The concept of complex fuzzy sets is a generalization of ordinary fuzzy sets. In this paper, we introduce the concept of complex fuzzy subhypergroups ($H_{v}$-subgroups) as well as the concept of complex anti-fuzzy subhypergroups ($H_{v}$-subgroups). We investigate their properties and their relations with the traditional fuzzy (anti-fuzzy) subhypergroups ($H_{v}$-subgroups), and we prove some ...

We give de nitions for fuzzy subalgebras, for fuzzy relations on fuzzy sets, and for fuzzy compatibility, which generalize, improve and correct the existing ones. The unit interval is replaced here by a partially ordered algebra. Then we study their connection with the corresponding crisp concepts through their newly de ned Q-cuts.

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

in this paper we obtain a necessary and a sufficient condition for the set of ω_0-nearest points ( ω_0-farthest points) to be non-empty or a singleton set in normed linear spaces. we shall find a necessary and a sufficient condition for an uniquely remotal set to be a singleton set.

E cannot always use the classical methods to solve complicated problems in economics, engineering, social sciences, medical sciences etc. because different types of uncertainties are present in these theories. These days so many theories are available to deal with such type of uncertainties, such as, theory of fuzzy sets [1], theory of intuitionistic fuzzy sets [2], [3], theory of vague sets [4...

Type-1 Fuzzy Logic Systems (FLSs) have been applied to date with great success to different applications. However, for many real-world applications, there is a need to cope with large amounts of uncertainties. The traditional Type-1 FLSs that use crisp Type-1 fuzzy sets cannot directly handle such uncertainties. Type-2 FLSs that use Type2 fuzzy sets can handle such uncertainties to produce a be...

A computational verb set (verb set for short) consists of a computational verb and a crisp set or a fuzzy set. Verb sets generalize the other sets from linguistic structure “BE+statement” to “verb+statement”. Verb sets are strongly connected to computational verbs and their contexts. In this paper, the framework of verb sets and some basic concepts and properties of verb sets are given. An appl...

Small-scale autonomous vehicle navigation may involve the use of classical or “crisp” sets for control. In this paper, we discuss the successful application of fuzzy sets to such a vehicle's steering module, which results in an improvement in the vehicle's navigational capabilities. Key-Words: Fuzzy sets, microcontroller, RC car, autonomous navigation, robot.

Introduction. Classical logics are based on the bivalence principle, that is, the set of truth-values V has cardinality |V | = 2, usually with V = {T,F} where T and F stand for truthhood and falsity, respectively. Many-valued logics generalize this requirement to more or less arbitrary sets of truth-values, rather referred to as truth-degrees in that context. Popular examples of many-valued log...