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Order-Sorted Feature (OSF) logic is a knowledge representation and reasoning language based on function-denoting feature symbols and set-denoting sort symbols ordered in a subsumption lattice. OSF logic allows the construction of record-like terms that represent classes of entities and that are themselves ordered in a subsumption relation. The unification algorithm for such structures provides an efficient calculus of type subsumption, which has been applied in computational linguistics and implemented in constraint logic programming languages such as LOGIN and LIFE and automated reasoners such as CEDAR. This work generalizes OSF logic to a fuzzy setting. We give a flexible definition of a fuzzy subsumption relation which generalizes Zadeh's inclusion between fuzzy sets. Based on this definition we define a fuzzy semantics of OSF logic where sort symbols and OSF terms denote fuzzy sets. We extend the subsumption relation to OSF terms and prove that it constitutes a fuzzy partial order with the property that two OSF terms are subsumed by one another in the crisp sense if and only if their subsumption degree is greater than 0. We show how to find the greatest lower bound of two OSF terms by unifying them and how to compute the subsumption degree between two OSF terms, and we provide the complexity of these operations.

The development of this research had the objective of obtaining a mathematical model called La Pitia that addresses the management capacity of construction companies so that they can respond: Why are the delivery dates of the works not being met? Why is the quality pre-established in the regulations not being met? Why is industrial safety not complied with? Why are they exceeding planned costs? Why does construction management become a factor that generates pathologies? It is part of a job in the area of ​​construction prognosis, whose scope is to predict success. In this search, functions were obtained that model the company's ability to reduce the risks that it will face during the execution process, which have been called Expertise, which indicates how far or close it could be to the desired success in the execution of the work. The vast majority of construction companies in Venezuela do not receive feedback on the results obtained from their works, nor do they have a formal data arrangement system that allows reliable forecasts to be made, which is why the mathematical development of this work was based on concepts of Approximate Reasoning and Fuzzy Logic, El desarrollo de esta investigación ha tenido como objetivo obtener un modelo matemático denominado La Pitia que aborde la capacidad de gestión de las empresas constructoras con la finalidad de que puedan responder ¿Por qué no se cumplen las fechas de entrega de las obras? ¿Por qué no se cumple con la calidad preestablecidas en las normativas? ¿Por qué no se cumple con la seguridad industrial? ¿Por qué se exceden en los costos planificados? ¿Por qué la gestión de obra se transforma en un factor generador de patologías? Es parte de un trabajo en el área de la prognosis en la construcción, cuyo alcance es predecir el éxito. En esa búsqueda, se obtuvieron funciones que modelan la capacidad de la empresa en reducir los riesgos que confrontará durante el proceso de ejecución, a las que se les ha denominado Experticia, la cual indica, cuán lejos o cerca se podría estar del éxito deseado en la ejecución de la obra. La gran mayoría de las empresas constructoras en Venezuela no se retroalimentan de los resultados obtenidos de sus obras, ni tienen un sistema de arreglo formal de data que permita realizar pronósticos confiables, razón por la cual, el desarrollo matemático de este trabajo se apoyó en conceptos del Razonamiento Aproximado y de la Lógica Difusa

The aim of this paper is to propose a new approach for the automatic treatment of linguistic vagueness. Our motivation is the feeling that most existing approaches dealing with linguistic information are based on converting vague meaning into crisp meaning using some conversions to precise measurements. As a result, existing approaches are adequate and easy to implement, but do not closely model the human thought process. To help alleviate this deficiency, we propose the use of linguistic relations to provide a natural language interface to an end user. We show a possible linguistic Prolog model based on an extension of the syntactic unification algorithm using synonymy and antonymy, as well as the extension of the resolution principle. Our approach does not aim to provide a well-founded formal semantics for such a linguistic Prolog, but a simple model supported by two experiments focused on the use of vague language, both of them executed in Spanish (an analysis of the data of the first experiment it is also available in that language at [1]). Thus, the purpose of this paper is to contribute to the mechanization of approximate reasoning by being respectful of the semantics of the vague terms involved in it; i.e., by paying attention to how they are evaluated by linguistic users under experimentation

