Yager's new class of implications Jf and some classical tautologies

• Authors: J. Balasubramaniam
• Venue: Information Sciences: an International Journal
• Year: 2007

Recently, Yager [R. Yager, On some new classes of implication operators and their role in approximate reasoning, Information Sciences 167 (2004) 193-216] has introduced a new class of fuzzy implications, denoted J"f, called the f-generated implications and has discussed some of their desirable properties, such as neutrality, exchange principle, etc. In this work, we discuss the class of J"f implications with respect to three classical logic tautologies, viz., distributivity, law of importation and contrapositive symmetry. Necessary and sufficient conditions under which J"f implications are distributive over t-norms and t-conorms and satisfy the law of importation with respect to a t-norm have been presented. Since the natural negations of J"f implications, given by N"J"""f(x)=J"f(x,0), in general, are not strong, we give sufficient conditions under which they become strong and possess contrapositive symmetry with respect to their natural negations. When the natural negations of J"f are not strong, we discuss the contrapositivisation of J"f. Along the lines of J"f implications, a new class of implications called h-generated implications, J"h, has been proposed and the interplay between these two types of implications has been discussed. Notably, it is shown that while the natural negations of J"f are non-filling those of J"h are non-vanishing, properties which determine the compatibility of a contrapositivisation technique.