Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...

Matrix descriptions of even dimensional fuzzy spherical branes S in Matrix Theory and other contexts in Type II superstring theory reveal, in the large N limit, higher dimensional geometries SO(2k+1)/U(k), which have an interesting spectrum of SO(2k+1) harmonics and can be up to 20 dimensional, while the spheres are restricted to be of dimension less than 10. In the case k = 2, the matrix descr...

The Kac-Moody algebras has been attracting the attention of a lot of Mathematicians because of its various connections and applications to different branches of Mathematics and Mathematical Physics since the introduction of the subject in 1968, developed simultaneously and independently by Kac and Moody. On the other hand, Fuzzy sets first originated in a seminar paper by Lotfi A.Zadeh in 1965....

Spatial database systems and geographical information systems are currently only able to support geographical applications that deal with only crisp spatial objects, that is, objects whose extent, shape, and boundary are precisely determined. Examples are land parcels, school districts, and state territories. However, many new, emerging applications are interested in modeling and processing geo...

There are various types of uncertainty in the real world. This is a motivation to investigate the behavior of uncertain phenomena. Random phenomena is one class of objective uncertain phenomena which has been well studied. Probability theory is an efficient tool to study the behavior of random phenomena. Besides randomness, fuzziness is a basic type of subjective uncertainty initiated by Zadeh....

In this paper, a novel sliding mode control theory-based learning algorithm is proposed to train an interval type-2 fuzzy neural network using type-2 fuzzy triangular membership functions. The structure considered is a type-2 Takagi–Sugeno–Kang fuzzy logic system in which the antecedents are type-2 fuzzy sets, and consequents are crisp numbers (A2-C0). In the proposed learning algorithm, instea...

the notion of strong arcs in a fuzzy graph was introduced bybhutani and rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. in mordeson and yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.in this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

in this paper we define intuitionistic fuzzy metric and normedspaces. we first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. in section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. finally,we consider some properties of...

One of the advantages systems based on fuzzy logic (fuzzy systems) is possibility a soft switch from one set values input parameters system to another, when different conclusions are drawn for sets these values. A type 2 direct generalization an ordinary set. In this paper, we review some branches theory type-2 and systems. We discuss operations sets, relations, centroids describe functional re...