CHARACTERIZATION OF ORDERED SEMIGROUPS BASED 0N (|;qk)-QUASI-COINCIDENT WITH RELATION

Based on generalized quasi-coincident with relation, new types of fuzzy bi-ideals of an ordered semigroup S are introduced. Level subset and characteristic functions are used to linked ordinary bi-ideals and (2;2_(|;qk))fuzzy bi-ideals of an ordered semigroup S: Further, upper/lower parts of (2;2 _(|;qk))-fuzzy bi-ideals of S are determined. Finally, some well known classes of ordered semigroups like regular, left (resp. right) regular and completely regular ordered semigroups are characterized by the properties of (2;2_(|;qk))-fuzzy bi-ideals

Conjuntos construibles en modelos valuados en retículos

We investigate different set-theoretic constructions in Residuated Logic based on Fitting’s work on Intuitionistic Kripke models of Set Theory. Firstly, we consider constructable sets within valued models of Set Theory. We present two distinct constructions of the constructable universe: L B and L B , and prove that the they are isomorphic to V (von Neumann universe) and L (Gödel’s constructible universe), respectively. Secondly, we generalize Fitting’s work on Intuitionistic Kripke models of Set Theory using Ono and Komori’s Residuated Kripke models. Based on these models, we provide a general- ization of the von Neumann hierarchy in the context of Modal Residuated Logic and prove a translation of formulas between it and a suited Heyting valued model. We also propose a notion of universe of constructable sets in Modal Residuated Logic and discuss some aspects of it.Investigamos diferentes construcciones de la teoría de conjuntos en Lógica Residual basados en el trabajo de Fitting sobre los modelos intuicionistas de Kripke de la Teoría de Conjuntos. En primer lugar, consideramos conjuntos construibles dentro de modelos valuados de la Teoría de Conjuntos. Presentamos dos construcciones distintas del universo construible: L B y L B , y demostramos que son isomorfos a V (universo von Neumann) y L (universo construible de Gödel), respectivamente. En segundo lugar, generalizamos el trabajo de Fitting sobre los modelos intuicionistas de Kripke de la teoría de conjuntos utilizando los modelos residuados de Kripke de Ono y Komori. Con base en estos modelos, proporcionamos una generalización de la jerarquía de von Neumann en el contexto de la Lógica Modal Residuada y demostramos una traducción de fórmulas entre ella y un modelo Heyting valuado adecuado. También proponemos una noción de universo de conjuntos construibles en Lógica Modal Residuada y discutimos algunos aspectos de la misma. (Texto tomado de la fuente)MaestríaMagíster en Ciencias - MatemáticasLógica matemática, teoría de conjunto

Cubic Interior Ideals in Semigroups

In this paper we apply the cubic set theory to interior ideals of a semigroup. The notion of cubic interior ideals is introduced, and related properties are investigated. Characterizations of (cubic) interior ideals are established, and conditions for a semigroup to be left (right) simple are provided

Propositional dynamic logic for searching games with errors

We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the (n+1)-valued Kripke models and a corresponding language based on a modal extension of {\L}ukasiewicz many-valued logic. We illustrate the definitions by providing a framework for an analysis of the R\'enyi - Ulam searching game with errors. Our main result is the axiomatization of the theory of the (n+1)-valued Kripke models. This result is obtained through filtration of the canonical model of the smallest (n+1)-valued propositional dynamic logic

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