Knowledge representation and acquisition in expert systems for pattern recognition

A new approach to the design of fuzzy expert systems is proposed. The representation of knowledge and the formation of statements by fuzzy logic tools are discussed in detail. A model of fuzzy inference is described. Primary attention is given to automatic extraction of knowledge (fuzzy inference rules) from a set of precedents. Various performance criteria for rules are introduced, and an algorithm for their generation (the method of effective restrictions) is proposed. An extension of the type of admissible rules by introducing a fuzzy disjunction operation is described. The possibility of optimizing the rules found is explored. The benefits of the approaches proposed are illustrated by experiments.     

An action learning approach for assessing the consistency of pairwise comparison data

Pairwise comparison data are used in various contexts including the generation of weight vectors for multiple criteria decision making problems. If this data is not sufficiently consistent, then the resulting weight vector cannot be considered to be a reliable reflection of the evaluator’s opinion. Hence, it is necessary to measure its level of inconsistency. Different approaches have been proposed to measuring the level of inconsistency, but they are often based on ‘rules of thumb” and/or randomly generated matrices, and are not interpretable. In this paper we present an action learning approach for assessing the consistency of the input pairwise comparison data that offer interpretable consistency measures.     

Clustering bivariate mixed-type data via the cluster-weighted model

The cluster-weighted model (CWM) is a mixture model with random covariates that allows for flexible clustering/classification and distribution estimation of a random vector composed of a response variable and a set of covariates. Within this class of models, the generalized linear exponential CWM is here introduced especially for modeling bivariate data of mixed-type. Its natural counterpart in the family of latent class models is also defined. Maximum likelihood parameter estimates are derived using the expectation-maximization algorithm and some computational issues are detailed. Through Monte Carlo experiments, the classification performance of the proposed model is compared with other mixture-based approaches, consistency of the estimators of the regression coefficients is evaluated, and several likelihood-based information criteria are compared for selecting the number of mixture components. An application to real data is also finally considered.     

基于L~*-格值逻辑上的BCK-代数中直觉不分明化理想

在L~*-格值逻辑的语义框架下,以L~*-格值上的Lukasiewicz蕴涵算子为工具定义了L~*-格值逻辑上的直觉不分明化BCK-代数的概念,将用集论所刻画的BCK-代数中理想、正定蕴涵理想和蕴涵理想等概念在L~*-格值谓词演算下给予了新的刻画,讨论了它们的性质及其关系,研究了这些理想与其同态象、同态原象之间关系,获得了同类理想之积仍为该类理想.     

New methods for computing inferences in first order logic

Recent improvements in satisfiability algorithms for propositional logic have made partial instantiation methods for first order predicate logic computationally more attractive. Two such methods have been proposed, one by Jeroslow and a hypergraph method for datalog formulas by Gallo and Rago. We show that they are instances of two general approaches to partial instantiation, and we develop these approaches for a large decidable fragment of first order logic (the fragment).Working Paper 1991-11. Supported in part by the Air Force Office of Scientific Research, Grant number AFOSR-87-0292.     

A fuzzy logic for an ordinal sum t-norm

Among the class of residuated fuzzy logics, a few of them have been shown to have standard completeness both for propositional and predicate calculus, like Gödel, NM and monoidal t-norm-based logic systems. In this paper, a new residuated logic NMG, which aims at capturing the tautologies of a class of ordinal sum t-norms and their residua, is introduced and its standard completeness both for propositional calculus and for predicate calculus are proved.     

An axiomatization of events

Most approaches to information modelling are so-called snapshot approaches. This means that they focus on static properties of a universe of discourse only. Some approaches consider the temporal dimension of a universe of discourse. In these approaches the concept of event is central. It is used to denote, e.g., a decision or an action which takes place at a certain time point.In this paper the concept of event is analyzed within the framework of first-order predicate logic. An axiom system for discrete time points and axiom schemes for events is presented. It is shown that the axiom schemes obtained apply to a number of cases with wide applicability. Further, several remaining problems are pointed out.This work is supported by the National Swedish Board for Technical Development (STU).     

