Pairwise Comparisons Of Alternatives Research Articles

Strategy-proofness of the randomized Condorcet voting system

In this paper, we study the strategy-proofness properties of the randomized Condorcet voting system (RCVS). Discovered at several occasions independently, the RCVS is arguably the natural extension of the Condorcet method to cases where a deterministic Condorcet winner does not exists. Indeed, it selects the always-existing and essentially unique Condorcet winner of lotteries over alternatives. Our main result is that, in a certain class of voting systems based on pairwise comparisons of alternatives, the RCVS is the only one to be Condorcet-proof. By Condorcet-proof, we mean that, when a Condorcet winner exists, it must be selected and no voter has incentives to misreport his preferences. We also prove two theorems about group-strategy-proofness. On one hand, we prove that there is no group-strategy-proof voting system that always selects existing Condorcet winners. On the other hand, we prove that, when preferences have a one-dimensional structure, the RCVS is group-strategy-proof.

A New Approach of Indonesian University Webometrics Ranking Using Entropy and PROMETHEE II

The webometric ranking system is currently one of the most widely used methods to rank website quality including for university websites. It uses pre-determined weights for the criteria assessed in these method; therefore, raised a question whether the pre-determined weigh is objective. Entropy method provides a more objective weighing method criterion. This study aims to compare the use of the entropy method followed by PROMETHEE II methods to evaluate 27 Indonesian university websites. The entropy method assesses four indicators: visibility, presence, openness and excellence of the website performance. The PROMETHEE II method was conducted to provide a complete ranking of university websites from the best to the worst, based on a pair-wise comparison of alternatives along each recognized criterion. The entropy method resulted in 0,3; 0,17;0,23; and 0,27 for visibility, presence, openness and excellence weights, respectively. The website ranking using PROMETHEE II method was not significantly different from the ranking generated from the webometric ranking system. To conclude, the use of entropy as a more objective method followed by PROMETHEE II is a reasonable alternative of the webometric system for ranking university websites, at least in the Indonesian context.

On Learning of Choice Models with Interactive Attributes

Introducing recent advances in the machine learning techniques to state-of-the-art discrete choice models, we develop an approach to infer the unique and complex decision making process of a decision-maker (DM), which is characterized by the DM's priorities and attitudinal character, along with the attributes interaction, to name a few. On the basis of exemplary preference information in the form of pairwise comparisons of alternatives, our method seeks to induce a DM's preference model in terms of the parameters of recent discrete choice models. To this end, we reduce our learning function to a constrained non-linear optimization problem. Our learning approach is a simple one that takes into consideration the interaction among the attributes along with the priorities and the unique attitudinal character of a DM. The experimental results on standard benchmark datasets suggest that our approach is not only intuitively appealing and easily interpretable but also competitive to state-of-the-art methods.

Decision-making in natural resources use taking into account the risk of lost opportunities based on pairwise comparison of alternatives

The necessity of consideration of the risk of lost opportunities as a component of the total risk in decision-making in environmental management at risk has been justified. The general terms and regulations are formulated and fundamental generalizations, definitions and assertions regarding decision-making in natural resources use taking into account the risk of lost opportunities are presented. The functions are proposed of the total risk of alternatives as linear combinations that combine system (own) risks of alternatives and risks of lost opportunities where last ones are treated as advantageous effects of alternatives that are rejected. The assertion has been formulated that the set of optimal alternatives on the criterion of minimal risk as a result of solving the problem of decision-making while taking into account the risk of lost opportunities coincides with the set of optimal alternatives on the criterion of the maximum utility. It is shown how to determine the components of the total risk of alternatives when filling decision tables on pairwise comparisons of alternatives and algorithms are proposed for choosing the optimal alternative in view of the risk of lost opportunities.

