摘要 :
In this article, we present a probabilistic framework which serves as the base from which instance-based algorithms for solving the supervised ranking problem may be derived. This framework constitutes a simple and novel approach ...
展开
In this article, we present a probabilistic framework which serves as the base from which instance-based algorithms for solving the supervised ranking problem may be derived. This framework constitutes a simple and novel approach to the supervised ranking problem, and we give a number of typical examples of how this derivation can be achieved. In this general framework, we pursue a cumulative and stochastic approach, relying heavily upon the concept of stochastic dominance. We show how the median can be used to extract, in a consistent way, a single (classification) label from a returned cumulative probability distribution function. We emphasize that all operations used are mathematically sound, i.e. they only make use of ordinal properties. Mostly, when confronted with the problem of learning a ranking, the training data is not monotone in itself, and some cleansing operation is performed on it to remove these 'inconsistent' examples. Our framework, however, deals with these occurrences of 'reversed preference' in a non-invasive way. On the contrary, it even allows to incorporate information gained from the occurrence of these reversed preferences. This is exactly what happens in the second realization of the main theorem.
收起
摘要 :
We equip the set of reciprocal relations with an appropriate order relation capturing the bipolar semantics, turning this set into a complete join-semilattice. We also introduce the notion of a compatible family of reciprocal rela...
展开
We equip the set of reciprocal relations with an appropriate order relation capturing the bipolar semantics, turning this set into a complete join-semilattice. We also introduce the notion of a compatible family of reciprocal relations and show that such a family has an infimum. Moreover, we discuss the one-to-one correspondence between the set of 3-valued reciprocal relations and the set of complete crisp relations. We refine the theorem of Bandler and Kohout concerning the existence of closures of elements of a poset w.r.t. some given property, rendering it applicable to the above join-semilattice. The paper is solely dedicated to the transitivity property. Although uniquely defined for 3-valued reciprocal relations, general reciprocal relations can exhibit various types of transitivity. We characterize the mappings g and h for which the corresponding g-stochastic and h-isostochastic transitive closure exists for any reciprocal relation. In particular, it follows that weak and strong stochastic transitive closures always exist, while this is not the case for moderate stochastic transitivity. Moreover, max-isostochastic transitivity turns out to be the only practically relevant type of isostochastic transitivity. Finally, we provide algorithms realizing each of these transitive closures.
收起
摘要 :
We introduce the notion of a dice model as a framework for describing a class of probabilistic relations. We investigate the transitivity of the probabilistic relation generated by a dice model and prove that it is a special type ...
展开
We introduce the notion of a dice model as a framework for describing a class of probabilistic relations. We investigate the transitivity of the probabilistic relation generated by a dice model and prove that it is a special type of cycle-transitivity that is situated between moderate stochastic transitivity or product-transitivity on the one side, and Lukasiewicz-transitivity on the other side. Finally, it is shown that any probabilistic relation with rational elements on a three-dimensional space of alternatives which possesses this particular type of cycle-transitivity, can be represented by a dice model. The same does not hold in higher dimensions.
收起
摘要 :
A new method to construct semi-copulas is introduced. These semi-copulas are called ortholinear (resp. paralinear) semi-copulas and their construction is based on linear interpolation on segments that are perpendicular (resp. para...
展开
A new method to construct semi-copulas is introduced. These semi-copulas are called ortholinear (resp. paralinear) semi-copulas and their construction is based on linear interpolation on segments that are perpendicular (resp. parallel) to the diagonal of the unit square. The classes of ortholinear and paralinear (quasi-)copulas are characterized as well.
收起
摘要 :
We introduce two extreme methods to pairwisely compare ordered lists of the same length, viz. the comonotonic and the countermonotonic comparison method, and show that these methods are, respectively, related to the copula T_M (th...
展开
We introduce two extreme methods to pairwisely compare ordered lists of the same length, viz. the comonotonic and the countermonotonic comparison method, and show that these methods are, respectively, related to the copula T_M (the minimum operator) and the Lukasiewicz copula T_L used to join marginal cumulative distribution functions into bivariate cumulative distribution functions. Given a collection of ordered lists of the same length, we generate by means of T_M and T_L two probabilistic relations Q~M and Q~L and identify their type of transitivity. Finally, it is shown that any probabilistic relation with rational elements on a 3-dimensional space of alternatives which possesses one of these types of transitivity, can be generated by three ordered lists and at least one of the two extreme comparison methods.
