S. P. Tiwari

On algebraic study of fuzzy automata

This paper is towards the characterization of algebraic concepts such as subautomaton, retrievability and connectivity of a fuzzy automaton in terms of its layers, and to associate upper semilattices with fuzzy automata. Meanwhile, we provide a decomposition of a fuzzy automaton in terms of its layers and propose a construction of a fuzzy automaton corresponding to a given finite partially ordered set (poset). Finally, we establish an isomorphism between the poset of class of subautomata of a fuzzy automaton and an upper semilattice.

Fuzzy automata based on lattice-ordered monoid with algebraic and topological aspects

The purpose of this work is to study some algebraic and topological concepts of fuzzy automata with the membership values in lattice-ordered monoids. Unlike the usual fuzzy automata, we show that such concepts are affected by the associated monoid structure.

IF-preorder, IF-topology and IF-automata

The concept of topologies are widely used in machine learning, and fuzzy automata are used as models of machine learning systems. An advantage of employing fuzzy automaton as a model of machine learning system is its simplicity in design and computation. Also, some standard topological concepts and ideas are used in fuzzy automata and IF-automata to obtain certain results therein. In view of above, it seems that IF-topologies and IF-automata may play vital role in the study of machine learning; the purpose of this work is to introduce and study IF-topologies and to use such studies in the theory of IF-automata.

On coverings of rough transformation semigroups

The purpose of this paper is towards the algebraic study of rough finite state machines, i.e., to introduce the concept of homomorphisms between two rough finite state machines, to associate a rough transformation semigroup with a rough finite state machine and to introduce the concept of coverings of rough finite state machines as well as rough transformation semigroups.

On minimal realization for a fuzzy language and Brzozowski’s algorithm

The purpose of the present work is to provide a simpler solution of a well-known characterization of fuzzy regular languages and a minimal realization for given fuzzy language by using Brzozowski’s algorithm. In between, we associate two crisp deterministic fuzzy automata with a given crisp deterministic fuzzy automaton and show that the reachability and observability maps of the given crisp deterministic fuzzy automaton turn out to be morphisms of category of all crisp deterministic fuzzy

Fuzzy Preorder, Fuzzy Topology and Fuzzy Transition System

The purpose of this work is to show that the observations made regarding fuzzy transition systems can be easily obtained by using the fuzzy preordered and fuzzy topological concepts.

On a category of fuzzy automata with relations

The purpose of present work is to introduce a new category of fuzzy automata with morphisms as relations. We introduce and study the categorical concepts such as biproducts, monomorphisms, epimorphisms, injectives and projectives in this category. Finally, two functorial relationships are introduced between this new category of fuzzy automata and the category of fuzzy automata introduced and studied in (1).

On the Topological Structure of Rough Soft Sets

The concept of rough soft set is introduced to generalize soft sets by using rough set theory, and then the soft topologies on soft sets are introduced.

On relationship between generalized rough multisets and multiset topologies

The purpose of this paper is to investigate the relationship between multiset topology (M-topology) and generalized rough multiset induced by multiset relation. The notion of transitive closure of a relation is proposed in multiset context. The notable results we establish here are (1) any serial multiset relation induce an M-topology (2) any reflexive multiset relation R and its transitive closure t(R) induce the same M-topology, i.e.,