Consistency-based risk assessment with probabilistic linguistic preference relation

In recent years, the “Belt and Road” has aroused great attention of international society. It not only produces opportunities for China but also brings challenges: when Chinese investors invest to other countries, they will analyze the present situation of alternative countries and then assess the investment risk of these countries. Hence, how to assess the risk level of alternative countries correctly is pivotal. Moreover, affected by many factors such as decision makers (DMs)’ lacking of knowledge and the complexity of decision making problems, the DMs usually cannot use precise numbers to describe their preference information. Therefore, the use of linguistic variables is practical. As a type of linguistic term set, the probabilistic linguistic term set (PLTS) can reflect different importance degrees or weights of all possible evaluation values of a specific object. What’s more, when the DMs use linguistic variables to express their judgements, they sometimes cannot give their evaluation values for attributes directly. In such a case, the DMs usually provide their judgements by pairwise comparison of alternatives. In this paper, we introduce the concept of probabilistic linguistic preference relation (PLPR) to present the DMs’ preferences. The additive consistency of the PLPR is discussed from the perspective of the preference relation graph. Then, the consistency index of the PLPR is defined to measure the consistency. We also introduce the acceptable consistency of the PLPR. Moreover, as for the unacceptable consistent PLPR, an automatic optimization method is proposed to improve its consistency until acceptable. Once all the PLPRs are of acceptable consistency, we directly use the aggregation operators to obtain the comprehensive preference values of alternatives and then rank the alternatives according to the derived preference values. Finally, an application example involving the “Belt and Road” is given and the discussion about the results is conducted.

Explaining robust additive utility models by sequences of preference swaps

As decision-aiding tools become more popular everyday—but at the same time more sophisticated—it is of utmost importance to develop their explanatory capabilities. Some decisions require careful explanations, which can be challenging to provide when the underlying mathematical model is complex. This is the case when recommendations are based on incomplete expression of preferences, as the decision-aiding tool has to infer despite this scarcity of information. This step is key in the process but hardly intelligible for the user. The robust additive utility model is a necessary preference relation which makes minimal assumptions, at the price of handling a collection of compatible utility functions, virtually impossible to exhibit to the user. This strength for the model is a challenge for the explanation. In this paper, we come up with an explanation engine based on sequences of preference swaps, that is, pairwise comparison of alternatives. The intuition is to confront the decision maker with “elementary” comparisons, thus building incremental explanations. Elementary here means that alternatives compared may only differ on two criteria. Technically, our explanation engine exploits some properties of the necessary preference relation that we unveil in the paper. Equipped with this, we explore the issues of the existence and length of the resulting sequences. We show in particular that in the general case, no bound can be given on the length of explanations, but that in binary domains, the sequences remain short.

Metric measurements for optimization of forest road network alternatives in GIS-based programs

An efficient forest road network can increase accessibility to entire forest lands and decrease construction and maintenance costs. In this study, first cost layer for road construction in the semi-mountainous Hyrcanian forest was developed by overlaying thematic layers of slope steepness, soil depth, and proximity to hydrograph network in geographical information system (GIS). Analytical network process (ANP) was used to determine the importance of the layers. Nine road network alternatives were designed on cost layer using PEGGER and then the efficiency of each alternative was evaluated according to the metric of road passage percentage from cost classes. Technical assessment was done by analyzing metrics of overlaps, opened area, and corrected ton-km. The optimum forest road network alternative was selected by pairwise comparison of alternatives with respect to metrics. Based on our findings, we strongly recommend the use of alternative 8 whenever possible, because the construction cost, corrected ton-km, and overlaps were lower, and the opened area was higher than those of the other alternatives.

A method for large group decision-making based on evaluation information provided by participators from multiple groups

Large group decision-making (LGDM) is a special group decision-making (GDM) problem, in which a large number of persons take part in decision process, while research concerning this issue is still relatively scarce. The objective of this paper is to develop a method to solve the LGDM problem, in which a large number of persons from multiple groups take part in the decision process and express their personal evaluations on the alternatives according to the pre-established identifier set. In the method, the percentage distribution on evaluations of each group concerning each alternative is determined. The decision weight of each group concerning each alternative is obtained by aggregating the subjective weight, which is provided by the organizer, and the objective weight, determined according to the level of consensus among participators' evaluations. According to the percentage distributions and decision weights, the dominance degrees on pairwise comparisons of alternatives are calculated, and a ranking of alternatives can be determined using the PROMETHEE II method. Finally, an example is given to illustrate the use of the proposed method.

Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees

Considering the hesitancy degrees on pair-wise comparisons of alternatives as interval-valued intuitionistic fuzzy (IVIF) sets (IVIFSs), we develop a new fuzzy mathematical programming method for solving heterogeneous multiattribute decision-making problems based on the Linear Programming Technique for Multidimensional Analysis of Preference. In this method, IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers, linguistic variables, intervals and real numbers are used to represent multiple types of attribute values and the attribute weights are not completely known. The preference relations between alternatives given by decision maker are expressed with IVIFSs of ordered pairs of alternatives. The consistency and inconsistency indices are defined as IVIFSs on the basis of comparisons of alternatives with IVIF truth degrees. The attribute weights and fuzzy ideal solution (FIS) are estimated through constructing a fuzzy mathematical programming model, which is solved by the technically developed method of IVIF mathematical programming. Hereby the distances of alternatives to the FIS are computed to rank the alternatives. Some generalization and discussion on the constructed IVIF mathematical programming model are also presented. A green supplier selection example is provided to illustrate the effectiveness of the proposed model and method. The comparison analyses verify the superiorities of the proposed method.

The informational basis of scoring rules

We consider voting wherein voters assign a certain score to each of the many available alternatives. We study the normative properties of procedures that aggregate the scores collected in the ballot box. A vast class of ballot aggregators, including procedures based on the pairwise comparison of alternatives, satisfy May’s famous conditions in our framework. We prove that, within such a plethora of procedures, scoring rules are singled out by a property related to their informational basis: in order to determine the winner, they do not take into account the specific distribution of scores chosen by each voter. The result is shown to hold regardless of the introduction of asymmetry among the alternatives.

МЕХАНИЗМ СИСТЕМНОГО УПРАВЛЕНИЯ ИННОВАЦИОННЫМ РАЗВИТИЕМ

The paper researches the issues of post-industrial innovative development. The objective of the research is to create a universal methodology of innovation development management based on the analysis of interaction forms between economy entities. According to the abovementioned objective, a few tasks have been set – to analyze links between the elements of social and economic system conditional on social and institutional development; to explore the most relevant approach to development of complex relations; to create methodology of management of innovation development processes; to test the proposed scheme in subsystem of regional sectoral management. As a result of the research, a methodology of management of innovation development has been created and implemented in the form of software application, and tested in the system of regional power industry management. The analysis of modern theories has shown that a “triple spiral” interaction proves to be the most relevant to modern Russian conditions; with this approach the process of socio-economic development of society is determined by three elements: science, government and business. These institutions are acting on the principle of equitable relations outlined in a contract, and partially perform each other’s functions. Difficulties arise from the consequences of different objectives and criteria of their achievement, not only between the institutions but also depending on the management level. As a solution to the problems of complex systems management, the author offers object-oriented approach with pairwise comparison of alternatives. Such a scheme, in author’s opinion, allows on the one hand to clearly formalize the decision-making process, and on the other hand a psychological problem is solved – a person cannot effectively compare a large number of alternatives. The author considers that a person should only compare not more than two alternatives. This approach is formalized in the form of software application, tested in the management system of regional energy sector. The approach is currently implemented in the management system of applied research. The paper justifies the management issues of applied science, which are subject to different stages of formation of scientific knowledge, as well as various evaluation criteria. It is the object-oriented approach that will resolve the complex and sometimes antagonistic contradictions.

Застосування методу аналізу ієрархій при виборі інструментальних засобів розробки програмного забезпечення

The article is devoted to decision-making systems which are built using hierarchy analysis method. This approach is used for decision-making about choosing integrated software development environment. Respectively a process of integrated software development environment choosing is taken as a research subject and the DSS appears to be an object. For building such a system an example of problem decomposition to its’ parts an building appropriate hierarchy is supplied. On the basis of expert meanings a pairwise comparison of certain criteria of decision relatively to the problem and also a pairwise comparison of alternatives themselves relatively to these criteria is performed. All the results of such comparison are transformed to numbers by a determined algorithm, which continue to be used for estimating ratings of alternative decision variants. These final ratings are used to make a decision about choosing certain alternative.