收起
摘要 :
In many modelling problems, there is some inherent monotone relationship between one or more of the input variables and the output variable. We consider the prototypical case of an increasing relationship between each of the input...
展开
In many modelling problems, there is some inherent monotone relationship between one or more of the input variables and the output variable. We consider the prototypical case of an increasing relationship between each of the input variables and the output variable. When using fuzzy rule-based models, this desired monotonicity is reflected in the rule base, given an appropriate ordering on the fuzzy sets involved in the respective input and output domains. More specifically, the larger the antecedent fuzzy sets, the larger the consequent fuzzy set. However, fuzzy rule-based modelling involves a final defuzzification step, possibly resulting in a function that is no longer monotone. In the context of Mamdani-Assilian conjunctive fuzzy models, ample attention has been paid to this problem, both for the centre-of-gravity defuzzification and mean-of-maxima defuzzification methods. In this paper, we show that for implicative fuzzy models, the non-monotonicity problem can be circumvented by making explicit the semantics of the fuzzy rules by subjecting the antecedent and consequent fuzzy sets to the at-least and/or at-most modifiers.
收起
摘要 :
For a reciprocal relation Q on a set of alternatives A, two transitivity frameworks which generalize both T-transitivity and stochastic transitivity are compared: the framework of cycle-transitivity, introduced by the present auth...
展开
For a reciprocal relation Q on a set of alternatives A, two transitivity frameworks which generalize both T-transitivity and stochastic transitivity are compared: the framework of cycle-transitivity, introduced by the present authors (Soc. Choice Welf., to appear) and which is based upon the ordering of the numbers Q(a, b), Q(b, c) and Q(c, a) for all (a, b, c) ∈ A~3, and the framework of FG-transitivity, introduced by Switalski (Fuzzy Sets and Systems 137 (2003) 85) as an immediate generalization of stochastic transitivity. The rules that enable to express FG-transitivity in the form of cycle-transitivity and cycle-transitivity in the form of FG-transitivity, illustrate that for reciprocal relations the concept of cycle-transitivity provides a framework that can cover more types of transitivity than does the concept of FG-transitivity.
收起
摘要 :
Daily ruminal pH variation can be summarized by a cumulative logistic curve based on the amount of time below multiple pH points and characterized by 2 parameters @b"0 and @b"1 . Moreover, rumen pH variation affects the rumen micr...
展开
Daily ruminal pH variation can be summarized by a cumulative logistic curve based on the amount of time below multiple pH points and characterized by 2 parameters @b"0 and @b"1 . Moreover, rumen pH variation affects the rumen microbiome as well as the biohydrogenation pathways resulting in a modified secretion of milk fatty acids FA . The aims of this study were to assess the shifts in milk FA due to rumen pH changes and to estimate the relationship between milk FA and the 2 parameters of the logistic curve. The data consisted of milk samples of 2 experiments. In experiment 1, 3 cows were subjected to 5 treatments in which the type and amount of concentrate were changed during 33 d: 1 control diet 1, 2 stepwise replacement of a standard concentrate CONC by a CONC rich in rapidly fermentable carbohydrates, 3 increase in the total amount of CONC, 4 treatment with a buffer solution, and 5 control diet 2. A 3x3 Latin square design with 3 cows was used in the second experiment. During the first 14 d of each period, the cows received a control diet with a standard CONC, whereas in the last 7 d the standard CONC was replaced step-by-step by a CONC rich in rapidly fermentable carbohydrates and the amount of CONC was increased. During each period, a different buffer treatment was added to the diet. Milk FA and pH reacted similarly in both experiments: decreasing proportions of iso FA and increasing proportions of odd-chain FA were observed. However, an abrupt change to a 76% CONC diet as for one cow of experiment 1 led to almost a 10-fold increase in C18:1 trans-10 0.79 vs. 6.75g/100g of FA . In experiment 2, the stepwise approach of adding CONC and the continuous supplementation of buffer led to minimal increases in C18:1 trans-10 and decreases in rumen pH compared with the diet with standard CONC only. Fatty acid proportions were influenced by the level of rumen pH @b"1 or the rumen pH variation @b"0 , or both. High proportions of C18:1 trans-10 above 4g/100g of FA occurred with low and largely fluctuating pH low @b"1, low @b"0 , whereas situations with low, stable pH low @b"1, great @b"0 did not induce a shift toward the secondary biohydrogenation pathway. C18:1 trans-11 and C18:2 cis-9, trans-11 were only influenced by the pH variation and not by the average pH, whereas iso C14:0 and iso C16:0 FA were only dependent on the average pH and not influenced by diurnal pH variation. Overall, milk FA changes were related to pH changes; however, this relationship is not straightforward and needs further research.
