In this paper, the upper bounds for a multivariable fuzzy logic controller under G/Sdel's implication are investigated and a generalized multivariable structure of fuzzy controller are proposed. Contribution operators, such as max (v) operation, ensure the greatest upper bound as well as the least upper bound. Conditions which determine an appropriate upper bound are also determined. This theor...

In this paper, the grade of similarity, LA. B of tWO fuzzy sets A and B is defined and its properties are given. The set G(R, b) of grades of similarity associated with the set of the solutions of the Inverse Problem "given a fuzzy matrix R and a fuzzy vector b find all a such that a o R = b" is also defined and several properties are shown.

The starting point of this paper is the classical well-known theorem due to G. BIRKHOFF, P. HALL, and J. SCHMIDT which establishes a one-to-one correspondence between compact closure operators, inductive closure operators, inductive closure systems, and closure operators generated in universal algebras (and generated in deductive systems, respectively). In the paper presented we make first step...

and Applied Analysis 3 Conversely, if the pair of functions α and β satisfy the conditions 1 – 4 , then there exists a unique u ∈ E1 such that u λ α− λ , β λ for each λ ∈ 0, 1 , 9 . The fuzzy number u corresponding to the pair of functions α and β is defined by u : R → 0, 1 , u x sup{λ : α x ≤ λ ≤ β x }, 5 . A sequence u uk of fuzzy numbers is a function u from the set N, the set of all positiv...

In spacetime dimensions larger than 2, whenever a global symmetry G is spontaneously broken to a subgroup H, and G and H are Lie groups, there are Nambu -Goldstone modes described by fields with values in G/H. In two-dimensional spacetimes as well, models where fields take values in G/H are of considerable interest even though in that case there is no spontaneous breaking of continuous symmetri...

The domination number γ(G) of the fuzzy graph G is the minimum cardinality taken over all minimal dominating sets of G. The independent domination number i(G) is the minimum cardinality taken over all maximal independent sets of G. The irredundant number ir(G) is the minimum cardinality taken over all maximal irredundant sets of G. In this paper we prove the result that relate the parameters ir...

Let G= (V,E,σ,μ) be a simple connected undirected fuzzy graph. In this paper, we use a fuzzy graph model to represent a traffic network of a city and discuss a method to find the different type of accidental zones in a traffic flows. This paper is based on fuzzy coloring of fuzzy graphs and fuzziness of vertices. Using this approach, we can minimize the total waiting time of a traffic flow. It ...

*Correspondence: [email protected] 1School of Mathematics and Statistics, Tianshui Normal University, Tianshui, 741001, P.R. China 2School of Mathematics, Beijing Institute of Technology, Beijing, 100081, P.R. China Full list of author information is available at the end of the article Abstract In the present paper, an extension of the Edelstein contraction theorem for cyclic contrac...

Fuzzy implications are one of the most important fuzzy logic connectives. In this work, we conduct a systematic algebraic study on the set I of all fuzzy implications. To this end, we propose a binary operation, denoted by ~, which makes (I,~) a non-idempotent monoid. While this operation does not give a group structure, we determine the largest subgroup S of this monoid and using their represe...