On witnessed models in fuzzy logic II

First the expansion of the ?ukasiewicz (propositional and predicate) logic by the unary connectives of dividing by any natural number (Rational ?ukasiewicz logic) is studied; it is shown that in the predicate case the expansion is conservative w.r.t. witnessed standard 1‐tautologies. This result is used to prove that the set of witnessed standard 1‐tautologies of the predicate product logic is Π₂‐hard. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extending Removed Sets Revision to partially preordered belief bases

Most of belief revision operations have been proposed for totally preordrered information. However, in case of partial ignorance, pieces of information are partially preordered and few effective approaches of revision have been proposed. The paper presents a new framework for revising partially preordered information, called Partially Preordered Removed Sets Revision (PPRSR). The notion of removed set, initially defined in the context of the revision of non ordered or totally preordered information is extended to partial preorders. The removed sets are efficiently computed thanks to a suitable encoding of the revision problem into logic programming with answer set semantics. This framework captures the possibilistic revision of partially preordered information and allows for implementing it with ASP. Finally, it shows how PPRSR can be applied to a real application of the VENUS european project.     

Axiomatising the Prior Future in Predicate Logic

Prior investigated a tense logic with an operator for ‘historical necessity’, where a proposition is necessary at a time iff it is true at that time in all worlds ‘accessible’ from that time. Axiomatisations of this logic all seem to require non-standard axioms or rules. The present paper presents an axiomatisation of a first-order version of Prior’s logic by using a predicate which enables any time to be picked out by an individual in the domain of interpretation.     

On the completeness and the decidability of strictly monadic second-order logic

Regarding strictly monadic second-order logic (SMSOL), which is the fragment of monadic second-order logic in which all predicate constants are unary and there are no function symbols, we show that a standard deductive system with full comprehension is sound and complete with respect to standard semantics. This result is achieved by showing that in the case of SMSOL, the truth value of any formula in a faithful identity-standard Henkin structure is preserved when the structure is “standardized”; that is, the predicate domain is expanded into the set of all unary relations. In addition, we obtain a simpler proof of the decidability of SMSOL.     

Fuzzy inequational logic

We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic entailment and provability in graded setting which allows to draw partially true conclusions from partially true assumptions. We follow the Pavelka approach and define general degrees of semantic entailment and provability using complete residuated lattices as structures of truth degrees. We prove the logic is Pavelka-style complete. Furthermore, we present a logic for reasoning about graded if–then rules which is obtained as particular case of the general result.     

Interpolation in superintuitionistic predicate logics with equality

It is shown that the Craig interpolation property and the Beth property are preserved under passage from a superintuitionistic predicate logic to its extension via standard axioms for equality, and under adding formulas of pure equality as new axioms. We find an infinite independent set of formulas which, though not equivalent to formulas of pure equality, may likewise be added as new axiom schemes without loss of the interpolation, or Beth, property. The formulas are used to construct a continuum of logics with equality, which are intermediate between the intuitionistic and classical ones, having the interpolation property. Moreover, an equality-free fragment of the logics constructed is an intuitionistic predicate logic, and formulas of pure equality satisfy all axioms of the classical predicate logic. Supported by RFFR grant No. 96-01-01552. Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 543–561, September–October, 1997.     

Application of fuzzy control to a road tunnel ventilation system

This paper deals with the serious problems of ventilation system in a large road tunnel. Higher visibility and lower concentration of carbon monoxide are the key issues concerning the ventilation system. Prior to designing the fuzzy control model, a configuration layout of the ventilation system including sensing, control and traffic prediction as well is conceptually constructed. Based on the layout that offers assignments of sensors and control elements, a fuzzy logic control model is developed. Membership functions of sensor errors and control increments are physically submitted in order to set up the fuzzy logic rules. Timing and spacing filtering in terms of weighting approaches is employed in the fuzzy logic rules. A dynamic equation describing the concentration of air pollution is also given so as to cooperate with the fuzzy logic rules and to play roles in the computer simulation. The result of computer simulation involving five cases indicates that a multi-level scheme is able to solve the engineering problems.     

