A relation algebraic approach to universal integrals
In a series of papers Klement et al. investigated discrete integrals such as the Choquet and Sugeno integral and their axiomatization. As part of their study they showed that universal integrals are based on semicopulas, and they provided lower ...
The weak dominance between t-norms and t-conorms revisited
The weak dominance relation between two binary operations was introduced as an extension of the dominance relation and the modularity equation. This paper continues the study of the weak dominance between t-norms and t-conorms. First, we present ...
On Stonean triangle algebras
We introduce the notion of Stonean triangle algebra and consider it in details and give the relationships between Stonean triangle algebra and some of algebraic structures such as Gödel-triangle algebras. The notion of L-IVRL(Interval Valued ...
Projection depth and L r -type depths for fuzzy random variables
Statistical depth functions are a standard tool in nonparametric statistics to extend order-based univariate methods to the multivariate setting. Since there is no universally accepted total order for fuzzy data (even in the univariate case) and ...
On fuzzy order in fuzzy sets based on t-norm fuzzy arithmetic
In this paper we study some fuzzy order in fuzzy sets based on t-norm fuzzy arithmetic. The definition of the order comes from the extension principle for interval order: a > b iff a − b > 0 and from measurement sciences. In measurement sciences ...
On the representation of internal uninorms on a bounded lattice
Internal uninorms on a bounded lattice always output one of the two input values and are nothing else but idempotent uninorms when the lattice is a chain. In this paper, we study the existence and representation of internal uninorms with a given ...
Fuzzy three-way rule learning and its classification methods
Rules play a crucial role in classification tasks, driving the advancement of artificial intelligence. However, how to improve the interpretability of extracted rules while ensuring the performance of classification tasks is always a challenge, ...
A Radon-Nikodym theorem for monotone measures
A version of Radon-Nikodym theorem for the Choquet integral w.r.t. monotone measures is proved. Without any presumptive condition, we obtain a necessary and sufficient condition for the ordered pair ( μ , ν ) of finite monotone measures to have ...
Dissipative control for quaternion-valued fuzzy memristive neural networks: Nonlinear scalarization approach
This paper deals with the dissipative control for a class of quaternion-valued fuzzy memristive neural networks. By constructing proper Lyapunov functionals and using adaptive controller, the strictly ( Q , S , R )-dissipative are characterized ...
The general algebraic solution of dual fuzzy linear systems and fuzzy Stein matrix equations
In this paper, we present a new method for solving a dual fuzzy linear system (DFLS), A X ˜ + C ˜ = B X ˜ + D ˜, where the coefficient matrices A and B are arbitrary real m × n matrices and C ˜ and D ˜ are given fuzzy number vectors. A necessary ...
Fuzzification using the extension principle and the expression in decomposition theorem
Fuzzifying the crisp functions is a well-known methodology to study the problems under fuzzy uncertainty. The traditional way for fuzzifying the crisp functions is based on the extension principle. In this paper, by referring to the expression in ...
EFNN-Nul0- a trustworthy knowledge extraction about stress identification through evolving fuzzy neural networks
This paper presents a novel hybrid architecture, denoted as EFNN-Nul0 (evolving neuro-fuzzy system based on null-unineurons), meticulously crafted for stress identification within the realm of pattern classification. The model seamlessly ...
