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Pseudo-hoops with Internal States

  • Lavinia Corina Ciungu
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In this chapter we study the internal states for the more general fuzzy structures, namely the pseudo-hoops, and we present state pseudo-hoops and state-morphism pseudo-hoops. We define the notions of state operator, strong state operator, state-morphism operator, weak state-morphism operator and we study their properties. We prove that every strong state pseudo-hoop is a state pseudo-hoop and any state operator on an idempotent pseudo-hoop is a weak state-morphism operator. One of the main results of the chapter consists of proving that every perfect pseudo-hoop admits a state operator. Other results refer to the connection of the state operators with states and generalized states on a pseudo-hoop. Some conditions are given for a state operator to be a generalized state and for a generalized state to be a state operator.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lavinia Corina Ciungu
    • 1
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA

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