Analysis ◽  
Professional Competence ◽  
Pedagogical Knowledge ◽  
Future Teacher ◽  
Piano Performance ◽  
Priority Vector ◽  
Theoretical Substantiation ◽  
The Future ◽  
Auditory Experience ◽  
The Individual

We examine and study the category “Culture of piano performance and intonation”, an important component of the education of professional competence and skill of the future teacher-musician. The subject of the research is the process of educating the culture of piano performance-intonation. The purpose of the research is a scientific and theoretical substantiation of the concept of education of the piano intonation culture. The relevance of the research is that there is a need to study the features of the process of educating the culture of piano performance and intonation. It is established that the content aspects of educating the culture of piano performance and intonation depend on the target setting for the development of a competent personality of the future teacher-musician and, in this regard, the priority vector of development is not only the development of professional musical and pedagogical knowledge, skills and abilities, but also personal qualities. The research methodology is based on the use of comparative analysis and systematization of scientific-theoretical and musical-pedagogical knowledge on the research topic; cultural approach to the problem of studying the phenomenon of piano performance and intonation; hermeneutical approach to the interpretation of the concepts under study; pedagogical experience gained in the course of teaching students in the discipline “Musical and Instrumental Training” at pedagogical university. As a result of this research, the concept of educating the culture of piano performance and intonation is formulated. It is concluded that the culture of piano performance and intonation – is a complex integrative property of the personality, based on the individual style – intonation auditory experience of the individual. The field of application of the obtained results is the practical activity of a teacher-musician.

Interval probability hesitant fuzzy linguistic analytic hierarchy process and its application in talent selection

2020 ◽  
Vol 39 (3) ◽  
pp. 2627-2645
Author(s):  
Sidong Xian ◽  
Hailin Guo ◽  
Jiahui Chai ◽  
Wenhua Wan
Keyword(s):  
Linguistic Variable ◽  
Interval Probability ◽  
Priority Vector ◽  
Operation Rules ◽  
Possibility Degree ◽  
Talent Selection ◽  
Multiple Attribute ◽  
Geometric Consistency ◽  
Fuzzy Linguistic Variable ◽  
Fuzzy Linguistic

Hesitant fuzzy linguistic term set (HFLTS) can handle the qualitative and hesitant information in multiple attribute decision making (MADM) problems which are widely used in various fields. However, the experts’ evaluation of information is not completely reliable in the situation where their own knowledge background is insufficient. In order to deal with deviations due to incomplete reliability of the evaluation, this paper first proposes the interval probability hesitant fuzzy linguistic variable (IPHFLV), which takes the HFLTS as the evaluation part and adds a novel element-reliability of evaluation, thus can describe the different credibility of information evaluation due to the familiarity of experts with schemes and the differences in knowledge cognition. The operation rules and comparison methods are also illustrated. Particularly, under the inspiration of probability theory, we propose the possibility degree of the IPHFLVs. Then we propose IPHFL-AHP based on the AHP and interval probability hesitant fuzzy linguistic variable. Especially, the general geometric consistency index (G-GCI) based on the unbiased estimator of the variance is presented to measure the consistency and the iterative algorithm is constructed to improve the consistency. We use the possibility degree to calculate the priority vector to acquire the total ranking and introduce the process of IPHFL-AHP. Finally, case study of talent selection is given to illustrate the effectiveness and feasibility of the proposed method.

Group priority vector based on comparison judgments

2011 ◽  
Author(s):  
Junhong Li ◽  
Mingjuan Dong ◽  
Fengchun Zhang ◽  
Liyu Nie
Keyword(s):  
Priority Vector
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