After more than three decades since the introduction of linguistic variables and their application to approximate reasoning by Zadeh [1], the ability of fuzzy logic systems (FLSs) for modeling real world applications is not a secret to anyone. Currently there are two basic approaches to determine fuzzy model of a system in the literature which are, 1-direct approach, and 2-indirect approach. In direct approach rules are generated via knowledge extraction from experienced experts, while in indirect approach historical data of a system determine the governing rules. The first method is involved with extracting knowledge from experts who in some cases are not available, or they avoid providing us with useful information. In the second method which is dealt with historical data, clustering is the proper tool for structure identification of a system under investigation. Determining the structure of a system relying only on past data also has its own problems. In this paper we try to develop a hybrid approach in interval type-2 fuzzy system modeling (IT2FSM) which benefits from the advantages of both direct and indirect methods. At first stage the modified approach to interval type-2 fuzzy c-mean clustering (IT2FCM) is applied to identify the structure of system and in the second stage the hybrid of direct and indirect approach in system modeling is used to complete the rule base of a model. © 2012 IEEE., Minist. Commun. Inf. Technol. Republic Azerbaijan

After more than three decades since the introduction of linguistic variables and their application to approximate reasoning by Zadeh [1], the ability of fuzzy logic systems (FLSs) for modeling real world applications is not a secret to anyone. Currently there are two basic approaches to determine fuzzy model of a system in the literature which are, 1-direct approach, and 2-indirect approach. In direct approach rules are generated via knowledge extraction from experienced experts, while in indirect approach historical data of a system determine the governing rules. The first method is involved with extracting knowledge from experts who in some cases are not available, or they avoid providing us with useful information. In the second method which is dealt with historical data, clustering is the proper tool for structure identification of a system under investigation. Determining the structure of a system relying only on past data also has its own problems. In this paper we try to develop a hybrid approach in interval type-2 fuzzy system modeling (IT2FSM) which benefits from the advantages of both direct and indirect methods. At first stage the modified approach to interval type-2 fuzzy c-mean clustering (IT2FCM) is applied to identify the structure of system and in the second stage the hybrid of direct and indirect approach in system modeling is used to complete the rule base of a model. © 2012 IEEE., Minist. Commun. Inf. Technol. Republic Azerbaijan

Logic programming languages based on first-order terms (FOTs) have been extended with a similarity relation on functor symbols in order to perform approximate reasoning, which may allow flexible querying and retrieval from a knowledge base. More flexibility is also provided by the terms of Order-Sorted Feature (OSF) logic, which relax a few syntactic restrictions of FOTs. Moreover, OSF term unification takes into account a subsumption ordering on sort symbols, which makes computations more efficient. This document presents the current efforts by the authors in defining similarity-based reasoning with OSF logic: the goal is to achieve a more flexible, but still efficient, processing of queries.

Taxonomies are frequently used to represent knowledge; a taxonomy is a set of concepts partially ordered by a subsumption (is-a) relation. Recently, the CEDAR project has proposed a CEDAR Semantic Web reasoner based on OSF logic, which has shown very promising results with respect to both efficiency and scalability. Indeed, the basic operations behind the reasoning mechanism of CEDAR amount to answering Boolean queries on a taxonomy. For instance, CEDAR answers a conjunctive query on a taxonomy by computing the greatest lower bound of a subset of its elements. This paper proposes a generalization of this operation to the setting where the taxonomy is regarded as a fuzzy partially ordered set and an answer to a conjunctive query is associated with a satisfaction (approximation) degree. A conjunctive query on the fuzzy taxonomy can be answered by applying the same encoding technique of the CEDAR reasoner, while the approximation degree of an answer can be computed by adapting shortest path algorithms for directed acyclic graphs that can be further optimized thanks to the information provided by the encoding.

