This article concerns a connection of fuzzy logic and lattice theory. Namely, the fuzzy sets form a Heyting lattice with union and intersection of fuzzy sets as meet and join operations. The lattice of fuzzy sets is defined as the product of interval posets. As the final result, we have characterized the composition of fuzzy relations in terms of lattice theory and proved its associativity.

Fuzzy set theory has been used to model systems that are hard to define precisely. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into the model formulation and solution process. Fuzzy set theory represents an attractive tool to aid research in production management when the dynamics of the production environment limit the specification of model objectives, constra...

Generalized Geraghty type fuzzy mappings oncomplete metric spaces are introduced and a fixed point theorem thatgeneralizes some recent comparable results for fuzzy mappings incontemporary literature is obtained. Example is provided to show thevalidity of obtained results over comparable classical results for fuzzymappings in fixed point theory. As an application, existence of coincidencefuzzy p...

This paper presents an applicable health monitoring method for Li-ion batteries based on profust reliability theory. The word “profust” derives from “probability” and “fuzzy-state”, which means that the profust reliability theory is a kind of fuzzy reliability theory based on probability assumption and fuzzy-state assumption. It defines a concept of transition from fuzzy success to fuzzy failur...

A theory of fuzzy partitions is an important part of any theory meant to provide a formal framework for fuzzy mathematics. In [3], Henkin-style higher-order fuzzy logic is introduced and proposed as a foundational theory for fuzzy mathematics. Here we investigate the properties of fuzzy partitions within its formal framework. We follow closely the methodology of [2]. Therefore the notions intro...

This article concerns a connection of fuzzy logic and lattice theory. Namely, the fuzzy sets form a Heyting lattice with union and intersection of fuzzy sets as meet and join operations. The lattice of fuzzy sets is defined as the product of interval posets. As the final result, we have characterized the composition of fuzzy relations in terms of lattice theory and proved its associativity.

Fuzzy logic is an extension of the classical (Boolean) logic that can be used to handle mathematically the vagueness of human linguistics and thinking (Tanaka, 1996). In other words, it provides a logical system to formalize approximate reasoning (Zedeh, 1994; 1996). Actually, the foundation of fuzzy logic is the fuzzy set theory that was initially introduced by Zedeh (1965). However, currently...

In this paper we show that some applications of a fuzzy methodology in medical diagnosis were ”inspired” by probabilistic approaches. Although probability theory and fuzzy set theory describe different facets of uncertainty. In this paper we trace the transformation of statistical measures of diagnostic accuracy to fuzzy occurrence, exclusion and confirmation relations, applied in several fuzzy...

Fuzzy-trace theory has recently been used to account for various types of "false memories" (Brainerd & Reyna, 1998, this issue). Although components of fuzzy-trace theory-in particular the distinction between gist and verbatim traces-overlap with distinctions made in other theories of memory, those in fuzzy-trace theory provide an illuminating account of the conditions under which semantic asso...

the aim of this paper is to introduce and study set- valued homomorphism on lattices and t-rough lattice with respect to a sublattice. this paper deals with t-rough set approach on the lattice theory. the result of this study contributes to, t-rough fuzzy set and approximation theory and proved in several papers. keywords: approximation space; lattice; prime ideal; rough ideal; t-rough set; set...