Lexicographic derivatives developed by Nesterov and directed subdifferentials developed by Baier, Farkhi, and Roshchina are both essentially nonconvex generalized derivatives for nonsmooth nonconvex functions and satisfy strict calculus rules and mean-value theorems. This article aims to clarify the relationship between the two generalized derivatives. In particular, for scalar-valued functions...

In this paper, we introduce the notion of Pythagorean Anti fuzzy graph. We then define Cartesian product and Lexicographic on It is proved that two graphs graph general, lexicographic regular need not be Necessary sufficient conditions for to are determined. Further, concept isomorphism with suitable example.

We consider a multicriteria lexicographic Boolean problem of minimizing absolute deviations of linear functions from zero. We investigate the stability radius which can be understood as a limit level of independent perturbations of the parameters, for which new lexicographic optima do not appear. Lower and upper accessible bounds of the stability radius are obtained.

We consider a family of exchange economies where consumers have multiprior preferences representing their ambiguity aversion. Under a linear independence assumption, we prove that regular economies are generic. Regular economies exhibit enjoyable properties: odd finite number of equilibrium prices, local constancy of this number and local differentiable selections of the equilibrium prices. Thu...

In this paper we explore the use of selectional preferences for detecting noncompositional verb-object combinations. To characterise the arguments in a given grammatical relationship we experiment with three models of selectional preference. Two use WordNet and one uses the entries from a distributional thesaurus as classes for representation. In previous work on selectional preference acquisit...

In decision making, negotiation, and other kinds of practical reasoning, it is necessary to model preferences over possible outcomes. Such preferences usually depend on multiple criteria. We argue that the criteria by which outcomes are evaluated should be the satisfaction of a person’s underlying interests: the more an outcome satisfies his interests, the more preferred it is. Underlying inter...

We examine racial preferences in dating. We employ a Speed Dating experiment that allows us to directly observe individual decisions and thus infer whose preferences lead to racial segregation in romantic relationships. Females exhibit stronger racial preferences than males. The richness of our data further allows us to identify many determinants of same-race preferences. Subjects’ backgrounds,...

This paper introduces a propositional encoding of the recursive path order (RPO) on terms which is a combination of a multiset path order and a lexicographic path order which considers permutations of the arguments in the lexicographic comparison. The proposed encoding allows us to use SAT solvers in order to determine whether a given term rewrite system is RPO terminating. An implementation is...

The present paper introduces an approach to construct lexicographic compositions of similarity-based fuzzy orderings. This construction is demonstrated by means of non-trivial examples. As this is a crucial feature of lexicographic composition, the preservation of linearity is studied in detail. We obtain once again that it is essential for meaningful results that the t-norm under consideration...

We generalize the main result of [K–K–S] concerning the convex embeddings of a chain Γ in a lexicographic power ∆Γ. For a fixed non-empty chain ∆, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functional equations (∆) ≃ Γ , (∆) ≃ Γ and (∆) ≃ Γ .