In his 1991 seminal paper, Enrique H. Ruspini proposed a similarity-based semantics for fuzzy sets and approximate reasoning which has been extensively used by many other authors in various con- texts. This brief note, which is our humble contribution to honor Ruspini¿s great legacy, describes some of the main developments in the field of logic that essentially rely on his ideas

The Logic of Approximate Entailment (LAE) is a graded counterpart of classical propositional calculus, where conclusions that are only approximately correct can be drawn. This is achieved by equipping the underlying set of possible worlds with a similarity relation. When using this logic in applications, however, a disadvantage must be accepted; namely, in LAE it is not possible to combine conclusions in a conjunctive way. In order to overcome this drawback, we propose in this paper a modification of LAE where, at the semantic level, the underlying set of worlds is moreover endowed with an order structure. The chosen framework is designed in view of possible applications.

In this thesis two models of syllogistic reasoning for dealing with arguments that involve fuzzy quantified statements and approximate chaining are proposed. The modeling of quantified statements is based on the Theory of Generalized Quantifiers, which allows us to manage different kind of quantifiers simultaneously, and the inference process is interpreted in terms of a mathematical optimization problem, which allows us to deal with more arguments that standard deductive ones. For the case of approximate chaining, we propose to use synonymy, as used in a thesaurus, for calculating the degree of confidence of the argument according to the degree of similarity between chaining terms. As use cases, different types of Bayesian reasoning (Generalized Bayes' Theorem, Bayesian networks and probabilistic reasoning in legal argumentation) are analysed for being expressed through syllogisms.

In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional, comparative and exception) taken from Theory of Generalized Quantifiers and similarity quantifiers, taken from statistics, are considered and (ii) any number of premises can be taken into account within the reasoning process. Furthermore, a systematic reasoning procedure to solve the syllogism is also proposed, interpreting it as an equivalent mathematical optimization problem, where the premises constitute the constraints of the searching space for the quantifier in the conclusion.

Two interpretations about syllogistic statements are described in this paper. One is the so-called set-based interpretation, which assumes that quantified statements and syllogisms talk about quantity-relationships between sets. The other one, the so-called conditional interpretation, assumes that quantified propositions talk about conditional propositions and how strong are the links between the antecedent and the consequent. Both interpretations are compared attending to three different questions (existential import, singular statements and non-proportional quantifiers) from the point of view of their impact on the further development of this type of reasoning.

Fuzzy logic dates back to 1965 and it is related not only to current areas of knowledge, such as Control Theory and Computer Science, but also to traditional ones, such as Philosophy and Linguistics. Like any logic, fuzzy logic is concerned with argumentation, but unlike other modalities, which focus on the crisp reasoning of Mathematics, it deals with common sense reasoning; i.e., with approximate reasoning. Although the teaching of logic has formed part of mainstream education for many years, fuzzy logic is a much more recent inclusion. In this paper we emphasize the desirability of having illustrative examples related to students’ everyday activities, such as sports, in order to introduce fuzzy logic in higher education. Taking an example from cycling, we show, step by step, how to model an approximate reasoning regarding the choice of a ratio (a combination of freewheel and chainring) in order to advance more or less with each rotation of the pedals. Led by this example, a number of alternatives attending to the formal representation of the premises and the ways of inferring a plausible conclusion are analyzed. The choices made between alternatives are justified. We show that the conclusion inferred in the example is consistent with the models selected for premises and fuzzy inference and similar to that concluded by a human being

This paper focuses on approximate reasoning based on the use of approximation spaces. Approximation spaces and the approximated relations induced by them are a generalization of the rough set-based approximations of Pawlak. Approximation spaces are used to define neighborhoods around individuals and rough inclusion functions. These in turn are used to define approximate sets and relations. In any of the approaches, one would like to embed such relations in an appropriate logical theory which can be used as a reasoning engine for specific applications with specific constraints. We propose a framework which permits a formal study of the relationship between properties of approximations and properties of approximation spaces. Using ideas from correspondence theory, we develop an analogous framework for approximation spaces. We also show that this framework can be strongly supported by automated techniques for quantifier elimination., Funding Agencies|Swedish Research Council (VR) Linnaeus Center CADICS||ELLIIT Excellence Center at Linkoping-Lund in Information Technology||CUAS project||SSF, the Swedish Foundation for Strategic Research, CADICS, ELLIIT, CUAS

Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law Modus Ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. One of the premises is formed as the implication, which is represented by different mathematical approaches, but we are especially fond of the results brought by the early implication proposed by Zadeh, which is modified in our practical model concerning a medical application. The approximate reasoning system, grounded on the extended and modified version of Modus Ponens law, will be employed here to predict a chance of survival after the operation for a patient who suffers from cancer. The patient’s symptom levels are the indicators of the disease. If the symptoms do not exceed their critical values there is still a chance to save the patient’s life by trying surgery. We wish to evaluate the verbal prognosis of the surgery by involving specifically designed fuzzy sets in the algorithm of approximate reasoning. Since the chance of successful surgery depends on the interactions of several symptoms then we will name the decision model multi-dimensional.

This project explores the interaction between logical and non-logical reasoning systems. It is primarily concerned with forging links between two relatively distinct sub-fields within artificial intelligence and to provide both theoretical and practical benefits. The project's fundamental goal was to explore methods for practical reasoning in the context of robotics. The project made advances in dealing with erroneous information, approximate reasoning, topological reasoning and languages for practical reasoning systems. These developments are currently being implemented on a domestic robot (a Segway RMP) operating in a home environment. The project therefore demonstrates practical reasoning in complex environments.

The compositional rule of inference, grounded on the modus ponens law, is one of the most effective fuzzy systems. We modify the classical version of the Zadeh rule to propose an original model, which concerns determining an operation chance for gastric cancer patients. The operation prognosis will be dependent on values of biological markers indicating the progress of the disease.

The compositional rule of inference, grounded on the modus ponens law, is one of the most effective fuzzy systems. We modify the classical version of the Zadeh rule to propose an original model, which concerns determining an operation chance for gastric cancer patients. The operation prognosis will be dependent on values of biological markers indicating the progress of the disease.

The compositional rule of inference, grounded on the modus ponens law, is one of the most effective fuzzy systems. We modify the classical version of the Zadeh rule to propose an original model, which concerns determining an operation chance for gastric cancer patients. The operation prognosis will be dependent on values of biological markers indicating the progress of the disease.

The compositional rule of inference, grounded on the modus ponens law, is one of the most effective fuzzy systems. We modify the classical version of the Zadeh rule to propose an original model, which concerns determining an operation chance for gastric cancer patients. The operation prognosis will be dependent on values of biological markers indicating the progress of the disease.

The compositional rule of inference, grounded on the modus ponens law, is one of the most effective fuzzy systems. We modify the classical version of the Zadeh rule to propose an original model, which concerns determining an operation chance for gastric cancer patients. The operation prognosis will be dependent on values of biological markers indicating the progress of the disease.

The compositional rule of inference, grounded on the modus ponens law, is one of the most effective fuzzy systems. We modify the classical version of the Zadeh rule to propose an original model, which concerns determining an operation chance for gastric cancer patients. The operation prognosis will be dependent on values of biological markers indicating the progress of the disease.

Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law Modus Ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. There exist different approaches to an implication, being the crucial part of the rule, but we are especially fond of the results brought by the early implication proposed by Zadeh, which is modified in our practical model concerning a medical application. The approximate reasoning system, grounded on the extended version of Modus Ponens law, will be employed here to predict a chance of positive effects of the operation on a patient who suffers from stomach cancer. The patient’s CRP (C-reactive proteins) symptom level, pathologically heightened, indicates the presence of a disease. When the CRP-value does not exceed a critical border it can be realistic to try surgery to recover the patient from his/her illness due to Do-Kyong Kim. We wish to evaluate the verbal prognosis of the surgery by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.

