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Predicting chaotic time series is an applicable issue so many scientists have introduced different methods to predict their behavior. Artificial neural networks are a tool that forecasts system behavior. These tools should be trained and backpropagation algorithms used as learners. But this training process may be falling into trap of local optimum. Heuristic methods are introduced to solve this challenge.

Interval data are usually applied where inaccuracy and variability must be considered. This paper presents a learning method for Interval Extreme Learning Machine (IELM) in classification. IELM has two steps similar to well known ELM. At first weights connecting the input and the hidden layers are generated randomly and in the second step, ELM uses the Moore–Penrose generalized inverse to determine the weights connecting the hidden and output layers. In order to use Moore–Penrose generalized inverse for determining second layer weights in IELM, this paper proposes four classification methods to handle symbolic interval data based on ELM. The first one uses a midpoint of intervals for each feature value then it applies a classic ELM. The second one considers each feature value as a pair of quantitative features and implements a conjoint for classic extreme learning machine. The third one represents interval features by their vertices and performs a classic extreme learning machine as well. The fourth one takes each interval as a pair of quantitative features after that two separated classic extreme learning machines are performed on these features and combines the results accordingly. Algorithms are tested on the synthetic and real datasets. A synthetic dataset is applied to determine the number of hidden layer nodes in an IELM. The classification error rate is considered as a comparison criterion. The error rate obtained for each proposed methods is 19.1667%, 15% , 6.5358% and 18.3333% respectively. Experiments demonstrate the usefulness of these classifiers to classify symbolic interval data.

In this paper, generalization of the fuzzy BCK/BCI-algebras of type (α, β)* are introduced. Then we state and prove some theorems that determine the relationship between these notions and subalgebras of BCK/BCI-algebras. Characterizations of (α, β)*-fuzzy subalgebras in a BCK/BCI-algebras are given.

In this paper, we introduce the notion of fuzzy n-folds (P, implicative and fantastic) ideals in BCH-algebras which is a natural generalization of notion of n-folds (P, implicative and fantastic) ideals in BCH-algebras and we stated and proved some theorems which determines the relationship between these notions. Finally we give some computational Algorithms for these notions.

In this note, by using the concept of Bipolar-valued fuzzy set, the notion of bipolar-valued fuzzy BCK/BCI-algebra is introduced. Moreover, the notions of (strong) negative s-cut, (strong) positive t-cut are introduced and the relationship between these notions and crisp subalgebras are studied.