In this paper, we present equivalent characterizations of L-closure systems on lower bounded complete L-ordered sets and complete L-lattices, respectively. These results demonstrate the feasibility of notion of fuzzy closure system developed in our previous work (L.-K. Guo, G.-Q. Zhang, Q.-G. Li: Fuzzy closure systems on L-ordered sets. Math. Log. Quart. 57 (3) (2011), 281-291.). Also we develo...

In this paper, we introduce triangle algebras: a variety of residuated lattices equipped with approximation operators, and with a third angular point u, different from 0 and 1. We show that these algebras serve as an equational representation of intervalvalued residuated lattices (IVRLs). Furthermore, we present Triangle Logic (TL), a system of many-valued logic capturing the tautologies of IVR...

Concept of combined extraction of topological and directional relations information developed by J. Malki et al. [1] by employing the Allen’s temporal relations in 1D spatial domain was improved by Matsakis and Nikitenko [2]. This latter algorithm has high computational complexity due to its limitations of object approximation and segment fuzzification. In this paper, fuzzy Allen relations are ...

Since many real-world engineering systems are too complex to be defined in precise terms, imprecision is often involved in any engineering design process. Fuzzy linear programming problems have an essential role in fuzzy modeling, which can formulate uncertainty in actual environment. One of the most practicable subjects in recent studies is based on LR fuzzy number, which was defined and used ...

Our primary interest in the present paper is to prove a Korovkintype approximation theorem for n−multiple sequences of fuzzy positive linear operators via statistical convergence. Also, we display an example such that our method of convergence is stronger than the usual convergence. Mathematics Subject Classification (2010): 26E50, 40G15, 41A36.

In the framework of fuzzy algebras with fuzzy equalities and acomplete lattice as a structure of membership values, we investigate fuzzyequational classes. They consist of special fuzzy algebras fullling the samefuzzy identities, dened with respect to fuzzy equalities. We introduce basicnotions and the corresponding operators of universal algebra: construction offuzzy subalgebras, homomorphisms...

In this paper we propose an approximation of piecewise linear membership functions with the help of sigmoid functions and certain arithmetic operations. The gradient-based tuning of piecewise linear membership functions can be achieved with the proposed efficient approximation because it has simple continuous derivatives. With this construction we can even approximate the Łukasiewicz operator f...

Abstract The fuzzy transform setting (F-transform) is proposed as a tool for representation and approximation of type-1 and type-2 fuzzy numbers; the inverse F-transform on appropriate fuzzy partition of the membership interval [0,1] is used to characterize spaces of fuzzy numbers in such a way that arithmetic operations are de…ned and expressed in terms of the F-transform of the results. A typ...

The concept of fuzzy sets and fuzzy set operations were first introduced by Zadeh [30], fuzzy logic has become an important area of research in various branches of Mathematics such as metric and topological spaces, theory of functions, approximation theory etc. Subsequently several authors have discussed various aspects of the theory and applications of fuzzy sets. The concept of fuzzyiness has...