Several axioms concerning probabilistic beliefs are examined here, and the relations between them are established, using belief spaces that generalize Harsanyi type spaces. Two axioms concerning highorder probabilistic beliefs are investigated in particular. The first is the triviality axiom, which says that one is certain (that is, has a belief of degree one) of one’s own beliefs. The second i...

Abstract—This paper proposes the analysis and design of robust fuzzy control to Stochastic Parametrics Uncertaint Linear systems. This system type to be controlled is partitioned into several linear sub-models, in terms of transfer function, forming a convex polytope, similar to LPV (Linear Parameters Varying) system. Once defined the linear sub-models of the plant, these are organized into fuz...

Finite sets are one of the most fundamental mathematical structures. In the absence of the axiom of choice there are many different inequivalent definitions of finite even in classical logic. When we allow incomplete existence as in fuzzy sets the situation gets even more complicated. This paper gives nine distinct definitions of finite in a fuzzy context together with examples showing how the ...

Effective use of labor, providing system flexibility, increasing productivity, decreasing lead times and costs are some of the most important factors influencing selection of material handling equipment. In this study, a decision support system (MHAD) considering these factors for material handling equipment selection is developed. MHAD consists of a database, a rulebased system and multi-attri...

In this article we present the two classical negations of Euclid’s Fifth Postulate (done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of these we propose a partial negation (or a degree of negation) of an axiom in geometry. The most important contribution of this article is the introduction of the degree of negation (or partial negation) of an axiom and, more gener...

Employment or Leadership: None declared. Consultant or Advisory Role: None declared. Stock Ownership: None declared. Honoraria: None declared. Research Funding: R. Ensenauer, German Federal Ministry of Education and Research (BMBF) grant no. 0315088; J. Gmach, German Federal Ministry of Education and Research (BMBF) grant no. 0315088; Ina Nehring, German Federal Ministry of Education and Resear...

We consider the Gödel bi-modal logic determined by fuzzy Kripke models where both the propositions and the accessibility relation are infinitely valued over the standard Gödel algebra [0,1] and prove strong completeness of Fischer Servi intuitionistic modal logic IK plus the prelinearity axiom with respect to this semantics. We axiomatize also the bi-modal analogues of T, S4, and S5 obtained by...

In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multim...