the aim of this paper is to study the categorical relations betweenmatroids, goetschel-voxman’s fuzzy matroids and shi’s fuzzifying matroids.it is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. the category of matroids can be embedded in that offuzzifying matroids as a simul...

philosophers from one hand take the “al-vahed” axiom for granted, and on the other hand, they assume that the almighty to be of absolute power. now the question is whether: this is at odds with the “al- vahed” axiom? how can we accept at the same time the absolute power of the almighty and the “al-vahed” axiom? we should say here: majority of philosophers, mystics and kalam specialists have cla...

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

We provide the first behavioral characterization of nested logit, a foundational and widely applied discrete-choice model, through introduction nonparametric version logit that we call “nested stochastic choice” (NSC). NSC is characterized by single axiom weakens independence irrelevant alternatives on basis revealed similarity to allow for effect. Nested an additional menu-independence axiom. ...

Fuzzy relations are mappings from pairs of elements into the interval [0, 1]. As a replacement for the complement operation one can use the mapping that sends x to 1 − x. Together with the concepts of t-norm and t-conorm a weak form of Boolean algebra can be defined. However, to our knowledge so far no notion of domain or codomain has been investigated for fuzzy relations. These might, however,...