Optimization of Backward Fuzzy Reasoning Based on Rule Knowledge (original) (raw)

Inverted Fuzzy Implications in Backward Reasoning

Lecture Notes in Computer Science, 2015

Fuzzy inference systems generate inference results based on fuzzy IF-THEN rules. Fuzzy implications are mostly used as a way of interpretation of the IF-THEN rules with fuzzy antecedent and fuzzy consequent. From over eight decades a number of different fuzzy implications have been described, e.g. [6-10]. This leads to the following question: how to choose the proper function among basic fuzzy implications. In our paper, we propose a new method for choosing implication. Our method allows to compare two fuzzy implications. If the truth value of the consequent and the truth value of the implication are given, by means of inverse fuzzy implications we can easily optimize the truth value of the implication antecedent. In other words, we can choose the fuzzy implication, which has the highest or the lowest truth value of the implication antecedent or which has higher or lower truth value than another implication.

Inverted Fuzzy Implications in Backward Reasoning Without Yager Implication

2015

One of the most popular methods of knowledge representation are the fuzzy rules. One of the ways of representation of fuzzy rules is the functional representation. From over eight decades a number of different fuzzy implications have been described, e.g. [5]-[9]. This leads to the following question: how to choose the proper function among basic fuzzy implications. This paper is a continuation of study [15], where we proposed a new method for choosing implications in backward reasoning. Here we presented a way of simplify the analysis by skipping Yager fuzzy implication.

Patterns of fuzzy rule-based inference

International Journal of Approximate Reasoning, 1994

Processing information in fuzzy rule-based systems generally employs one of two patterns of inference: composition or compatibility modification. Composition originated as a generalization of binary logical deduction to fuzzy logic, while compatibility modification was developed to facilitate the evaluation of rules by separating the evaluation of the input from the generation of the output. The first step in compatibility modification inference is to assess the degree to which the input matches the antecedent of a rule. The result of this assessment is then combined with the consequent of the rule to produce the output. This paper examines the relationships between these two patterns of inference and establishes conditions under which they produce equivalent results. The separation of the evaluation of input from the generation of output permits a flexibility in the methods used to compare the input with the antecedent of a rule with multiple clauses. In this case, the degree to which the input and the rule antecedent match is determined by the application of a compatibility measure and an aggregation operator. The order in which these operations are applied may affect the assessment of the degree of matching, which in turn may cause the production of different results. Separability properties are introduced to define conditions under which compatibility modification inference is independent of the input evaluation strategy.

Survey on three single rule reasoning methods

A GAMF Közleményei, 2006

Single Rule Reasoning (SRR) methods aim the determination of the conclusionfrom the observation and an intermediate (interpolated) rule. They are applied infuzzy systems, which use an inference technique that follows the concepts of theGeneralized Methodology (GM) [1] of Fuzzy Rule Interpolation (FRI). This paper surveys and evaluates three SRR methods, namely SURE-p [2],SURE-LS [4] and REVE. The first two are overviewed briefly by recalling theirmain steps and essential features that are necessary for the evaluation andcomparison. REVE is a new method based on the concept Vague Environment(VE). Therefore the paper contains its presentation in details.

A fuzzy inference model based on an uncertainty forward propagation approach

International Journal of Approximate Reasoning, 1993

The management of uncertainty and imprecision is becoming more and more important in knowledge-based systems. Fuzzy logic provides a systematic basis for representing and inferring with this kind of knowledge. This paper describes an approach for fuzzy inference based on an uncertainty forward propagation method and a change in the granularity of the elements involved. The proposed model is able to handle very general kinds of facts and rules, and it also verifies the most usual properties required by a fuzzy inference model.

Efficient deduction in fuzzy logic

1986

The generalized modus ponens is a fuzzy logic pattern of reasoning that permits to make inferences with rules having imprecision both in their antecedent and consequent parts. Though it is a very powerful approximate reasoning tool (from a theoretical point of view), this technique may result in unacceptably slow executions if inappropriately implemented. There are several ways to avoid the inefficiency bottleneck. One of them, that is the object of this paper, consists in introducing an approximation technique focussing only of what is semantically important. This approximation technique is conceived so as to be used in situations where the dependency between two given variables is described via a collection of rules. Moreover, this paper addresses the problem in the setting having the main features that follow: the possibility distributions involved in facts and rules are continuous (the referential is the real line), normalized, unimodal and expressed by parametrized functions; only single antecedent rules are considered; the rules are consistent and it is assumed that their antecedents and consequents do not overlap too much; the deduction process is based on the ‘min’ conjunction and Gödel implication operators. The ultimate goal of this work is to render the generalized modus ponens technique usable in practical deduction systems.

Logical foundations of rule-based systems

Fuzzy Sets and Systems, 2006

This paper is focused on the evolution of the theory of fuzzy IF-THEN rules and its contribution to the establishment of fuzzy logic. I advocate that Hájek's fuzzy logic is a right methodology for development of special logical theories. A theory of fuzzy IF-THEN rules (as a special theory in this sense) is proposed. This theory is for all practitioners who want to create a system of fuzzy IF-THEN rules free of conflicts (logically consistent) and rich enough to be able to make non-trivial conclusions or answer inquires.

Fuzzy logic-a modern perspective

IEEE Transactions on Knowledge and Data Engineering, 1999

Traditionaly, fuzzy logic has been viewed in the AI community as an approach for managing uncertainty. In the 1990's, however, fuzzy logic has emerged as a paradigm for approximating a functional mapping. This complementary mordern view about the technology offers new insights about the foundation of fuzzy logic as well as new challenges regarding the identification of fuzzy models. In this paper, we will first review some of the major milestones in the history of developing fuzzy logic technology. After a short summary of major concepts in fuzzy logic, we discuss a mordern view about the foundation of two types of fuzzy rules. Finally, we review some of the research in addressing various challenges regarding automated identification of fuzzy rule-based models.

An hybrid architecture integrating forward rules with fuzzy ontological reasoning

Hybrid Artificial …, 2010

In recent years there has been a growing interest in the combination of rules and ontologies. Notably, many works have focused on the theoretical aspects of such integration, sometimes leading to concrete solutions. However, solutions proposed so far typically reason upon crisp concepts, while concrete domains require also fuzzy expressiveness.

Generalized Implicative Model of a Fuzzy Rule Base and its Properties

COGNITIVE 2011, The Third International Conference …, 2011

In this contribution, an implicative variant of the conjunctive normal form will be recalled and further studied. This normal form is an alternative to the Perfilieva's conjunctive normal form. It will be shown that it is a suitable model for a particular case of graded fuzzy rules introduced as a generalization of classical fuzzy rules. Moreover, approximation properties of the implicative variant of the conjunctive normal form provide a view on a class of fuzzy relations that can be "efficiently" approximated using this normal form. Newly, a suitable inference rule the graded rules formalized using the implicative variant of the conjunctive normal form will be introduced and analyzed. Results in this field extend the theory of approximate reasoning as well as the theory of fuzzy functions.