This paper reviews and compares theories of fuzzy sets and rough sets. Two approaches for
the formulation of fuzzy sets are reviewed, one is based on many-valued logic and the other …

Some information and knowledge are usually represented by human language like “about
100km”,“approximately 39° C”,“roughly 80kg”,“low speed”,“middle age”, and “big size”. How …

The history of triangular norms started with the paper" Statistical metrics"[Menger 1942]. The
main idea of Karl Menger was to construct metric spaces where probability distributions …

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This monograph is an attempt to unify existing works in the field of random sets, random
variables, and linguistic random variables with respect to statistical analysis. It is intended to …

This paper gives the first comprehensive account on various systems of axioms of fixed-
basis, L-fuzzy topological spaces and their corresponding convergence theory. In general …

* Al< 8, then no matter how you computed A and B, yon will know for certain that X lies in the
interval lA* BA'rB]. The idea naturally occurred to investigate computations with intervals …

The Choquet and the Sugeno integral provide a useful tool in many problems in engineering
and social choice where the aggregation of data is required. However, their applicability is …

This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to
explain the emergence of fuzzy sets from an historical perspective. Looking back to the …

We prove a decomposition theorem for hesitant fuzzy sets, which states that every typical
hesitant fuzzy set on a set can be represented by a well-structured family of fuzzy sets on …