Incorporating Managerial Thinking in Prediction and Control: Case Study of Market Penetration

Managerial strategies, especially at the higher echelons of management, are often linguistically stated. This is because they need to be based on information which often defies quantification. Such verbal strategies and qualitative information have often been found to be difficult to incorporate in quantitative models. Thus, the quantitative effects of implementing one strategy as opposed to another have generally been difficult to forecast.In this paper, we show that, through the use of fuzzy logic, we can incorporate such qualitative (linguistically stated) information. Furthermore, we show that a fuzzy controller can be designed so as to reach desired goals while being cognizant of linguistically stated strategies, scenarios, and decision rules as well as quantitative data types.The approach is applied to the modeling and control of market penetration, a field which has attracted considerable attention in recent years.     

The use of fuzzy sets for resource allocation in an advance request vehicle brokerage system—a case study

Community transport vehicle brokerage operators match the needs of groups without minibuses with the spare capacity of groups which own minibuses. They take bookings in advance, and allocate vehicles without knowing what the total demand will be for travel at a certain time. An approach has been developed which ranks vehicles according to a sequence number which indicates how ‘difficult to book’ they are, and presents the most difficult to book to the broker first, with the intention of maintaining the maximum flexibility in the system. The concept difficult to book is not easy to define exactly. Fuzzy set theory provides a mechanism for dealing with imprecise concepts, and through fuzzy logic for reasoning about such concepts. Fuzzy inferencing systems consist of linguistic variables, fuzzy sets, rules, and methods to combine the sets and produce a final result. Fuzzy logic has been used to provide a means of automating the allocation of sequence numbers to vehicles. Three different approaches to developing the rules for this system have been tested, by simulating bookings, and the one which produced the best results was based on a knowledge acquisition process involving booking staff. This approach resulted in the allocation of the highest number of trips and in leaving the least hours of travel unallocated.     

Rough set theory: a novel approach for extraction of robust decision rules based on incremental attributes

Rough set theory is a new data mining approach to manage vagueness. It is capable to discover important facts hidden in the data. Literature indicate the current rough set based approaches can’t guarantee that classification of a decision table is credible and it is not able to generate robust decision rules when new attributes are incrementally added in. In this study, an incremental attribute oriented rule-extraction algorithm is proposed to solve this deficiency commonly observed in the literature related to decision rule induction. The proposed approach considers incremental attributes based on the alternative rule extraction algorithm (AREA), which was presented for discovering preference-based rules according to the reducts with the maximum of strength index (SI), specifically the case that the desired reducts are not necessarily unique since several reducts could include the same value of SI. Using the AREA, an alternative rule can be defined as the rule which holds identical preference to the original decision rule and may be more attractive to a decision-maker than the original one. Through implementing the proposed approach, it can be effectively operating with new attributes to be added in the database/information systems. It is not required to re-compute the updated data set similar to the first step at the initial stage. The proposed algorithm also excludes these repetitive rules during the solution search stage since most of the rule induction approaches generate the repetitive rules. The proposed approach is capable to efficiently and effectively generate the complete, robust and non-repetitive decision rules. The rules derived from the data set provide an indication of how to effectively study this problem in further investigations.     

On tautologies in Ω+-valued logic

The connection is established in this paper between the tautologies of theΩ ⁺-valued predicate logic studied in [1] and the tautologies of m-valued logic for various m <Ω. As a consequence it is proven that the set of tautologies ofΩ ⁺-valued predicate logic is an ??-set. An algorithm is constructed which, for any arbitrary formula ofΩ ⁺-valued logic, recognizes whether or not that formula is anΩ ⁺-valued tautology; one axiomatization is proposed for theΩ ⁺-valued propositional logic.     

Clausal resolution for normal modal logics

We present a clausal resolution-based method for normal modal logics. Differently from other approaches, where inference rules are based on the syntax of a particular set of axioms, we focus on the restrictions imposed on the binary accessibility relation for each particular normal logic. We provide soundness and completeness results for all fifteen families of multi-modal normal logics whose accessibility relations have the property of being non-restricted, reflexive, serial, transitive, Euclidean, or symmetric.