Soft set theory, proposed by Molodtsov has been regarded as an effective mathematical tool to deal with uncertainties. Vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of [0, 1]. Such a set is characterized by a truth-membership function and a falsemembership function. Thus, a vague set is actually a form of fuzzy set, albeit a more ...

Previous studies have presented correlation analyses among fuzzy attributes. This study proposes a correlation analysis method among crisp attributes and fuzzy attributes to investigate their linear relationships. If A and B are two attributes, A is a nominal-dichotomous attribute, and B is a fuzzy attribute. Thus, identifying the relationship between A and B is possible by using the pointbiser...

fuzzy rules based classifier systems (FRBS) have gained more popularity in recent years. This classifier suffers from the problem of pattern space partitioning, to reach a compact set of rules that provides high classification power. In this paper, we propose an adaptive hierarchical fuzzy partitioning method based on tree decomposition. This decomposition is controlled by the grade of certaint...

In this paper I will introduce the trapezoidal intuitionistic fuzzy numbers (IF numbers) and will prove some operations for them. Also I am going to propose a new ordering method for IF numbers in which I will consider two characteristic values of membership and non-membership functions for an IF number. These values are defined by the integral of the inverse fuzzy membership and non-membership...

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for e...

Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature In the definition of fuzzy erosio...

On the basis of the concept of grades of a fuzzy point to belongingness (∈) or quasi-coincident (q) or belongingness and quasi-coincident (∈ ∧q) or belongingness or quasi-coincident (∈ ∨q) in an intuitionistic fuzzy set of a ring, the notion of a (α,β )intuitionistic fuzzy subring and ideal is introduced by applying the Lukasiewicz 3-valued implication operator. Using the notion of fuzzy cut se...

Intuitionistic fuzzy sets introduced by Atanassov are generalization of fuzzy sets as they also handle the nondeterminacy which is caused by degree of hesitation of decision maker. The present study proposes a computational method of forecasting for fuzzy time series. In the proposed method the notion of intuitionistic fuzzy set is used in fuzzy time series forecasting with simplified computati...