Fuzzy sets are naturally ordered by the subsethood relation A ⊆ B. If we only know which set which fuzzy set is a subset of which – and have no access to the actual values of the corresponding membership functions – can we detect which fuzzy sets are crisp? In this paper, we show that this is indeed possible. We also show that if we start with interval-valued fuzzy sets, then we can similarly d...

To avoid self-contradictions in Fuzzy Set Theory, it is needed to consider only fuzzy sets that are not selfcontradictory and whose complements are also not selfcontradictory. This paper deals with a subset Fnc(E) in [0, 1] , where the above conditions are satisfied. A particular Fuzzy Set Theory is defined in Fnc(E) with adequate logical connectives. Finally, which classical properties hold in...

In this paper we aim to give an introduction to fuzzy logic using the language Haskell to implement our solutions. We shall see how the high-level, declarative nature of a functional language allows us to implement easily and eeciently solutions to problems using fuzzy logic and, in particular, how the presence of functions as rst-class values allows us to model the key concept of the fuzzy sub...

A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals gene...

The FuTI–library is a collection of classes and methods for representing and manipulating fuzzy time intervals. Fuzzy time intervals are represented as polygons over integer coordinates. FuTI is an open source C++ library with many advances operations and highly optimised algorithms. Version 1.0 is now available from the URL http://www.pms.ifi.lmu.de/CTTN/FuTI. 1 Fuzzy Time Intervals Fuzzy Inte...

The notion of bipolar fuzzy set was initiated by Lee (2000) as a generalization of the notion fuzzy sets and intuitionistic fuzzy sets, which have drawn attention of many mathematicians and computer scientists. In this paper, we initiate a study on bipolar ( ,   )-fuzzy sets in -semihypergroups. By using the concept of bipolar ( ,   )-fuzzy sets (Yaqoob and Ansari, 2013), we introduce the ...

A kind of new fuzzy compactness, called near SR-compactness, is de4ned for an arbitrary L-subset and for L a complete DeMorgan algebra. This kind of fuzzy compactness is between Lowen’s strong fuzzy compactness and the second author’s SR-compactness. Characterizations and examples of near SR-compact L-subsets are given, and its topological properties are systematically investigated. c © 2003 El...

Let G be a fuzzy graph. A subset D of V is said to be Fuzzy dominating set if every vertex u ∈ V (G) there exists a vertex v ∈ V −D such that uv ∈ E(G) and μ(uv) 6 σ(u) ∧ σ(v). The minimum Cardinality of fuzzy dominating set is denoted by γf . A graph G is said to be fuzzy excellent if every vertex of G belongs to γf -sets of G. In this paper, we give a construction to imbedded non-excellent fu...

An AG-groupoid is a non-associative algebraic structure mid way between a groupoid and a commutative semigroup. The left identity in an AGgroupoid if exists is unique [9]. An AG-groupoid is non-associative and non-commutative algebraic structure, nevertheless, it posses many interesting properties which we usually find in associative and commutative algebraic structures. An AG-groupoid with rig...

Feature Selection (FS) methods based on fuzzy-rough set theory (FRFS) have employed the dependency function to guide the FS process with much success. More recently a method has been developed which uses fuzzy-entropy [9] to perform this task. Such use of fuzzy-entropy as an evaluation measure in fuzzy-rough feature selection can result in smaller subset sizes than those obtained through FRFS a...