Arithmetic operators in interval-valued fuzzy set theory
We introduce the addition, subtraction, multiplication and division on LI L I , where LI L I is the underlying lattice of both interval-valued fuzzy set theory [R. Sambuc, Fonctions ?-floues. Application  laide au diagnostic en pathologie thyroidienne, Ph.D. Thesis, Universit de Marseille, France, 1975] and intuitionistic fuzzy set theory [K.T. Atanassov, Intuitionistic fuzzy sets, 1983, VII ITKRs Session, Sofia (deposed in Central Sci. Technical Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian)]. We investigate some algebraic properties of these operators. We show that using these operators the pseudo-t-representable extensions of the ?ukasiewicz t-norm and the product t -norm on the unit interval to LI L I and some related operators can be written in a similar way as their counterparts on ([0,1],?) ( [ 0 , 1 ] , ? ) .
addition subtraction multiplication product t -norm on li l i li l i li l i l i arithmetic operators on li l i li l i li l i l i sum difference quotient