Related papers: Fuzzy Set with Hyperbolic Valued Membership Functi…
Continuing to pursue a research direction that we already explored in connection with G\"odel-Dummett logic and Ruspini partitions, we show here that {\L}ukasiewicz logic is able to express the notion of pseudo-triangular basis of fuzzy…
The mathematical representation of uncertainty has led to a proliferation of preference structures, such as interval-valued fuzzy sets, intuitionistic fuzzy sets, and various granular models. While these extensions are often studied…
An investigation of deep fuzzy systems is presented in this paper. A deep fuzzy system is represented by recursive fuzzy systems from an input terminal to output terminal. Recursive fuzzy systems are sequences of fuzzy grade memberships…
The concept of a visible point of a convex set relative to a given point is introduced. A number of basic properties of such visible point sets is developed. In particular, it is shown that this concept is useful in the study of best…
We present structures comprised of identical convex polyhedra which are interlocked geometrically. These sets cannot be disassembled by removing individual polyhedra by translations and/or rotations. The shapes that permit interlocking…
We discuss how hadronic bag models can be generalized in the framework of fuzzy set theory to implement effects of a smooth and extended phase boundary.
In this paper, it shows that for each fuzzy set $u$ on $\mathbb{R}^m$, the set $D(u)$ is at most countable. Based on this, it modifies the proof of assertion (I) in step 2 of the sufficiency part of Theorem 4.1 in paper: Characterizations…
n-Dimensional fuzzy sets is a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0,1] orderly increased, called n-dimensional intervals. The set of n-dimensional intervals is denoted by…
In this paper we generalize the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Several examples are presented. Also, a geometric interpretation of the Neutrosophic Set is given using…
In 2004 Anna Maria Radzikowska et al \cite{RK2004} investigated the fuzzy rough sets where the set of truth values is an arbitrary residuated lattice. In this paper, we extend their work by considering a residuated multilattice $M$ as the…
In this work, we first define relations on the fuzzy parametrized soft sets and study their properties. We also give a decision making method based on these relations. In approximate reasoning, relations on the fuzzy parametrized soft sets…
In this work, we first define intuitionistic fuzzy parametrized soft sets (intuitionistic FP-soft sets) and study some of their properties. We then introduce an adjustable approaches to intuitionistic FP-soft sets based decision making. We…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After…
In this book we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), plithogenic logic (as generalization of classical, fuzzy, intuitionistic fuzzy, and neutrosophic logics),…
In this paper we provide a general setting to deal with level continuous fuzzy-valued functions. Namely, we embed such functions into a product of spaces of real-valued functions of two variables satisfying certain types of left-continuity,…
This paper deals with conditions under which the quotient of $L$-fuzzy up-sets forms a complete lattice by using terminologies of closure operators. It first gives a condition that a family of some subsets of a nonempty set can be…
Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A contains B. We characterize, for subgroups of G, when…
Crisp and $L$-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or $L$-fuzzy) ambiguous…
We analyse the intersection of positively and negatively sectional-hyperbolic sets for flows on compact manifolds. First we prove that such an intersection is hyperbolic if the intersecting sets are both transitive (this is false without…
Fuzzy implication functions have been widely investigated, both in theoretical and practical fields. The aim of this work is to continue previous works related to fuzzy implications constructed by means of non necessarily associative…