Computation intelligence paradigms including artificial neural networks, fuzzy systems, evolutionary computing techniques, intelligent agents and so on provide a basis for human like reasoning in medical systems. Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed in our practical model concerning a medical application. The approximate reasoning system presented in this work considers evaluation of a risk in the situation when physicians weigh necessity of the operation on a patient. The patient’s clinical symptom levels, pathologically heightened, indicate the presence of a disease possible to recover by surgery. We wish to evaluate the extension of the operation danger by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.

We present a language for defining paraconsistent rough sets and reasoning about them. Our framework relates and brings together two major fields: rough sets [23] and paraconsistent logic programming [9]. To model inconsistent and incomplete information we use a four-valued logic. The language discussed in this paper is based on ideas of our previous work [21, 32, 22] developing a four-valued framework for rough sets. In this approach membership function, set containment and set operations are four-valued, where logical values are t (true), f (false), i (inconsistent) and u (unknown). We investigate properties of paraconsistent rough sets as well as develop a paraconsistent rule language, providing basic computational machinery for our approach.

Computation intelligence paradigms including artificial neural networks, fuzzy systems, evolutionary computing techniques, intelligent agents and so on provide a basis for human like reasoning in medical systems. Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed in our practical model concerning a medical application. The approximate reasoning system presented in this work considers evaluation of a risk in the situation when physicians weigh necessity of the operation on a patient. The patient’s clinical symptom levels, pathologically heightened, indicate the presence of a disease possible to recover by surgery. We wish to evaluate the extension of the operation danger by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.

Computation intelligence paradigms including artificial neural networks, fuzzy systems, evolutionary computing techniques, intelligent agents and so on provide a basis for human like reasoning in medical systems. Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed in our practical model concerning a medical application. The approximate reasoning system presented in this work considers evaluation of a risk in the situation when physicians weigh necessity of the operation on a patient. The patient’s clinical symptom levels, pathologically heightened, indicate the presence of a disease possible to recover by surgery. We wish to evaluate the extension of the operation danger by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.

Computation intelligence paradigms including artificial neural networks, fuzzy systems, evolutionary computing techniques, intelligent agents and so on provide a basis for human like reasoning in medical systems. Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed in our practical model concerning a medical application. The approximate reasoning system presented in this work considers evaluation of a risk in the situation when physicians weigh necessity of the operation on a patient. The patient’s clinical symptom levels, pathologically heightened, indicate the presence of a disease possible to recover by surgery. We wish to evaluate the extension of the operation danger by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.

Computation intelligence paradigms including artificial neural networks, fuzzy systems, evolutionary computing techniques, intelligent agents and so on provide a basis for human like reasoning in medical systems. Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed in our practical model concerning a medical application. The approximate reasoning system presented in this work considers evaluation of a risk in the situation when physicians weigh necessity of the operation on a patient. The patient’s clinical symptom levels, pathologically heightened, indicate the presence of a disease possible to recover by surgery. We wish to evaluate the extension of the operation danger by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.

Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed by Zadeh in our practical model concerning a medical application. The approximate reasoning system presented in this work considers evaluation of a risk in the situation when physicians weigh necessity of the operation on a patient. The patient’s clinical symptom levels, pathologically heightened, indicate the presence of a disease possible to recover by surgery. We wish to evaluate the extension of the operation danger by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.

Computation intelligence paradigms including artificial neural networks, fuzzy systems, evolutionary computing techniques, intelligent agents and so on provide a basis for human like reasoning in medical systems. Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed in our practical model concerning a medical application. The approximate reasoning system presented in this work considers evaluation of a risk in the situation when physicians weigh necessity of the operation on a patient. The patient’s clinical symptom levels, pathologically heightened, indicate the presence of a disease possible to recover by surgery. We wish to evaluate the extension of the operation danger by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.

