In this work, we investigate a relationship between extensionality and continuity of fuzzy relations in the frame of BL-algebras. We found conditions when extensionality implies continuity and vice versa. Problem is formulated and solved algebraically.

In this paper we suggest that social robots should not mirror exactly human social behavior (facial expressions, language, etc) but need to be able to produce believable social behaviors that provide a minimal set of actions by which human-companion cooperation can be achieved. For implementing such an ethologically inspired social robot behavior, a platform based on fuzzy automaton (fuzzy stat...

By means of a kind of new idea, we consider  the $(in,ivq)$-fuzzy$h$-ideals of a hemiring.  First, the concepts of $(in,ivq)$-fuzzyleft(right) $h$-ideals of a hemiring are provided and some relatedproperties are investigated. Then, a kind  of quotient hemiring  ofa hemiring by an $(in,ivq)$-fuzzy $h$-ideal is presented andstudied. Moreover, the notions of generalized $varphi$-compatible$(in,ivq...

Fuzzy formal logics were introduced in order to handle graded truth values instead of only ‘true’ and ‘false’. A wide range of such logics were introduced successfully, like Monoidal T-norm based Logic, Basic Logic, Gödel Logic, Lukasiewicz Logic etc. However, in general, fuzzy set theory is not only concerned with vagueness, but also with uncertainty. A possible solution is to use intervals in...

In order to research the logical system whose propositional value is given in a lattice from the semantic viewpoint, Xu [7] proposed the concept of lattice implication algebras, and discussed some of their properties. Xu and Qin [8] introduced the notion of implicative filters in a lattice implication algebra, and investigated some of their properties. Turunen [5] introduced the notion of Boole...

It has been shown that neural networks are able to infer regular crisp grammars from positive and negative examples. The fuzzy grammatical inference (FGI) problem however has received considerably less attention. In this paper we show that a suitable two-layer neural network model is able to infer fuzzy regular grammars from a set of fuzzy examples belonging to a fuzzy language. Once the networ...

The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this paper to the general non-involutive case, i. e. to MTL-algebras. To this end we describe the radical of MTL-algebras and characterize perfect MTL-algebras as those for which the quotient by the radical is isomorphic to the two-element Boolean algebra, and a special class of bipartite MTL-algebras, B...