Similarity of fuzzy choice functions

Arrow Index of Fuzzy Choice Function

“…In [12], [13], [14], [15] we have considered fuzzy choice functions C for which the domain and the range are made of fuzzy subsets of X. Banerjee fuzzifies only the range of a choice function; we use a fuzzification of both the domain and the range of a choice function. In our case, the available sets of alternatives are fuzzy subsets of X.…”

“…In [11], [12], [13], [14], [15], [16] we worked with a more general definition of fuzzy choice functions. Banerjee fuzzifies only the range of a choice function, in our approach both the domain and the range of a choice function are made of fuzzy subsets of a universe of alternatives.…”

“…Works [12], [13], [14], [15], [16] are an attempt to build a theory of revealed preference for these fuzzy choice functions. In [15] we have introduced the Fuzzy Arrow Axiom F AA and we have proved that a fuzzy choice function satisfies F AA iff it is full rational.…”

“…In [15] we have introduced the Fuzzy Arrow Axiom F AA and we have proved that a fuzzy choice function satisfies F AA iff it is full rational. This result extends a classical result of [1] which establishes the equivalence between the Arrow Axiom and the full rationality of crisp choice functions (see also [31]).…”

Asymmetric Equivalences in Fuzzy Logic

“…Based on this formula of equivalence, Georgescu [3] investigated the similarity of fuzzy choice functions. Jin et al [4] and Dai et al [5] investigated the robustness of fuzzy inference methods, and Wang et al [6] and Duan et al [7] discussed fuzzy logic metric structures.…”