In this paper we compare the expressive power of elementary representation formats for vague, incomplete or conflicting information. These include Boolean valuation pairs introduced by Lawry and Gonzalez-Rodriguez, orthopairs of sets of variables, Boolean possibility and necessity measures, three-valued valuations, supervaluations. We make explicit their connections with strong Kleene logic and...

In this paper, the concept of set-valued contraction of Nadler type in the setting of tvscone spaceswas introduced and a fixed point theorem in the setting of tvs-cone spaceswith respect to a solid conewas proved. Obtained results extend and generalize themain results of [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific Journal of Mathematics 30 (1969) 475–488] and [D. Wardowski, On ...

Uncertainty reasoning is one of the important issues of many research fields, such as artificial intelligence, knowledge-based systems, data-mining etc.. This paper proposes the theory of uncertainty reasoning in the “If...then...” type uncertainty reasoning mode based on the lattice-valued first-order logic Lvfl. The “If...then...” rule presented here is the rule in which both antecedent and c...