Similarity-based graded modal logic

Within the approximate reasoning Cramework, several systems oC modallogic have been proposed to formalize several kinds oC reasoning models ([MP94], [HM92], [FH91]). In particular, in [EGG95] a Kripke model-like theory for a logic of graded necessity and possibility operators is presented to model similarity-based reasoning. In this paper, we propose an axiomatization for this logic and we show that it is sound and complete with respect to classes oC models based where the accesibility relation is defined in terms of fuzzy similarity relations on the set oC possible worlds. Finally, we indicate how this logic can be used to characterize several graded entailments proposed in [DEG*95].Eje: 2do. Workshop sobre aspectos teóricos de la inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI

Constraint Solving over Multiple Similarity Relations

Similarity relations are reflexive, symmetric, and transitive fuzzy relations. They help to make approximate inferences, replacing the notion of equality. Similarity-based unification has been quite intensively investigated, as a core computational method for approximate reasoning and declarative programming. In this paper we consider solving constraints over several similarity relations, instead of a single one. Multiple similarities pose challenges to constraint solving, since we can not rely on the transitivity property anymore. Existing methods for unification with fuzzy proximity relations (reflexive, symmetric, non-transitive relations) do not provide a solution that would adequately reflect particularities of dealing with multiple similarities. To address this problem, we develop a constraint solving algorithm for multiple similarity relations, prove its termination, soundness, and completeness properties, and discuss applications

A Framework of Subjective Performance Evaluation Using Fuzzy Technique

This research proposes the framework of subjective performance evaluation using fuzzy technique for ranking the attributes of different types of datasets under a multi-criteria environment. Some previous studies on fuzzy techniques have been attempted in assessment and evaluation methods. The techniques such as fuzzy similarity function, fuzzy synthetic decision and satisfaction function have been adopted in these fuzzy evaluation methods. However, research that discover a scaling measurement which can express the subjectivity element and integrate the organisation‘s objectives and goals into the evaluation processes by utilising the fuzzy rule in the subjective evaluation method seem limited. Hence, this framework uses the application of fuzzy sets, and approximate reasoning to determine the performance evaluation of various characteristics in decision-making. The framework based upon fuzzy sets has initiated the idea of membership set score valued evaluation of each criterion alternative enables to include requirements which are incomplete and imprecise. The approximate reasoning of the method allows decision maker to make the best choice in accordance of human thinking and reasoning processes. The method introduces an approach of normalising data using similarity function which dampens the extreme value that exists in the data. The framework is suitable for dealing with evaluations in situations that involve subjectivity, vagueness and imprecise information, such as the grading system of evaluation which involves subjectivity, vagueness and imprecise information, such as the grading system evaluation which involves many hedges like "good", "bad" and "satisfactory"

Effective retrieval and new indexing method for case based reasoning: Application in chemical process design

In this paper we try to improve the retrieval step for case based reasoning for preliminary design. This improvement deals with three major parts of our CBR system. First, in the preliminary design step, some uncertainties like imprecise or unknown values remain in the description of the problem, because they need a deeper analysis to be withdrawn. To deal with this issue, the faced problem description is soften with the fuzzy sets theory. Features are described with a central value, a percentage of imprecision and a relation with respect to the central value. These additional data allow us to build a domain of possible values for each attributes. With this representation, the calculation of the similarity function is impacted, thus the characteristic function is used to calculate the local similarity between two features. Second, we focus our attention on the main goal of the retrieve step in CBR to find relevant cases for adaptation. In this second part, we discuss the assumption of similarity to find the more appropriated case. We put in highlight that in some situations this classical similarity must be improved with further knowledge to facilitate case adaptation. To avoid failure during the adaptation step, we implement a method that couples similarity measurement with adaptability one, in order to approximate the cases utility more accurately. The latter gives deeper information for the reusing of cases. In a last part, we present a generic indexing technique for the base, and a new algorithm for the research of relevant cases in the memory. The sphere indexing algorithm is a domain independent index that has performances equivalent to the decision tree ones. But its main strength is that it puts the current problem in the center of the research area avoiding boundaries issues. All these points are discussed and exemplified through the preliminary design of a chemical engineering unit operation

Similarity-based graded modal logic

Within the approximate reasoning Cramework, several systems oC modallogic have been proposed to formalize several kinds oC reasoning models ([MP94], [HM92], [FH91]). In particular, in [EGG95] a Kripke model-like theory for a logic of graded necessity and possibility operators is presented to model similarity-based reasoning. In this paper, we propose an axiomatization for this logic and we show that it is sound and complete with respect to classes oC models based where the accesibility relation is defined in terms of fuzzy similarity relations on the set oC possible worlds. Finally, we indicate how this logic can be used to characterize several graded entailments proposed in [DEG*95].Eje: 2do. Workshop sobre aspectos teóricos de la inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI

Structured Knowledge Representation for Image Retrieval

We propose a structured approach to the problem of retrieval of images by content and present a description logic that has been devised for the semantic indexing and retrieval of images containing complex objects. As other approaches do, we start from low-level features extracted with image analysis to detect and characterize regions in an image. However, in contrast with feature-based approaches, we provide a syntax to describe segmented regions as basic objects and complex objects as compositions of basic ones. Then we introduce a companion extensional semantics for defining reasoning services, such as retrieval, classification, and subsumption. These services can be used for both exact and approximate matching, using similarity measures. Using our logical approach as a formal specification, we implemented a complete client-server image retrieval system, which allows a user to pose both queries by sketch and queries by example. A set of experiments has been carried out on a testbed of images to assess the retrieval capabilities of the system in comparison with expert users ranking. Results are presented adopting a well-established measure of quality borrowed from textual information retrieval

Approximate syllogistic reasoning: a contribution to inference patterns and use cases

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