With the increasing interest in expressive ontologies for the Semantic Web, it is critical to develop scalable and efficient ontology reasoning techniques that can properly cope with very high data volumes. For certain application domains, approximate reasoning solutions, which trade soundness or completeness for increased reasoning speed, will help to deal with the high computational complexities which state of the art ontology reasoning tools have to face. In this paper, we present a comprehensive overview of the SCREECH approach to approximate instance retrieval with OWL ontologies, which is based on the KAON2 algorithms, facilitating a compilation of OWL DL TBoxes into Datalog, which is tractable in terms of data complexity. We present three different instantiations of the Screech approach, and report on experiments which show that the gain in efficiency outweighs the number of introduced mistakes in the reasoning process.

This paper focuses on approximate reasoning based on the use of similarity spaces. Similarity spaces and the approximated relations induced by them are a generalization of the rough set-based approximations of Pawlak [17, 18]. Similarity spaces are used to define neighborhoods around individuals and these in turn are used to define approximate sets and relations. In any of the approaches, one would like to embed such relations in an appropriate logic which can be used as a reasoning engine for specific applications with specific constraints. We propose a framework which permits a formal study of the relationship between approximate relations, similarity spaces and three-valued logics. Using ideas from correspondence theory for modal logics and constraints on an accessibility relation, we develop an analogous framework for three-valued logics and constraints on similarity relations. In this manner, we can provide a tool which helps in determining the proper three-valued logical reasoning engine to use for different classes of approximate relations generated via specific types of similarity spaces. Additionally, by choosing a three-valued logic first, the framework determines what constraints would be required on a similarity relation and the approximate relations induced by it. Such information would guide the generation of approximate relations for specific applications.

In real world applications robots and software agents often have to be equipped with higher level cognitive functions that enable them to reason, act and perceive in changing, incompletely known and unpredictable environments. One of the major tasks in such circumstances is to fuse information from various data sources. There are many levels of information fusion, ranging from the fusing of low level sensor signals to the fusing of high level, complex knowledge structures. In a dynamically changing environment even a single agent may have varying abilities to perceive its environment which are dependent on particular conditions. The situation becomes even more complex when different agents have different perceptual capabilities and need to communicate with each other. In this paper, we propose a framework that provides agents with the ability to fuse both low and high level approximate knowledge in the context of dynamically changing environments while taking account of heterogeneous and contextually limited perceptual capabilities. To model limitations on an agent's perceptual capabilities we introduce the idea of partial tolerance spaces. We assume that each agent has one or more approximate databases where approximate relations are represented using lower and upper approximations on sets. Approximate relations are generalizations of rough sets. It is shown how sensory and other limitations can be taken into account when constructing and querying approximate databases for each respective agent. Complex relations inherit the approximativeness of primitive relations used in their definitions. Agents then query these databases and receive answers through the filters of their perceptual limitations as represented by (partial) tolerance spaces and approximate queries. The techniques used are all tractable. © 2005 Elsevier B.V. All rights reserved.

We propose a new technique for approximate ABox reasoning with OWL DL ontologies. Essentially, we obtain substantially improved reasoning performance by disregarding non-Horn features of OWL DL. Our approach comes as a side-product of recent research results concerning a new transformation of OWL DL ontologies into negation-free disjunctive datalog, and rests on the idea of performing standard resolution over disjunctive rules by treating them as if they were non-disjunctive ones. We analyse our reasoning approach by means of non-monotonic reasoning techniques, and present an implementation, called Screech.

This paper describes an experimental platform for approximate knowledge databases called the Approximate Knowledge Database (AKDB), based on a semantics inspired by rough sets. The implementation is based upon the use of a standard SQL database to store logical facts, augmented with several query interface layers implemented in JAVA through which extensional, intensional and local closed world nonmonotonic queries in the form of crisp or approximate logical formulas can be evaluated tractably. A graphical database design user interface is also provided which simplifies the design of databases, the entering of data and the construction of queries. The theory and semantics for AKDBs is presented in addition to application examples and details concerning the database implementation., Special issue on implementation of logics

