Cellular neural networks (CNNs) are one type of interconnected neural network and differ from the well-known Hopfield model in that each cell has a piecewise linear output function. In this paper, we present a multi-valued CNN model in which each nonlinear element consists of a multi-valued output function. The function is defined by a linear combination of piecewise linear functions. We conduc...

Fault diagnosis is an important task for the normal operation and maintenance of equipment. In many real situations, the diagnosis data cannot provide deterministic values and are usually imprecise or uncertain. Thus, interval-valued fuzzy sets (IVFSs) are very suitable for expressing imprecise or uncertain fault information in real problems. However, existing literature scarcely deals with fau...

We introduce a scheme to simplify a multi-valued network using redundancy removal techniques. Recent methods [1], [2] for binary redundancy removal avoid the use of state traversal. Additionally, [2] finds multiple compatible redundancies simultaneously. We extend these powerful advances in the field of binary redundancy removal to perform redundancy removal for multi-valued networks. First we ...

Similarity measure is one of the most important measures of interval-valued intuitionistic fuzzy (IVIF) sets. This article will put forward a new similarity measure, which considers the impacts of membership degree, nonmembership degree and median point of IVIF sets. For cases with partially known attribute weight information in multi-attribute decision-making (MADM) problems, a new weighting m...

MV-algebras were introduced by Chang, 1958 as algebraic bases for multi-valued logic. MV stands for "multi-valued" and MV algebras have already occupied an important place in the realm of nonstandard (mathematical) logic applied in several fields including cybernetics. In the present paper, using the Loomis-Sikorski theorem for cr-MV-algebras, we prove that, with every element a in a cr-MV alge...

Contemporary inferences about evolution occasionally involve analyzing infinitely large feature spaces, requiring specific algorithmic techniques. We consider parsimony analysis over numerical characters, where knowing the feature values at terminal taxa allows one to infer ancestral features, namely, by minimizing the total number of changes on the edges using continuous-valued distance measur...

1. Optimal transportation set up Let D, D∗ be two domains on Sn−1 or bounded domains in a manifold (D might be contained in one manifold and D∗ in another) with |∂D| = 0. LetN be a multi-valued mapping from D onto D∗ such thatN(x) is single-valued a.e. on D. For F ⊂ D∗, we set T (F) = N−1(F) = {x ∈ D : N(x) ∩ F , ∅}. We sayN is measurable if T (F) is Lebesgue measurable for any Borel set F ⊂ D∗...