Regular cost functions form a quantitative extension of regular languages that share the array of characterisations the latter possess. In this theory, functions are treated only up to preservation of boundedness on all subsets of the domain. In this work, we subject the well known distance automata (also calledmin-automata), and their dualmax-automata to this framework, and obtain a number of ...

in this note first by considering the notion of general fuzzy automata (for simplicity gfa), we define the notions of direct product, restricted direct product and join of two gfa. also, we introduce some operations on (fuzzy) sets and then prove some related theorems. finally we construct the general fuzzy recognizers and recognizable sets and give the notion of (trim) reversal of a given gfa....

In an earlier companion paper [56] a supervised learning neural network pattern classifier called the fuzzy min-max classification neural network was described. In this sequel, the unsupervised learning pattern clustering sibling called the fuzzy min-max clustering neural network is presented. Pattern clusters are implemented here as fuzzy sets using a membership function with a hyperbox core t...

In this paper, we first define the notion of a complete general fuzzyautomaton with threshold c and construct an $H_{nu}$- group, as well as commutativehypergroups, on the set of states of a complete general fuzzy automatonwith threshold c. We then define invertible general fuzzy automata, discussthe notions of “homogeneity, “separation, “thresholdness connected, “thresholdnessinner irreducible...

in this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. we then define products of $fs$-matrices andstudy their properties. we finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.

In this paper we show that the problem of minimizing a nonlinear objective function subject to a system of fuzzy relational equations with max-min composition can be reduced to a 0-1 mixed integer programming problem. The reduction method can be extended to the case of fuzzy relational equations with max-T composition as well as those with more general composition.

Motivated by the practical demands for simplification of data toward being consistent with human thinking and problem-solving, as well tolerance uncertainty, information granules are becoming important entities in processing at different levels abstraction. This article proposes a method to construct classifiers from multiresolution hierarchical granular representations using hyperbox fuzzy set...

In this paper, we extend research done in max-min fuzzy neural networks in several important ways. We replace max and min operations used in the fuzzy operations by more general t-norms and co-norms, respectively. In addition, instead of the Łukasiewicz equivalence connective used in network of ReyesGarcia and Bandler, we employ in our hybridization a variety of equivalence connectives. We expl...

We present pumping lemmas for five classes of functions definable by fragments weighted automata over the min-plus semiring, max-plus semiring and natural numbers. As a corollary we show that hierarchy unambiguous, finitely-ambiguous, polynomially-ambiguous automata, full class is strict semirings.