There is a recognised need for the continued improvement of both the techniques and technology for spatial decision support in infrastructure site selection. Many authors have noted that current methodologies are inadequate for real-world site selection decisions carried out by heterogeneous groups of decision-makers under uncertainty. Nevertheless despite numerous limitations inherent in current spatial problem solving methods, spatial decision support systems have been proven to increase decision-maker effectiveness when used. However, due to the real or perceived difficulty of using these systems few applications are actually in use to support decision-makers in siting decisions. The most common difficulties encountered involve standardising criterion ratings, and communicating results. This research has focused on the use of Approximate Reasoning to improve the techniques and technology of spatial decision support, and make them easier to use and understand. The algorithm developed in this research (ARAISS) is based on the use of natural language to describe problem variables such as suitability, certainty, risk and consensus. The algorithm uses a method based on type II fuzzy sets to represent problem variables. ARAISS was subsequently incorporated into a new Spatial Decision Support System (InfraPlanner) and validated by use in a real-world site selection problem at Australia's Brisbane Airport. Results indicate that Approximate Reasoning is a promising method for spatial infrastructure planning decisions. Natural language inputs and outputs, combined with an easily understandable multiple decision-maker framework created an environment conducive to information sharing and consensus building among parties. Future research should focus on the use of Genetic Algorithms and other Artificial Intelligence techniques to broaden the scope of existing work.

Models of discrete choice analysis are usually based on the random utility framework. They assume that decision makers make decisions that maximize their utility. Alternative formulations of the problem have also been proposed in the literature. These approaches model the decision makers' perceptions of the attributes of the various alternatives using fuzzy sets and linguistic variables, and the decision process itself, using concepts from approximate reasoning and fuzzy control. The underlying assumption is that decision makers use a few simple rules that relate their vague perceptions of the various attributes to their preferences towards the available alternatives. The paper extends this approach by incorporating rule weights, which capture the importance of a particular rule in the decision process. It also presents an approach for calibrating the weights using concepts from neural networks. A case study, involving mode choice, is used to demonstrate the potential of the approach and compare it to alternative formulations and methodologies., QC 20100525

Currently, there is a great deal of interest in developing tools for the generation and use of ontologies on the WWW. These knowledge structures are considered essential to the success of the semantic web, the next phase in the evolution of the WWW. Much recent work with ontologies assumes that the concepts used as building blocks are crisp as opposed to approximate. It is a premise of this paper that approximate concepts and ontologies will become increasingly more important as the semantic web becomes a reality. We propose a framework for specifying, generating and using approximate ontologies. More specifically, (1) a formal framework for defining approximate concepts, ontologies and operations on approximate concepts and ontologies is presented. The framework is based on intuitions from rough set theory, (2) algorithms for automatically generating approximate ontologies from traditional crisp ontologies or from large data sets together with additional knowledge are presented. The knowledge will generally be related to similarity measurements between individual objects in the data sets, or constraints of a logical nature which rule out particular constellations of concepts and dependencies in generated ontologies. The techniques for generating approximate ontologies are parameterizable. The paper provides specific instantiations and examples.

This paper introduces a new class of fuzzy closure operators called implicative closure operators, which generalize some notions of fuzzy closure operators already introduced by different authors. We show that implicative closure operators capture some usual consequence relations used in Approximate Reasoning, like Chakraborty's graded consequence relation, Castro et al.'s fuzzy consequence relation, similarity-based consequence operators introduced by Dubois et al. and Gerla's canonical extension of classical closure operators. We also study the relation of the implicative closure operators to other existing fuzzy inference operators as the Natural Inference Operators defined by Boixader and Jacas and the fuzzy operators defined by Biacino, Gerla and Ying. © 2003 Elsevier Science Inc. All rights reserved.

