Soft computing can be used to build hybrid intelligent systems for achieving different goals in real-world applications. Soft Computing techniques include, at the moment, fuzzy logic, neural networks, genetic algorithms, chaos theory methods, and similar techniques that have been proposed in recent years. Each of these techniques has advantages and disadvantages, and several real-world problems...

The backing of the fuzzy ideal is normal ideal in some ring and in same time there fuzzy set whose is not fuzzy ideal and it backing set is ideal, i.e., it crisp is normal ideal. Consequently, in this paper we constructing a fuzziness function which defined on fuzzy sets and assigns membership grade for every fuzzy set whose it backing set are crisp ideal. Now, Let  be collection of all fuzzy s...

Rough set theory was proposed by Pawlak [1] as a mathematical tool to handle imprecision and uncertainty in data analysis. It has been successfully applied tomachine learning, intelligent systems, inductive reasoning, pattern recognition, mereology, image processing, signal analysis, knowledge discovery, decision analysis, expert systems, and many other fields [2–5]. The basic structure of roug...

In many geographical applications there is a need to model spatial phenomena not simply by sharply bounded objects but rather through vague concepts due to indeterminate boundaries. Spatial database systems and geographical information systems are currently not able to deal with this kind of data. In order to support these applications , for an important kind of vagueness called fuzziness, we p...

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

image segmentation is an essential issue in image description and classification. currently, in many real applications, segmentation is still mainly manual or strongly supervised by a human expert, which makes it irreproducible and deteriorating. moreover, there are many uncertainties and vagueness in images, which crisp clustering and even type-1 fuzzy clustering could not handle. hence, type-...

The idea of spherical fuzzy soft set (SFSS) is a new hybrid model (SS) and (SFS). An SFSS approach for information analysis fusion, modeling. We define the concepts spherical-fuzzy-soft-set topology (SFSS-topology) separation axioms. Several characteristics SFSS-topology are investigated related results derived. developed an extended choice value method (CVM) AHP-TOPSIS (analytical hierarchy pr...

In this paper, we dene the concepts of compatibility between twofuzzy subsets on Q, the set of states of a max- min general fuzzy automatonand transitivity in a max-min general fuzzy automaton. We then construct auniform structure on Q, and dene a topology on it. We also dene the conceptof semi-uniform structures on a nonempty set X and construct a semi-uniformstructure on the set of states of ...

Existence and uniqueness theorems are proved for Cauchy problems of second-order fuzzy differential equations. 1. Introduction. In 1972, Chang and Zadeh [2] first introduced the concept of fuzzy derivative, followed up ten years later by Dubois and Prade [5], who used the extension principle in their approach. In the mean time, Puri and Ralescu [12] used the notion of H-differentiability to ext...

After introducing many different types of prefilter convergence, we introduce an universal method to define various notions of compactness using cluster point and convergence of a prefilter and to prove the Tychonoff theorem using characterizations of ultra(maximal) prefilters. : prefilter convergence, universal method, Tychonoff theorem, ultra prefilter, good extension