收起
摘要 :
Daily ruminal pH variation can be summarized by a cumulative logistic curve based on the amount of time below multiple pH points and characterized by 2 parameters (β_0and β_1. Moreover, rumen pH variation affects the rumen micro...
展开
Daily ruminal pH variation can be summarized by a cumulative logistic curve based on the amount of time below multiple pH points and characterized by 2 parameters (β_0and β_1. Moreover, rumen pH variation affects the rumen microbiome as well as the biohydro-genation pathways resulting in a modified secretion of milk fatty acids (FA). The aims of this study were to assess the shifts in milk FA due to rumen pH changes and to estimate the relationship between milk FA and the 2 parameters of the logistic curve. The data consisted of milk samples of 2 experiments. In experiment 1, 3 cows were subjected to 5 treatments in which the type and amount of concentrate were changed during 33 d: (1) control diet 1, (2) stepwise replacement of a standard concentrate (CONC) by a CONC rich in rapidly fermentable carbohydrates, (3) increase in the total amount of CONC, (4) treatment with a buffer solution, and (5) control diet 2. A 3 x 3 Latin square design with 3 cows was used in the second experiment. During the first 14 d of each period, the cows received a control diet with a standard CONC, whereas in the last 7 d the standard CONC was replaced step-by-step by a CONC rich in rapidly fermentable carbohydrates and the amount of CONC was increased. During each period, a different buffer treatment was added to the diet. Milk FA and pH reacted similarly in both experi-. ments: decreasing proportions of iso FA and increasing proportions of odd-chain FA were observed. However, an abrupt change to a 76% CONC diet as for one cow of experiment 1 led to almost a 10-fold increase in C18:l trans-10 (0.79 vs. 6.75 g/100 g of FA). In experiment 2, the stepwise approach of adding CONC and the continuous supplementation of buffer led to minimal increases in C18:l trans-10 and decreases in rumen pH compared with the diet with standard CONC only. Fatty acid proportions were influenced by the level of rumen pH (β_1) or the rumen pH variation (β_0), or both. High proportions of C18:l trans-10 (above 4 g/100 g of FA) occurred with low and largely fluctuating pH (low β_1, low β_0), whereas situations with low, stable pH (low β_1, great (β_0) did not induce a shift toward the secondary biohydrogenation pathway. C18:l trans-11 and C18:2 cis-9, trans-11 were only influenced by the pH variation and not by the average pH, whereas iso C14:0 and iso C16:0 FA were only dependent on the average pH and not influenced by diurnal pH variation.
收起
摘要 :
In this paper different clustering algorithms are used to identify Takagi-Sugeno models in a data-driven manner. All but one of these clustering algorithms are based on the minimization of an objective function; the other one is t...
展开
In this paper different clustering algorithms are used to identify Takagi-Sugeno models in a data-driven manner. All but one of these clustering algorithms are based on the minimization of an objective function; the other one is the subtractive clustering algorithm. To guide the objective function-based clustering algorithms, an algorithm called ClusterFinder is developed in order to determine the optimal number of clusters as a compromise between model complexity and model accuracy. The hydrological case study considered concerns the modelling of unsaturated groundwater flow. The Takagi-Sugeno models are identified on the basis of an artificially generated training data set for a specific soil type, and can be incorporated into a fuzzy rule-based groundwater model.
收起
