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In this paper we examine in detail the definition of intuitionistic fuzzy (IF) connectives: negation, conjunction, disjunction and implication; we argue that some of the existing definitions that appear in the IF literature are not sufficiently general for all practical purposes, and suggest to replace them with new ones. One direct example to this effect will be the construction of an IF implicator that satisfies all Smets-Magrez axioms and that in the classical framework could not be expressed. Our approach will be algebraic: we treat IF connectives as lattice-valued mappings, and we translate desirable logical properties into algebraic equations to be satisfied.
Cornelis et al. (Tue,) studied this question.