The paper focuses on two large application areas of the Fuzzy Set Theory in ecological research, namely data analysis (in particular fuzzy cluster analysis and fuzzy kriging) and ecological modelling. Environmental data or classes of ecological objects can be defined as fuzzy sets with not sharply defined boundaries, that reflects better the continuous character of nature. Fuzzy sets are used t...

Recent studies have shown that both Mamdani-type and Takagi-Sugeno-type fuzzy systems are universal approximators in that they can uniformly approximate continuous functions defined on compact domains with arbitrarily high approximation accuracy. In this paper, we investigate necessary conditions for general multiple-input single-output (MISO) Mamdani fuzzy systems as universal approximators wi...

This paper proposes the FOGA (Fuzzy Ontology Generation frAmework) for automatic generation of fuzzy ontology on uncertainty information. The FOGA framework comprises the following components: Fuzzy Formal Concept Analysis, Fuzzy Conceptual Clustering and Fuzzy Ontology Generation. First, Fuzzy Formal Concept Analysis incorporates fuzzy logic into Formal Concept Analysis (FCA) to form a fuzzy c...

in the mathematical analysis, there are some theorems and definitions that established for both real and fuzzy numbers. in this study, we try to prove  bernoulli's inequality in fuzzy real numbers with some of its applications. also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.

this paper presents the basic concepts of stability in fuzzy linguistic models. theauthors have proposed a criterion for bibo stability analysis of fuzzy linguistic modelsassociated to linear time invariant systems [25]-[28]. this paper presents the basic concepts ofstability in the general nonlinear and linear systems. this stability analysis method is verifiedusing a benchmark system analysis.

Process capability indices (PCIs) can be used as an effective tool for measuring product quality and process performance. In classic quality control there are some limitations which prevent a deep and flexible analysis because of the crisp definition of PCA‟s parameters. Fuzzy set theory can be used to add more flexibility to process capability analyses. In this study, the fuzzy X ba and MRx ba...

This paper proposes a new perspective and methodology to model the behavior of the components as well as the system using the theory and methods for fuzzy sets. We propose to use the indicator or performance or substitute variable which is very well understood by the customer to fuzzify the states of the component or the system. Both component and system’s fuzzy reliability definitions and mode...

Resampling methods are among the best approaches to determine the number of clusters in prototype-based clustering. The core idea is that with the right choice for the number of clusters basically the same cluster structures should be obtained from subsamples of the given data set, while a wrong choice should produce considerably varying cluster structures. In this paper I give a brief overview...

One of the main problems in FCA (especially in fuzzy setting) is to reduce a concept lattice to appropriate size to make it graspable and understandable. We generalize known results on the correspondence of block relations of formal contexts and complete tolerances on concept lattices to fuzzy setting. Using an illustrative example we show that the results can be used for reduction of fuzzy con...