Topic
Pairwise comparison
About: Pairwise comparison is a research topic. Over the lifetime, 6804 publications have been published within this topic receiving 174081 citations.
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17 Oct 2005
TL;DR: A framework which can incorporate arbitrary pairwise constraints between body parts, such as scale compatibility, relative position, symmetry of clothing and smooth contour connections between parts is developed.
Abstract: The goal of this work is to recover human body configurations from static images. Without assuming a priori knowledge of scale, pose or appearance, this problem is extremely challenging and demands the use of all possible sources of information. We develop a framework which can incorporate arbitrary pairwise constraints between body parts, such as scale compatibility, relative position, symmetry of clothing and smooth contour connections between parts. We detect candidate body parts from bottom-up using parallelism, and use various pairwise configuration constraints to assemble them together into body configurations. To find the most probable configuration, we solve an integer quadratic programming problem with a standard technique using linear approximations. Approximate IQP allows us to incorporate much more information than the traditional dynamic programming and remains computationally efficient. 15 hand-labeled images are used to train the low-level part detector and learn the pairwise constraints. We show test results on a variety of images.
247 citations
01 Dec 2016
TL;DR: The concept of probabilistic linguistic preference relation (PLPR) is introduced to present the DMs preferences and an automatic optimization method is proposed to improve its consistency until acceptable.
Abstract: Display Omitted Propose the probabilistic linguistic preference relation (PLPR).Discuss the consistency of PLPR from the perspective of digraph.Present the consistency and acceptable consistency measures of PLPR.Establish an optimization model to improve the consistency of PLPR.Apply the proposed method to risk assessment. 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. Whats 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.
243 citations
TL;DR: A consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets in the decision making problems with linguistic preference relations is proposed and interval multiplicative preference relations are used in the pairwise comparisons method.
Abstract: The 2-tuple linguistic modeling is a popular tool for computing with words in decision making. In order to deal with the linguistic term sets that are not uniformly and symmetrically distributed, the numerical scale model has been developed to generalize the 2-tuple linguistic modeling. In the numerical scale model, the key task of the 2-tuple based models is the definition of a numerical scale function that establishes a one to one mapping between the linguistic information and numerical values. In this paper, we propose a consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets in the decision making problems with linguistic preference relations. This consistency-driven methodology is based on a natural premise regarding the consistency of preference relations. If linguistic preference relations provided by experts are of acceptable consistency, the corresponding transformed numerical preference relations by the established interval numerical scale are also consistent. Compared with the existing approach based on canonical characteristic values, the consistency-driven methodology provides a new way to set the interval numerical scale without the need of the semantics defined by interval type-2 fuzzy sets. Meanwhile, interval multiplicative preference relations are used in the pairwise comparisons method and the presented theory can be utilized in the pairwise comparisons method as it provides a novel approach to automatic construct interval multiplicative preference relations. Finally, we present the framework for the use of the consistency-driven automatic methodology in linguistic group decision making problems and two numerical examples are given to illustrate the feasibility and validity of this proposal.
243 citations
TL;DR: A new method for calculating the missing elements of an incomplete matrix of pairwise comparison values for a decision problem is proposed and it is shown that the optimal values are obtained by solving a linear system and unicity of the solution is proved under general assumptions.
241 citations
TL;DR: This paper introduces the concept of a grouping function, i.e., a specific type of aggregation function that combines two degrees of support (weak preference) into adegree of information or, say, a degree of comparability between two alternatives, and relates this new concept to that of incomparability.
Abstract: In this paper, we propose new aggregation functions for the pairwise comparison of alternatives in fuzzy preference modeling. More specifically, we introduce the concept of a grouping function, i.e., a specific type of aggregation function that combines two degrees of support (weak preference) into a degree of information or, say, a degree of comparability between two alternatives, and we relate this new concept to that of incomparability. Grouping functions of this type complement the existing concept of overlap functions in a natural way, since the latter can be used to turn two degrees of weak preference into a degree of indifference. We also define the so-called generalized bientropic functions that allow for a unified representation of overlap and grouping functions. Apart from analyzing mathematical properties of these types of functions and exploring relationships between them, we elaborate on their use in fuzzy preference modeling and decision making. We present an algorithm to elaborate on an alternative preference ranking that penalizes those alternatives for which the expert is not sure of his/her preference.
241 citations