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This paper addresses the preservation of numerous essential properties of a residuated lattice structure in extended algebras for partial fuzzy set theory and partial fuzzy logics. The preservation includes the residuated lattice axioms, the identities narrowing the classes of the residuated lattices, and some well-known additional properties. In this paper, we consider nine algebras for partial fuzzy logics which incorporate handling undefined values in a bit different way. In particular, we consider the Bochvar, the Bochvar external, the Sobociński, the Kleene, the McCarthy, the Nelson, and the Łukasiewicz algebras, and two recently developed ones, namely the Lower estimation and the Dragonfly algebras. We summarize the obtained results in a comprehensible form which allows readers to easily check the information for the preserved and non-preserved properties in a certain partial algebraic structure. The resulting shape of the contribution is a sort of "atlas book" that aims at providing researchers with a comfortable and comprehensible form of an overview of the (non)preservation of fundamental properties of residuated structures. [ABSTRACT FROM AUTHOR]

Recently the useful redefinition of the intuitionistic and interval-valued intuitionistic fuzzy set theories (A − I F S , A − I V I F S) based on the Dempster-Shafer theory of evidence (DST) was developed. It was named the "Belief-Plausibility" (BP) approach as only the basic mathematical tools of the DST were used for its foundation. In this paper, a new approach to compare the real, interval and fuzzy-valued intuitionistic fuzzy and BP numbers is proposed. Among known approaches to compare intuitionistic fuzzy objects, most justified and used in applications are those based on the so-called score and accuracy functions. The observed multiplicity of these functions treatments and modifications indicates that the source of such a divergence is the impossibility to solve this problem exclusively in the framework of the A − I F S. Therefore, to develop the reliable methods for the considered types of comparison, a redefinition of this problem based on the BP approach is proposed. This redefinition allows us to develop new two and three criteria methods for comparison of real, interval and fuzzy-valued intuitionistic fuzzy and BP numbers, based on the local criteria with transparent interpretation in the framework of the BP approach. [ABSTRACT FROM AUTHOR]

Many geosciences data are imprecise due to various limitations and uncertainties in the measuring process. In other situations, collocated measurements of variables from the same, yet unknown, distribution are characterized with separate models that may not respect the relatedness of the measurements. One way to preserve this imprecision or relatedness in a geostatistical mapping framework is to characterize the measurements as intervals rather than single numbers. To effectively analyze the interval-valued data, this paper develops an interval-valued kriging based on the modification of a previous attempt and the recent development of the random sets theory. Numerical implementation of our interval-valued kriging is provided using a penalty-based constrained optimization algorithm. An interval-valued kriging of design ground snow loads in Ohio, USA, demonstrates the applicability and advantages of the proposed methodology. [ABSTRACT FROM AUTHOR]