Most conventional data-mining algorithms identify the relationships among transactions using binary values and find rules at a single concept level. Transactions with quantitative values and items with taxonomic relations are, however, commonly seen in real-world applications. Besides, the taxonomic structures may also be represented in a fuzzy way. This paper thus proposes a fuzzy multiple-lev...

The concept of an image of a fuzzy set under a fuzzy relation has proved to be a very powerful tool in fuzzy set theoretical applications. In this paper, we explain how it can be used to model linguistic expressions. For the representation of expressions, such as “at least middle-aged”, “brighter than average”, we will use fuzzy ordering relations, while resemblance relations will be suitable t...

Data summarization is an enabling technique of Granular Computing, because of its promise to abstract from individual observations and to view a phenomenon as a whole. The linguistic summaries are built around a fuzzy quantifier which functions as the ‘summarizer’. Linguistic data summarization therefore presupposes an underlying model of fuzzy quantifiers, which is of crucial importance to the...

Yager’s ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts’ individual opinions or preferences for achieving an overall decision. The traditional Yager’s OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic te...

Fuzzy controllers are designed to work with knowledge in the form of linguistic control rules. But the translation of these linguistic rules into the framework of fuzzy set theory depends on the choice of certain parameters, for which no formal method is known. The optimization of these parameters can be carried out by neural networks, which are designed to learn from training data, but which a...

A new methodology to learn descriptive linguistic Fuzzy Rule-based System Knowledge Bases from examples based on the combination of fuzzy clustering and evolutionary simultaneous rule selection and membership functions tuning is presented in this work. Fuzzy clustering is used to achieve a preliminary description of the data, in other words to obtain information on the definition of the linguis...

The function for spatial queries has been provided in some image retrieval systems for finding images satisfying given spatial relations. However, images themselves may contain ambiguity or the image processing technologies adopted may extract objects not accurately enough. Processing image queries in a flexible way is thus desired. In this paper, we thus propose a fuzzy image matching algorith...

Based on linguistic term sets and hesitant fuzzy sets, the concept of hesitant fuzzy linguistic sets was introduced. The focus of this paper is the multicriteria decision-making (MCDM) problems in which the criteria are in different priority levels and the criteria values take the form of hesitant fuzzy linguistic numbers (HFLNs). A new approach to solving these problems is proposed, which is b...

The problem of a linguistic description of dependencies in data by a set of rules Rk: “If X is Tk then Y is Sk” is considered, where Tk’s are linguistic terms like SMALL, BETWEEN 5 AND 7 describing some fuzzy intervals Ak. Sk’s are linguistic terms like DECREASING and QUICKLY INCREASING describing the slopes pk of linear functions yk = pkx + qk approximating data on Ak. The decision of this pro...

Fuzzy relational models have been widely investigated and found to be an efficient tool for the identification of complex systems. However, little attention has been given to the linguistic interpretation of these models. The use of relational models is recommended since their development follows a natural sequence based on the original ideas about fuzzy sets and fuzzy logic, involving the esti...