Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transformation semigroup when the lattice consists of all the closed subintervals contained in [0, 1]. So, we can apply techniques of interval-valued fuzzy sets to fuzzy automata. In particular, we prove that Atanassov’s Kα operators allow us to retrieve the information given by the transition functions of...

In this paper we introduce the notion of interval-valued (∈,∈ ∨qm̃)− fuzzy subquasigroups and present some of their properties. We characterize interval-valued (∈,∈ ∨qm̃)− fuzzy subquasigroups by their level subsets. The implication-based such new fuzzy subquasigroups are also established.

Genetic Fuzzy Systems (GFS) are based on the use of Genetic Algorithms for designing fuzzy systems, and for providing them with learning and adaptation capabilities. In this context, fuzzy sets represent linguistic granules of information, contained in the antecedents and consequents of the rules, whereas the data used in the genetic learning is assumed to be crisp. GFS seldom deal with fuzzy-v...

*Correspondence: [email protected] 1Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, 710121, China Full list of author information is available at the end of the article Abstract This study aims to explore modular inequalities of interval-valued fuzzy soft sets characterized by Jun’s soft J-inclusions. Using soft product operations...

The evaluation is an important approach to promote the development of the E-Government. Since the rapid development of E-Government in the world, the E-Government performance evaluation has become a hot issue in the academia. In this paper, we develop a new evaluation method for the development of the E-Government based on the interval-valued intuitionistic fuzzy set which is a powerful techniq...

Single-valued neutrosophic hesitant fuzzy set (SVNHFS) is a combination of single-valued neutrosophic set and hesitant fuzzy set, and its aggregation tools play an important role in the multiple criteria decision-making (MCDM) process. This paper investigates the MCDM problems in which the criteria under SVNHF environment are in different priority levels. First, the generalized single-valued ne...

Some uniform categorical theoretical treatment of automata and lattice-valued fuzzy automata using quantale theory is studied in this paper. First, L-relational sheaves on a monoidM andQ-enriched categories are introduced for quantales L andQ, the equivalence of the corresponding categories are proved next. Then lattice-valued (fuzzy) automata are described by Q-enriched categories. In fact, la...

This paper presents research on applications of fuzzy logic and higher-order fuzzy logic systems to control filters reducing air pollution [1]. The filters use Selective Catalytic Reduction (SCR) method and, as for now, this process is controlled manually by a human expert. The goal of the research is to control an SCR system responsible for emission of nitrogen oxide (NO) and nitrogen dioxide ...

Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results ...

material presented at the tutorial as well as a useful list of references. Two-valued Boolean (Crisp) as well as their many-valued extensions (fuzzy relations) play increasingly important role in representation and computing with engineering and scientiic data and knowledge. Relations provide important tools in dealing with modal and belief logics used in AI. In intelligent systems and Knowledg...