O. R. Sayed

On seperation axioms in fuzzifying topology

Abstract In the present paper we introduce R 0 - and R 1 -separation axioms in fuzzifying topology and study their relations with T 1 - and T 2 -separation axioms, respectively. Furthermore, we introduce and study semi- T 0 -, semi- R 0 -, semi- T 1 -, semi- R 1 -, semi- T 2 (semi-Hausdorff)-, semi- T 3 (semi-regularity)- and semi- T 4 (semi-normality)-separation axioms in fuzzifying topology and give some of their characterizations as well as the relations of these axioms and other separation axioms in fuzzifying topology introduced by Shen, Fuzzy Sets and Systems 57 (1993) 111–123.

pre -Continuity and D(c,p) -continuity in fuzzifying topology

The concepts of fuzzy pre-continuity and fuzzy cpre-continuity are introduced and studied in fuzzifying topology essentially in order to give decompositions of fuzzy continuity.

a -continuity and ca -continuity in fuzzifying topology

The concepts of α-continuity and cα-continuity are considered and studied in fuzzifying topology and by making use of these concepts, some decompositions of fuzzy continuity are introduced. It is proved that the family of all α-sets in fuzzifying topology may not be a fuzzifying topology.

Fuzzy Soft Expert System in Prediction of Coronary Artery Disease

Coronary artery disease affects millions of people all over the world including a major portion in Egypt every year. Although much progress has been done in medical science, early detection of this disease is still a challenge for prevention. In this paper we, will extend the concept of fuzzy soft set theory so as to develop a knowledge-based system in medicine and devise a prediction system named fuzzy soft expert system consisting of four main components. These are a fuzzification which translates inputs into fuzzy values, fuzzification of data sets to obtain fuzzy soft sets, a new fuzzy soft set by normal parameter reduction of fuzzy soft set and an algorithm to produce the resultant output. The fuzzy soft expert system developed is then used to predict for coronary artery disease using systolic blood pressure, low-density lipoprotein cholesterol, maximum heart rate, blood sugar, old peak and age of patients. A preliminary study is conducted on nine male patients undergoing treatment in the Cardiac Unit of the Faculty of Medicine, Assiut University, Egypt. It is found that the fuzzy soft expert system developed is able is to help the expert doctor to decide whether a patient needs to be given drug therapy or intervention.

Completely continuous functions and R-map in fuzzifying topological space

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies introduced by Ying. The concepts of fuzzifying regular derived set, fuzzifying regular interior and fuzzifying regular convergence are studied and some results on above concepts are obtained. Also, the concepts of fuzzifying completely continuous functions and fuzzifying R-map are introduced and some important characterizations are obtained. Furthermore, some compositions of fuzzifying continuity with fuzzifying completely continuous functions and fuzzifying R-map are presented.

Corrigendum to “Almost continuity and δ-continuity in fuzzifying topology”: [Fuzzy Sets and Systems 116 (2000) 339–352]

Abstract In (2000), Zahran has introduced the concepts of δ-open sets, almost continuity and δ-continuity in fuzzifying topology. In this note we show that Lemma 2.2 and Theorem 2.4 are incorrect.

Some covering properties in semantic method of continuous valued logic

In this paper, some characterizations of fuzzifying semi-compactness are given, including characterizations in terms of nets and semi-subbases. Lastly, several characterizations of locally semi-compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

Supra b-irresolutness and Supra b-connectedness on Topolog- ical Space

In this paper, the concept of supra b-irresolute maps is introduced and several properties of it is investigated. Furthermore, the notion of supra b-connectedness is defined and researched by means of supra b-separated sets.

On Fuzzifying Nearly Compact Spaces

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies) introduced by Ying [16, (I)]. It investigates topological notions defined by means of regular open sets when these are planted into the framework of Yings fuzzifying topological spaces (in Łukasiewwicz fuzzy logic). The concept of fuzzifying nearly compact spaces is introduced and some of its properties are obtained. We use the finite intersection property to give a characterization of fuzzifying nearly compact spaces. Furthermore, we study the image of fuzzifying nearly compact spaces under fuzzifying completely continuous functions, fuzzifying almost continuity and fuzzifying R-map.