Related papers: Fuzzy numbers revisited: operations on extensional…
In this paper, we describe a correspondence between a fuzzy linear code and a family of nested linear codes. We also describe the arithmetic of fuzzy linear codes. As a special class of nested linear codes, we consider a family of nested…
Rule-based systems are a very popular form of explainable AI, particularly in the fuzzy community, where fuzzy rules are widely used for control and classification problems. However, fuzzy rule-based classifiers struggle to reach bigger…
We interpret a fuzzy set as a random availability function and provide sufficient conditions under which a preference relation over the set of all random availability functions can be represented by a utility function.
Closure operators are very useful tools in several areas of classical mathematics and in general category theory. In fuzzy set theory, fuzzy closure operators have been studied by G. Gerla (1966). These works generally define a fuzzy subset…
Multi-variable nonlinear fuzzy optimization problem is considered under linear order relation on fuzzy numbers. Using gH-differentiability of a fuzzy-valued function $\tilde{f}$, new necessary and sufficient optimality conditions are…
In recent years, the problem of fuzzy clustering has been widely concerned. The membership iteration of existing methods is mostly considered globally, which has considerable problems in noisy environments, and iterative calculations for…
Grainy numbers are defined as tuples of bits. They form a lattice where the meet and the join operations are an addition and a multiplication. They may be substituted for the real numbers in the definition of fuzzy sets. The aim is to…
Fuzzy rule-based systems have been mostly used in interpretable decision-making because of their interpretable linguistic rules. However, interpretability requires both sensible linguistic partitions and small rule-base sizes, which are not…
By using the space of fuzzy numbers, in e.g. [5] have been considered several complete metric spaces (called here {\bf FN}-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the…
Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on…
A fuzzy clustering algorithm for multidimensional data is proposed in this article. The data is described by vectors whose components are linguistic variables defined in an ordinal scale. The obtained results confirm the efficiency of the…
Building upon specific compatibility conditions, we establish fundamental structural results concerning ordering relations for triangular fuzzy numbers. We demonstrate that orders satisfying compatibility with arithmetic operations, MIN-MAX…
Fuzzy regression models have been applied to several Operations Research applications viz., forecasting and prediction. Earlier works on fuzzy regression analysis obtain crisp regression coefficients for eliminating the problem of…
To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and…
We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and…
This article presents a theory of differential and integral calculus for mapping between Banach spaces formed by subsets of fuzzy numbers called A-linearly correlated fuzzy numbers, where both the domain and codomain are spaces composed of…
Attack trees are important for security, as they help to identify weaknesses and vulnerabilities in a system. Quantitative attack tree analysis supports a number security metrics, which formulate important KPIs such as the shortest, most…
Fuzzy automata, whose input alphabet is a set of numbers or symbols, are a formal model of computing with values. Motivated by Zadeh's paradigm of computing with words rather than numbers, Ying proposed a kind of fuzzy automata, whose input…
This paper focuses on greedy expansions, one possible representation of numbers, and on arithmetical operations with them. Performing addition or multiplication some additional digits can appear. We study bounds on the number of such digits…
The concepts of fuzzy objects and their classes are described that make it possible to structurally represent knowledge about fuzzy and partially-defined objects and their classes. Operations over such objects and classes are also proposed…