The mathematical framework for studying of a fuzzy approximate reasoning is presented in this paper. Two important defuzzification methods (Area defuzzification and Height defuzzification) besides the center of gravity method which is the best well known defuzzification method are described. The continuity of the defuzzification methods and its application to a fuzzy feedback control are discus...

Fuzzy logic techniques are efficient in solving complex, ill-defined problems that are characterized by uncertainty of environment and fuzziness of information. Fuzzy logic allows handling uncertain and imprecise knowledge and provides a powerful framework for reasoning. Fuzzy reasoning models are relevant to a wide variety of subject areas such as engineering, economics, psychology, sociology,...

In many application areas there is a need to represent human-like knowledge related to spatio-temporal relations among multiple moving objects. This type of knowledge is usually imprecise, vague and fuzzy, while the reasoning about spatio-temporal relations is intuitive. In this paper we present a model of fuzzy spatio-temporal knowledge representation and reasoning based on high-level Petri ne...

The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities ar...

The problem of the combination of imprecision and uncertainty combination from the approximate reasoning point of view is addressed. An imprecise and uncertain information can be represented as a fuzzy quantity together with a certainty value. In order to simplify the use of such information, it is necessary to combine the imprecision and uncertainty of the fuzzy number. In this paper we propos...

Hesitant fuzzy linguistic term sets were introduced to grasp the uncertainty existing in human reasoning. In this paper, inspired by absolute order-of-magnitude qualitative reasoning techniques, an extension of the set of hesitant fuzzy linguistic term sets is presented to capture differences between non-compatible preferences. In addition, an order relation and two closed operations over this ...

Fuzzy relations are simple mathematical structures that enable a very general representation of fuzzy knowledge, and fuzzy relational calculus offers a powerful machinery for approximate reasoning. However, one of the most relevant limitations of approximate reasoning is the efficiency bottleneck. In this paper, we present a module for fast fuzzy inference through relational composition, with t...

The Disjunctive Fuzzy Temporal Constraint Network (DFTCN) model is a framework that allows reasoning with fuzzy qualitative and quantitative complex temporal constraints. However, its general complexity is exponential. In this work, we review methods that can reduce this complexity, based on graph topology and preprocessing. The final goal is to integrate all these methods into a general tool f...

Fuzzy extension of Description Logics (DLs) allows the formal representation and handling of fuzzy knowledge. In this paper, we consider fuzzy-EL, which is a fuzzy extension of EL. We first present revised completion rules for fuzzy-EL that can be handled by MapReduce programs. We then propose an algorithm for scale reasoning with fuzzy-EL ontologies based on MapReduce.

In this research, a hybrid approach by combining Self-Organizing Map (SOM) and Evolving Fuzzy Case-Based Reasoning (EFCBR) for flow time prediction is proposed. Genetic Algorithms (GAs) is applied to fine-tune the fuzzy term numbers and weights of fuzzy features in the CBR model. The flow time and related shop floor status are collected and fed into the SOM for classification. Then, correspondi...