Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic ...

At times, it is essential to re-affirm the philosophical and axiomatic foundations of Fuzzy Theory in order to search and discover new avenues of research and to shed a new light onto basic assumptions. For such a purpose, first, the perspectives of Pierce and Zadeh are review with regards to determinacy and indeterminacy. Secondly, the ontological and epistemological foundations of both the Cl...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

Abstract This author introduces the concept of Stepwise Strategy Approach (SSA) for dealing with a number of problems arises in the current age of technology. This new idea is combined with the knowledge of Grey Theory for adding flexibility to decision making process. Grey theory is useful for grasping the ambiguity exists in the utilized information and the fuzziness appears in the human judg...

text classification is an important research field in information retrieval and text mining. the main task in text classification is to assign text documents in predefined categories based on documents’ contents and labeled-training samples. since word detection is a difficult and time consuming task in persian language, bayesian text classifier is an appropriate approach to deal with different...

fuzzy control systems have had various applications in a wide range of science and engineering in recent years. since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). conceptually, there are two types of stability for control systems: lyapunov stability (a special case ...

In this paper, we turn our attention to model theory of higher-order fuzzy logic (fuzzy type theory). This theory generalizes model theory of predicate logic but has some interesting specificities. We will introduce few basic concepts related to homomorphism, isomorphism, submodel, etc. and show some properties of them.

Integral inequalities play critical roles in measure theory and probability theory. Given recent profound discoveries in the field of fuzzy set theory, fuzzy inequality has become a hot research topic in recent years. For classical Sandor type inequality, this paper intends to extend the Sugeno integral. Based on the (s,m)-convex function in the second sense, a new Sandor type inequality is pro...

in this paper, by presenting some notions and theorems, we obtaindifferent types of fuzzy topologies. in fact, we obtain somelowen-type  and chang-type fuzzy topologies on general fuzzyautomata. to this end, first we define a kuratowski fuzzy interioroperator which induces a  lowen-type  fuzzy topology on the  set ofstates of a max- min general   fuzzy automaton. also by  provingsome theorems, ...