Semi-unification is a generalization of both unification and matching with applications in proof theory, term rewriting systems, polymorphic type inference, and natural language processing. It is the problem of solving a set of term inequalities M1 ≤ N1, . . . ,Mk ≤ Nk, where ≤ is interpreted as the subsumption preordering on (first-order) terms. Whereas the general problem has recently been sh...

This paper is devoted to classify all idempotent uninorms defined on the finite scale Ln = {0, 1, . . . , n}, called discrete idempotent uninorms. It is proved that any discrete idempotent uninorm with neutral element e ∈ Ln is uniquely determined by a decreasing function g : [0, e]→ [e, n] and vice versa. Based on this correspondence, the number of all possible discrete idempotent uninorms on ...

In signal processing applications, a key role is played by the Fourier transforms. The mathematical structure underlying Fourier analysis is the linear structure. In the present paper we propose and study a tool designed for nonlinear signal and image processing, that is novel Fourier-like transforms, based on a pair of pseudo-operations consisting of a uninorm and an absorbing norm. We analyse...

Based on Lambek calculus and residuated lattices, psUL has been proposed by Metcalfe, Olivetti and Gabbay as a non-commutative version of the uninorm logic UL, but until recently the corresponding research has been lacking. The present paper mainly surveys the schematic extensions of psUL as well as the relation between non-commutative logics having been studied based on pseudo-t-norm. In parti...

In this paper we discuss the benefits of using full reinforcement operators for site selection in spacecraft landing on planets. Specifically we discuss a modified Uninorm operator for evaluating sites and a Fimica operator to aggregate pixels for constructing regions that will act as sites to be selected at lower spacecraft altitude. An illustrative case study of spacecraft target landing is p...

Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we la...