The Archimedean axiom in fuzzy set theory is critically discussed. The axiom is brought into perspective within a measurement theoretic framework and then its validity for fuzzy set theory is questioned. The discussion sheds light into what type of vagueness fuzzy set theory models.

An interpretation of lattice-valued logic, defined by Titani, in basic fuzzy logic, defined by Hájek, is presented. Moreover, Titani’s axioms of lattice-valued set theory are interpreted in fuzzy set theory, under slight modifications of the fuzzy set theory axiomatics.

Fuzzy-trace theory has been developed by Brainerd and Reyna (1998, this issue) to explain a variety of findings. Here we explore the way that fuzzy-trace theory handles three phenomena concerning the creation and maintenance of false memories. We show that fuzzy-trace theory can account for seemingly paradoxical findings, thus providing theoretical clarity that has heretofore been lacking in th...

In this paper the theory of fuzzy logic is mixed with the theory of Markov systems and the abstraction of a Markov system with fuzzy states introduced. The notions such as fuzzy transient, fuzzy recurrent etc., were introduced. The results based on these notions are introduced.

Molodtsov initiated soft set theory that provided a general mathematicalframework for handling with uncertainties in which we encounter the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as bipolar fuzzy set theory.The main object of this paper is to lay a foundation for providing a new application of bipolar fuzzy soft tool in ...

In this paper basic notions of the rough intuitionistic fuzzy set theory will be given. In fact the paper concerns a relationship between rough intuitionistic fuzzy sets and lattice theory. We shall introduce the notion of rough intuitionistic fuzzy lattice (resp rough intuitionistic fuzzy ideals). We also defined intuitionistic fuzzy rough set corresponding to a rough set and given conditions ...

Multi-fuzzy set theory is an extension of fuzzy set theory, which deals with the multi dimensional fuzziness. In this paper we introduce the concepts of multi-fuzzy subgroups and normal multi-fuzzy subgroups. Mathematics Subject Classification: MSC: 20N25; 03E72; 08A72

Measures on clans of fuzzy sets are traditionally studied as certain functionals on collections of [0, 1]-valued functions. The goal of this paper is to make first steps towards establishing this part of fuzzy mathematics as a formal theory over a suitable predicate fuzzy logic. Two concepts of formal measure theory are sketched within Henkin-style ω-order fuzzy logic.

The idea of validation arises naturally within the context of interval analysis where the theory and methods are well developed. Approaching fuzzy set theory through fuzzy interval analysis, we develop a validation theory for fuzzy sets. An algorithm is given and applied to an optimization problem.

Abstract This author introduces the concept of Stepwise Strategy Approach (SSA) for dealing with a number of problems arises in the current age of technology. This new idea is combined with the knowledge of Grey Theory for adding flexibility to decision making process. Grey theory is useful for grasping the ambiguity exists in the utilized information and the fuzziness appears in the human judg...