The concept of an M-approximative system is introduced. Basic properties of the category of M-approximative systems and in a natural way defined morphisms between them are studied. It is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of M-approximative systems. Keywords— Approximative operator...

A new algorithm is proposed to learn fuzzy partitions with a high interpretability degree. The set of input variables, the number of linguistic terms per variable, and the type (triangular or trapezoidal) and parameters of the membership functions are learnt by means of a meta-algorithm that uses a simple learning method to generate a fuzzy rule set from the derived fuzzy partitions. Interpreta...

conclusions using fuzzy logic provides an elegant mathematical solution for finding the optimum point of food groups in dietary pattern. results the optimum (lower attention – upper attention) recommended servings per day for fruits, vegetables, grain, meat, dairy, and oils of the 2000 kcal diet were 4.06 (3.75-4.25), 6.69 (6.25-7.00), 5.69 (5.75-6.25), 4.94 (4.5-5.2), 2.75(2.50-3.00), and 2.56...

Most fuzzy controllers and fuzzy expert systems must predefine membership functions and fuzzy inference rules to map numeric data into linguistic variable terms and to make fuzzy reasoning work. In this paper, we propose a general learning method as a framework for automatically deriving membership functions and fuzzy if-then rules from a set of given training examples to rapidly build a protot...

In this paper, we apply the concept of fuzzy soft sets to ordered semigroup theory. The concepts of (∈γ ,∈γ ∨qδ)-fuzzy left (right) ideals, (∈γ ,∈γ ∨qδ)-fuzzy biideals and (∈γ ,∈γ ∨qδ)-fuzzy quasi-ideals are introduced and some related properties are obtained. Three kinds of lattice structures of the set of all (∈γ ,∈γ ∨qδ)-fuzzy soft left (right) ideals of an ordered semigroup are derived. The...

In this article, we propose an axiomatic system for fuzzy “cardinality” measures (referred to as fuzzy c-measures for short) assigning to each finite fuzzy set a generalized cardinal that expresses the number of elements that the fuzzy set contains. The system generalizes an axiomatic system introduced by J. Casasnovas and J. Torrens (2003). We show that each fuzzy c-measure is determined by tw...

A novel approach to design fuzzy controllers using fuzzy-arithmetic-based Lyapunov function that gives a linguistic description on the plant and the control objective is presented in this paper. An inverted pendulum system is used as a benchmark dynamic nonlinear plant for evaluating the proposed method. It is shown that a set of stable fuzzy control rules can be derived from perception-based i...

The fuzzy measure can highlight important information in analyzing component features, patterns, and trends. However, fuzzy densities and interaction effects are usually unknown or uncertain for implications thus making the fuzzy measure limited in applications. This research proposes an extended fuzzy measure to derive the conditional fuzzy densities from dominance-based rough set approach (DR...

Fuzzy valued measure ([7], [10], [3], [5]) is a natural generalization of a set valued measure ([6]). Infinite addition is defined ([12]) as a Zadeh’s extension principle of continuity. In [9], using an additive fuzzy valued measure, an integral of single valued function is defined and some basic properties are given. In this paper we proceed to investigate specific properties of integrals in f...

A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...