In theory of interval type-2 (IT2) fuzzy sets, type-reduction is one of the most difficult parts. Karnik-Mendel (KM) algorithms have been the most popular method for computing type-reduction of IT2 fuzzy sets. These algorithms present two independent procedures for computing the generalized centroid of an IT2 fuzzy set: the first one for computing its left part (denoted by cl), and the second o...

The paper studies basic graded properties of unary and binary fuzzy connectives, i.e., unary and binary operations on the set of truth degrees of a background fuzzy logic extending the logic MTL of left-continuous t-norms. The properties studied in this paper are graded generalizations of monotony, Lipschitz continuity, null and unit elements, idempotence, commutativity, and associativity. The ...

We prove that an hypersemigroup H is regular if and only, for any fuzzy subset f of H, we have f f ◦ 1 ◦ f and it is intra-regular if and only if, for any fuzzy subset f of H, we have f 1 ◦ f ◦ f ◦ 1. An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of S we have f 1 ◦ f ◦ 1 ◦ f (resp. f f ◦ 1 ◦ f ◦ 1) and it is semisimple if and only if, for any fuz...

In this paper, the intuitionistic fuzzy counterparts of collineations defined in classical projective planes are planes. The properties plane left invariant under characterized depending on base point, line, membership degrees, and non-membership degrees plane.

We endow the set of real numbers with a family of fuzzy quasi-metrics, in the sense of George and Veeramani, which are compatible with the Sorgenfrey topology. Although these fuzzy quasi-metrics are not deduced explicitly from a quasi-metric, they possess interesting properties related to completeness. For instance, we prove that they are balanced and complete in the sense of Doitchinov and tha...

Potential field methods are rapidly gaining popularity in obstacle avoidance applications for mobile robots. The general principles of potential field path planning are presented first. The electrostatic potential field (EPF) path planner is then combined with a twolayered fuzzy logic inference engine and implemented for mobile robot navigation in a 2-D dynamic environment. The first layer of t...

The volumes of the left and right cardiac ventricles are important indexes for several cardiovascular diseases. In this paper, a semiautomatic algorithm based on 4D fuzzy connectedness is proposed for segmenting the cardiac ventricles in arbitrarily oriented cardiac cine MR images. The segmentation of the left ventricle was evaluated using 45 short axis images and a visual assessment of right v...

The volumes of the left and right cardiac ventricles are important indexes for several cardiovascular diseases. In this paper, a semiautomatic algorithm based on 4D fuzzy connectedness is proposed for segmenting the cardiac ventricles in arbitrarily oriented cardiac cine MR images. The segmentation of the left ventricle was evaluated using 45 short axis images and a visual assessment of right v...

If one of the axioms in ring, namely inverse axiom addition operation, is omitted, it will produce another algebraic structure, a semiring. Analogous to there are zero elements, ideal (left/right) semiring, and cross product semiring ideal. The analog fuzzy has (left/right), associated with membership value. This paper discuss cross-product two (more) ideals from Furthermore, always be But conv...

The main objective of this paper is to introduce a new class convexity called left-right–bi-convex fuzzy interval-valued functions. We study from the perspective fractional Hermite–Hadamard inequalities, involving integral left-right–AB integral. discuss several special cases that demonstrate our results are quite unifying. provide non-trivial numerical examples regarding means for positive rea...