The paper addresses the mathematical modelling of domains of linguistic variables, i.e. term-sets of linguistic variables, in order to obtain a suitable algebraic structure for the set of truth values of Zadeh's fuzzy logic. We shall give a unified algebraic approach to the natural structure of domains of linguistic variables, which was proposed by Ho and Wechler (Fuzzy Sets and Systems 35 (1990) 281) and, then, by Ho and Nam (Proc. NCST Vietnam 9 (1) (1997) 15; Logic, Algebra and Computer Science, Vol. 46, Banach Center Publications, PWN, Warsaw, 1999, p. 63). In this approach, every linguistic domain can be considered as an algebraic structure called hedge algebra, because properties of its unary operations reflect semantic characteristics of linguistic hedges. Many fundamental properties of refined hedge algebras (RH_algebras) are examined, especially it is shown that every RH_algebra of a linguistic variable with a chain of the primary terms is a distributive lattice. RH_algebras with exactly two distinct primary terms, one being an antonym of the other, will also be investigated and they will be called symmetrical RH_algebras. It is shown that a class of finite symmetrical RH_algebras has a rich enough algebraic structure., identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/4996

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth values is introduced., identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/4997

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth values is introduced.

The paper addresses the mathematical modelling of domains of linguistic variables, i.e. term-sets of linguistic variables, in order to obtain a suitable algebraic structure for the set of truth values of Zadeh's fuzzy logic. We shall give a unified algebraic approach to the natural structure of domains of linguistic variables, which was proposed by Ho and Wechler (Fuzzy Sets and Systems 35 (1990) 281) and, then, by Ho and Nam (Proc. NCST Vietnam 9 (1) (1997) 15; Logic, Algebra and Computer Science, Vol. 46, Banach Center Publications, PWN, Warsaw, 1999, p. 63). In this approach, every linguistic domain can be considered as an algebraic structure called hedge algebra, because properties of its unary operations reflect semantic characteristics of linguistic hedges. Many fundamental properties of refined hedge algebras (RH_algebras) are examined, especially it is shown that every RH_algebra of a linguistic variable with a chain of the primary terms is a distributive lattice. RH_algebras with exactly two distinct primary terms, one being an antonym of the other, will also be investigated and they will be called symmetrical RH_algebras. It is shown that a class of finite symmetrical RH_algebras has a rich enough algebraic structure.

We partition the time-line in different ways, for example, into minutes, hours, days, etc. When reasoning about relations between events and processes we often reason about their location within such partitions. For example, x happened yesterday and y happened today, consequently x and y are disjoint. Reasoning about these temporal granularities so far has focused on temporal units (relations between minute, hour slots). I shall argue in this paper that in our representations and reasoning procedures we need into account that events and processes often lie skew to the cells of our partitions (For example, 'happened yesterday' does not mean that x started at 12 a.m. and ended 0 p.m.) This has the consequence that our descriptions of temporal location of events and processes are often approximate and rough in nature rather than exact and crisp. In this paper I describe representation and reasoning methods that take the approximate character of our descriptions and the resulting limits (granularity) of our knowledge explicitly into account.

A widely used fuzzy reasoning algorithm was modified and implemented via an expert system to assess the potential risk of employee repetitive strain injury in the workplace. This fuzzy relational model, known as the Priority First Cover Algorithm (PFC), was adapted to describe the relationship between 12 cumulative trauma disorders (CTDs) of the upper extremity, and 29 identified risk factors. The algorithm, which finds a suboptimal subset from a group of variables based on the criterion of priority, was adopted to enable the inference mechanism of a constructed knowledge-based system to predict CTD occurrence.

This paper studies the problem of marginalizing convex polytopes of probabilities represented by a set of constraints. This marginalization is obtained as a special case of projection on a specific subspace. An algorithm that projects a convex polytope on any subspace has been built and the expression of the subspace, where the projection must be made for obtaining the marginalization, has been calculated.

Defuzzification is an essential problem in fuzzy systems that it is always solved in a heuristic way. The aim of this work is to give a semantic interpretation to this process with the help of indistinguishability operators, Peer Reviewed, Postprint (published version)

Firstly we present a geometric interpretation of interval-valued fuzzy sets. Secondly, we apply the method of least squares to the fuzzy inference rules when working with these sets. We begin approximating the lower and upper extremes of the membership intervals to axb type functions by means of the method of least squares. Then we analyze a technique for evaluating the conclusion of the generalized modus ponens and we verify the fulfillment of Fukami and alumni axioms [9].