We introduce partial lexicographic preference trees (PLPtrees) as a formalism for compact representations of preferences over combinatorial domains. Our main results concern the problem of passive learning of PLP-trees. Specifically, for several classes of PLP-trees, we study how to learn (i) a PLPtree consistent with a dataset of examples, possibly subject to requirements on the size of the tr...

In this article a special case of the class-teacher timetabling problem is described. This case takes into consideration a partial ordering between the topics of the curriculum and special requirements in respect to their daily lectures. The problem is modelled as a discrete lexicographic optimization problem. A heuristic procedure for solving the problem is developed. The method represents a c...

Abstract. In this paper, lexicographic products of two fuzzy graphs namely, lexicographic min-product and lexicographic max-product which are analogous to the concept lexicographic product in crisp graph theory are defined. It is illustrated that the operations lexicographic products are not commutative. The connected, effective and complete properties of the operations lexicographic products a...

Let R be a finite principal left ideal ring. Via a total ordering of the ring elements and an ordered basis a lexicographic ordering of the module R is produced. This is used to set up a greedy algorithm that selects vectors for which all linear combination with the previously selected vectors satisfy a pre-specified selection property and updates the to-be-constructed code to the linear hull o...

This paper develops a bi-level multi-objective model for road pricing optimization considering land use and transportation effects. The upper-level problem determines cordon-based scheme, while the lower-level models interaction between transportation. To facilitate decision-making in scenario characterized by hierarchical ordering of objectives, novel ?-conditional lexicographic method is esta...

This study explores the role of corpus linguistics in addressing lexicographic challenges over past ten years. It examines 25 studies published from 2012 to 2021 that employed solutions solve problems. Challenging tasks are either relevant macrostructure or microstructure dictionaries. In decade, lexicographers made extensive use tools create dictionaries and improve existing ones. effort inclu...

Abstract The paper examines whether the authors of very first Polish Sign Language dictionary, Słownik mimiczny dla głuchoniemych i osób z nimi styczność mających ‘A gestural dictionary for deaf and dumb persons who have contact with them’, published in 1879, may been influenced by any spoken monolingual dictionaries available at that time. As there is no historical documentation about circumst...

T authors propose two variants of lexicographic preference rules. They obtain the necessary and sufficient conditions under which a linear utility function represents a standard lexicographic rule, and each of the proposed variants, over a set of discrete attributes. They then: (i) characterize the measurement properties of the parameters in the representations; (ii) propose a nonmetric procedu...

A linear ordering (X,≺) is a Debreu chain (or has the Debreu property) if each subordering (Y,≺) of X can be embedded into X with an injective function that is both order-preserving and continuous with respect to the order topology on X and Y . The most typical example of a Debreu chain is the linearly ordered topological space (R, <, τ<) of real numbers endowed with its usual order < and the o...

An algorithm for converting a Grr obner basis, G 1 of an arbitrary ideal from one ordering < 1 to a Grr obner basis G 2 with respect to another target ordering < 2 is presented. Its behavior does not depend upon the dimension of the input ideal and it works for any positive or zero dimensional ideal. The target ordering can be any ordering including elimination orderings such as pure lexicograp...