Lattice-valued entropy functions defined by a lattice-valued possibilistic distribution π on a space Ω are defined as the expected value (in the sense of Sugeno integral) of the complement of the value π(ω) with ω ranging over Ω. The analysis is done in parallel for two alternative interpretations of the notion of complement in the complete lattice in question. Supposing that this complete latt...

We present a four-valued approach for recovering consistent data from inconsistent set of assertions. For a common family of knowledge-bases we also provide an eecient algorithm for doing so au-tomaticly. This method is particularly useful for making model-based diagnoses.

In this paper, two different ways of introducing alternation for lattice-valued (referred to as {L}valued)  regular tree grammars and {L}valued top-down tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the non-terminals of the grammar and the other is the way which combines state with alternation. The first way is ta...

In order to process the linguistic-valued information with uncertainty in the financial decisionmaking, the present work uses a lattice-valued logical algebra lattice implication algebra to deal with both comparable and incomparable linguistic truth-values. A new personal financial decision auxiliary modeling framework based on the lattice-ordered linguistic truth-valued logic is proposed. The ...

We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy vers...

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...

This paper focuses on multi-ary α-semantic resolution automated reasoning method based on multi-ary α-resolution principle for lattice-valued propositional logic LP(X) with truth-value in lattice implication algebras. The definitions of the multi-ary α-semantic resolution and multi-ary α-semantic resolution deduction in lattice-valued propositional logic LP(X) are given, respectively, and the s...

The present paper has been an attempt to investigate the general fuzzy automata on the basis of complete residuated lattice-valued ($L$-GFAs). The study has been chiefly inspired from the work by Mockor cite{15, 16, 17}. Regarding this, the categorical issue of $L$-GFAs has been studied in more details. The main issues addressed in this research include: (1) investigating the relationship betwe...