the aim of this paper is the study of fuzzy basis and dimensionof fuzzy hypervector spaces. in this regard, first the notions of fuzzy linearindependence and fuzzy basis are introduced and then some related results areobtained. in particular, it is shown that for a large class of fuzzy hypervectorspace the fuzzy basis exist. finally, dimension of a fuzzy hypervector space isdefined and the basi...

This chapter introduces the underlying theory of Fuzzy Probability and Statistics related to the differences and similarities between discrete probability and possibility spaces. Fuzzy Probability Theory for Discrete Case starts with the fundamental tools to implement an immigration of crisp probability theory into fuzzy probability theory. Fuzzy random variables are the initial steps to develo...

Fuzzy semigroup theory concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. In this paper, we introduce the concept of an ( , )-fuzzy filter of an ordered semigroup , where , , , , with . Since the concept of ( , )-fuzzy filter is an important and useful generalization of ordinary fuzzy filter,...

the notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. the extensionproperty for (fuzzy) absorbent orderedfilters is established. conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

Fuzzy ideal set and fuzzy local function of fuzzy ideals with fuzzy topologies were introduced and studied by D. Sarker [10]. The purpose of this paper deals with new sort of fuzzy ideal and fuzzy local function namely fuzzy ideal and r-fuzzy open local function. Many of its characterizations, properties and connections between it and other corresponding fuzzy notions are studied. Also, we intr...

Measuring uncertainty for fuzzy sets has been carried out by calculating fuzzy entropy. Fuzzy entropy of fuzzy set is derived with the help of distance measure. The distance proportional value between the fuzzy set and the corresponding crisp set is designed as the fuzzy entropy. The usefulness is verified by proving the proposed entropy. Generally, fuzzy entropy contains the complementary char...

Fuzzy semantics comprehension and fuzzy inference are two of the central abilities of human brains that play a crucial role in thinking, perception, and problem solving. A formal methodology for rigorously describing and manipulating fuzzy semantics and fuzzy concepts is sought for bridging the gap between humans and cognitive fuzzy systems. A mathematical model of fuzzy concepts is created bas...

in this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by shi and huang, is equivalent to the family of its bases de ned by p. lubczonok. secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however,...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...