33 research outputs found
A short note on fuzzy relational inference systems
This paper is a short note contribution to the topic of fuzzy relational inference systems and the preservation of their desirable properties. It addresses the two main fuzzy relational inferences – compositional rule of inference (CRI) and the Bandler–Kohout subproduct (BK-subproduct) – and their combination with two fundamental fuzzy relational models of fuzzy rule bases, namely, the Mamdani–Assilian and the implicative models.
The goal of this short note article is twofold. Firstly, we show that the robustness related to the combination of BK-subproduct and implicative fuzzy rule base model was not proven correctly in [24]. However, we will show that the result itself is still valid and a valid proof will be provided. Secondly, we shortly discuss the preservation of desirable properties of fuzzy inference systems and conclude that neither the above mentioned robustness nor any other computational advantages should automatically lead to a preference of the combinations of CRI with Mamdani–Assilian models or of the BK-subproduct with the implicative models
Componentwise concave copulas and their asymmetry
summary:The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the -measure of non-exchangeability for copulas belonging to this class
Interest Measures for Fuzzy Association Rules Based on Expectations of Independence
Lift, leverage, and conviction are three of the best commonly known interest measures for crisp association rules. All of them are based on a comparison of observed support and the support that is expected if the antecedent and consequent part of the rule were stochastically independent. The aim of this paper is to provide a correct definition of lift, leverage, and conviction measures for fuzzy association rules and to study some of their interesting mathematical properties
The variety generated by all the ordinal sums of perfect MV-chains
We present the logic BL_Chang, an axiomatic extension of BL (see P. H\'ajek -
Metamathematics of fuzzy logic - 1998, Kluwer) whose corresponding algebras
form the smallest variety containing all the ordinal sums of perfect MV-chains.
We will analyze this logic and the corresponding algebraic semantics in the
propositional and in the first-order case. As we will see, moreover, the
variety of BL_Chang-algebras will be strictly connected to the one generated by
Chang's MV-algebra (that is, the variety generated by all the perfect
MV-algebras): we will also give some new results concerning these last
structures and their logic.Comment: This is a revised version of the previous paper: the modifications
concern essentially the presentation. The scientific content is substantially
unchanged. The major variations are: Definition 2.7 has been improved.
Section 3.1 has been made more compact. A new reference, [Bus04], has been
added. There is some minor modification in Section 3.
The generalized index of maximum and minimum level and its application in decision making
The index of maximum and minimum level is a very useful technique, especially for decision making, which uses the Hamming distance and the adequacy coefficient in the same problem. In this paper, we suggest a generalization by using generalized and quasi-arithmetic means. As a result, we will get the generalized ordered weighted averaging index of maximum and minimum level (GOWAIMAM) and the Quasi-OWAIMAAM operator. These new aggregation operators generalize a wide range of particular cases such as the generalized index of maximum and minimum level (GIMAM), the OWAIMAM, the ordered weighted quadratic averaging IMAM (OWQAIMAM), and others. We also develop an application of the new approach in a decision making problem about selection of products.generalized mean, index of maximum and minimum level, quasi-arithmetic mean, decision making, owa operator
Hierarchical Control of Production Flow based on Capacity Allocation for Real-Time Scheduling of Manufacturing System
8International audienceThis paper considers the modelling and simulation of a hierarchical production-flow control system. It uses a continuous control approach for machine capacity allocation at the design level and real time scheduling at the shop-floor level. Particularly, at the design level, the control of machine throughput has been addressed by a set of distributed and supervised fuzzy controllers. The objective is to adjust the machine's production rates in such a way that satisfies the demand while maintaining the overall performances within acceptable limits. At the shop-floor level, the problem of scheduling of jobs is considered. In this case, the priority of jobs (actual dispatching times) is determined from the continuous production rates through a discretization procedure. A case study demonstrates the efficiency of the proposed methodology through a simulation case study
Pre-aggregation functions: construction and an application
In this work we introduce the notion of preaggregation
function. Such a function satisfies the same boundary
conditions as an aggregation function, but, instead of requiring
monotonicity, only monotonicity along some fixed direction (directional
monotonicity) is required. We present some examples
of such functions. We propose three different methods to build
pre-aggregation functions. We experimentally show that in fuzzy
rule-based classification systems, when we use one of these
methods, namely, the one based on the use of the Choquet
integral replacing the product by other aggregation functions,
if we consider the minimum or the Hamacher product t-norms
for such construction, we improve the results obtained when
applying the fuzzy reasoning methods obtained using two classical
averaging operators like the maximum and the Choquet integral.This work was supported in part by the Spanish Ministry of Science
and Technology under projects TIN2008-06681-C06-01, TIN2010-
15055, TIN2013-40765-P, TIN2011-29520
Interest Measures for Fuzzy Association Rules Based on Expectations of Independence
Lift, leverage, and conviction are three of the best commonly known interest measures for crisp association rules. All of them are based on a comparison of observed support and the support that is expected if the antecedent and consequent part of the rule were stochastically independent. The aim of this paper is to provide a correct definition of lift, leverage, and conviction measures for fuzzy association rules and to study some of their interesting mathematical properties