Fuzzy linear programming approach to multiattribute decision making with multiple types of attribute values and incomplete weight information

In the classical Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), the decision maker (DM) gives the pair-wise comparisons of alternatives with crisp truth degree 0 or 1. However, in the real world, DM is not sure enough in all comparisons and can express his/her opinion with some fuzzy truth degree. Thus, DM's preferences are given through pair-wise comparisons of alternatives with fuzzy truth degrees, which may be represented as trapezoidal fuzzy numbers (TrFNs). Considered such fuzzy truth degrees, the aim of this paper is to develop a new fuzzy linear programming technique for solving multiattribute decision making (MADM) problems with multiple types of attribute values and incomplete weight information. In this method, TrFNs, real numbers, and intervals are used to represent the multiple types of decision information. The fuzzy consistency and inconsistency indices are defined as TrFNs due to the alternatives’ comparisons with fuzzy truth degrees. Hereby a new fuzzy linear programming model is constructed and solved by the possibility linear programming method with TrFNs developed in this paper. The fuzzy ideal solution (IS) and the attribute weights are then obtained. The distances of alternatives from the fuzzy IS can be calculated to determine their ranking order. The implementation process of the method proposed in this paper is illustrated with a strategy partner selection example. The comparison analyzes show that the method proposed in this paper generalizes the classical LINMAP, fuzzy LINMAP and possibility LINMAP.

Applying multi-criteria decision analysis to select WSUD and LID technologies

Water Sensitive Urban Design (WSUD) and Low Impact Development (LID) principles were investigated in Dhaka's drainage network using ‘Regime in Balance’ strategy for Average Recurrence Interval (ARI), Y = 100 years. Three feasible alternatives, such as, leaky-well, soak-away and infiltration trench were identified and designed to improve Dhaka's present unsatisfactory stormwater drainage system into one which is sustainable. For selecting the best one, we applied a multi-criteria decision analysis approach and chose the Analytic Hierarchy Process (AHP) model. Eleven criteria under three categories (technical, economic and social) were considered to quantify relative priorities of alternatives. Pair-wise comparisons of alternatives were performed against each criterion and ranked using a scale from 0 to 9. During the process of applying AHP model, consistency of ranking was thoroughly checked and a reasonable level of inconsistency was accepted due to the nature of human judgement. After the analysis, it was found that leaky-well (percentage priority 43%) followed by soak-away (38%) was the most appropriate technology for improving urban stormwater management system in Dhaka, Bangladesh. The proposed model can also be used in better selecting WSUD and LID technologies in other geographic locations.

An Approach to Solve Group-Decision-Making Problems With Ordinal Interval Numbers

The ordinal interval number is a form of uncertain preference information in group decision making (GDM), while it is seldom discussed in the existing research. This paper investigates how the ranking order of alternatives is determined based on preference information of ordinal interval numbers in GDM problems. When ranking a large quantity of ordinal interval numbers, the efficiency and accuracy of the ranking process are critical. A new approach is proposed to rank alternatives using ordinal interval numbers when every ranking ordinal in an ordinal interval number is thought to be uniformly and independently distributed in its interval. First, we give the definition of possibility degree on comparing two ordinal interval numbers and the related theory analysis. Then, to rank alternatives, by comparing multiple ordinal interval numbers, a collective expectation possibility degree matrix on pairwise comparisons of alternatives is built, and an optimization model based on this matrix is constructed. Furthermore, an algorithm is also presented to rank alternatives by solving the model. Finally, two examples are used to illustrate the use of the proposed approach.

