Convergences in perfect BL-algebras

The aim of the paper is to investigate some concepts of convergence in the class of perfect BL-algebras. Similarity convergence was developed by G. Georgescu and A. Popescu in the case of the residuated lattices, while the convergence with a fixed regulator was studied by Cernák for lattice-ordered groups and MV-algebras and by the author for residuated lattices. In this paper we study the similarity convergence and the convergence with a fixed regulator for the perfect BL-algebras. The main result is the construction of Cauchy completion of a perfect BL-algebra.Peer Reviewe

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Reflective Full Subcategories of the Category of L

This paper focuses on the relationship between L-posets and complete L-lattices from the categorical view. By considering a special class of fuzzy closure operators, we prove that the category of complete L-lattices is a reflective full subcategory of the category of L-posets with appropriate morphisms. Moreover, we characterize the Dedekind-MacNeille completions of L-posets and provide an equivalent description for them

Projections in minimax algebra

An axiomatic theory of linear operators can be constructed for abstract spaces defined over (R, ⊕, ⊗), that is over the (extended) real numbersR with the binary operationsx ⊕ y = max (x,y) andx ⊗ y = x + y. Many of the features of conventional linear operator theory can be reproduced in this theory, although the proof techniques are quite different. Specialisation of the theory to spaces ofn-tuples provides techniques for analysing a number of well-known operational research problems, whilst specialisation to function spaces provides a natural formal framework for certain familiar problems of approximation, optimisation and duality

Reconciliation of Approaches to the Semantics of Logics without Distribution

This article contributes in that it clarifies and indeed completes an approach (initiated by Dunn and this author several years ago and again pursued by the present author over the last three years or so) to the relational semantics of logics that may lack distribution (Dunn's non-distributive gaggles). The approach uses sorted frames with an incidence relation on sorts (polarities), equipped with additional sorted relations, but, in the spirit of Occam's razor principle, it drops the extra assumptions made in the generalized Kripke frames approach, initiated by Gehrke, that the frames be separated and reduced (RS-frames). We show in this article that, despite rejecting the additional frame restrictions, all the main ideas and results of the RS-frames approach relating to the semantics of non-distributive logics are captured in this simpler framework. This contributes in unifying the research field, and, in an important sense, it complements and completes Dunn's gaggle theory project for the particular case of logics that may drop distribution