A method based on stochastic dominance degrees for stochastic multiple criteria decision making

In this paper, a novel method based on the stochastic dominance degree (SDD) is proposed to solve a discrete stochastic multiple criteria decision-making (MCDM) problem. Firstly, a concept of stochastic dominance degree is introduced to describe the degree that one alternative dominates another when the SD relation for each pair of alternatives is determined, and a computation formula of the SDD is given. Then, by calculating SDDs, the SDD matrix on pairwise comparisons of alternatives with respect to each criterion is built. Furthermore, the SDD matrices with respect to all the criteria are aggregated into an overall SDD matrix using the simple additive weighting method. Based on the overall SDD matrix, an approach based on the idea of the PROMETHEE-II is developed to obtain the ranking result of alternatives. Finally, two numerical examples are used to illustrate the applicability and effectiveness of the proposed method.

Selecting suppliers using a new fuzzy multiple criteria decision model: the fuzzy balancing and ranking method

In this paper, we present a fuzzy multiple criteria decision making (FMCDM) model known as fuzzy balancing and ranking. In contrast to other MCDM models, our proposed model does not require the weights of decision making criteria. First, we appraise the performance of alternatives against criteria via linguistic variables which are expressed as triangular fuzzy numbers. The foregoing model obtains the alternative rankings through a four-stage process. Second, an outranking matrix is derived indicating that the frequency with which one alternative is superior to all other alternatives based on each criterion. Third, the outranking matrix is triangularised to obtain an implicit pre-ordering or provisional order of alternatives. Fourth, the provisional order of alternatives is subjected to various screening and balancing operations that require sequential application of a balancing principle to the so-called advantages–disadvantages table that combines the criteria with the pair-wise comparisons of alternatives. Additionally, to demonstrate the procedural implementation of the proposed model and its effectiveness, we apply it on a case study regarding the problem of supplier selection.

Using multiple variables decision-making analysis for ERP selection

Enterprise Resource Planning (ERP) systems have been recognised as excellent tools for integrating information, reducing operational costs and enhancing competitiveness. However, they are expensive and complex software with a well-documented high risk of failure when implemented badly. The selection of an ERP system is therefore critical. This paper identifies a set of evaluating variables within three categories: supplier, product functionality and technical capacity. These variables were based on an extensive literature review and interviews with industry experts. ELECTRE I, a multiple variables decision-making method, may then be applied for pair-wise comparison of alternatives to provide an efficient and effective method for selecting an optimum ERP system for a given situation.

Justification for the selection of a reconfigurable manufacturing system: a fuzzy analytical hierarchy based approach

The aim of this article is to highlight a novel production system paradigm entitled the Reconfigurable Manufacturing System (RMS) and study its pre-design strategies. Here a decision-making module is established for the evaluation of existing and new generation manufacturing systems by trading off among the tangible and intangible design parameters. This difficult and time-consuming process is carried out using the Analytical Hierarchy Process (AHP), a widely used process to solve multi-criteria decision-making problems. In order to capture the vagueness and uncertainty of the decision-makers’ judgment, fuzzy logic is introduced into the pairwise comparison of alternatives. In order to provide the designers with a systematic framework to evaluate different alternatives to support their manufacturing system choice, in this paper a model has been proposed to quantify those features of MSs that aid in rapidly adjusting their capability to production functionality (convertibility). After providing the mathematical model to quantify the metrics of convertibility, a fuzzy logic based AHP model has been utilized to evaluate the importance of the individual matrices in measuring the system convertibility. We provide support with an effective case example.

Graded pairs comparison ‐ does strength of preference matter? Analysis of preferences for specialised nurse home visits for pain management

In the stated preference method called graded pairs comparisons respondents are asked to rate the intensity of their preference for their preferred alternative in a pairwise comparison of alternatives. Econometricians anticipate that the additional information will improve statistical efficiency compared to the standard DCE format. However, this paper reveals that added information inherent in graded pairs scale does not provide smaller standard deviations for the WTP estimated. Secondly, the ordered-response regression models employing the full range of the graded pairs data tend to overestimate WTP, which presumably is caused by the inherent tendency of the ordered-response models to 'predict to the extremes'.