The purpose of this paper is to introduce new types of neutrosophic crisp sets with three types 1, 2, 3. After given the fundamental definitions and operations, we obtain several properties, and discussed the relation- ship between neutrosophic crisp sets and others. Also, we introduce and study the neutrosophic crisp point and neu- trosophic crisp relations. Possible applications to data- base are touched upon.

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Neutrosophic Crisp Set Theory

Mixed fuzzy ideal topological spaces

A new class of generalized fuzzy open called fuzzy semi-I-open sets is introduced via fuzzy idealization. Also their properties are obtained and given a decomposition of fuzzy continuity.

Fuzzy semi-I-open sets and fuzzy semi-I-continuity via fuzzy idealization

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum particle physics in connection with string theory and E -infinity space time theory. In this paper, we introduce and study the notion of fuzzy pre- I -open sets, which is properly placed between fuzzy openness and fuzzy pre-openness regardless the fuzzy topological ideal. Moreover, we give a decomposition of fuzzy I -continuity by proving that a function f  : ( X ,  τ ,  I ) → (Y,  σ ) is fuzzy I -continuous if and only if it is fuzzy pre- I -continuous and fuzzy ∗- I -continuous.

On fuzzy pre-I-open sets and a decomposition of fuzzy I-continuity

In this paper we study the notion of connectedness in ideal topological spaces. AMS Mathematics Subject Classification (2000): 54A10, 54A05, 54A20

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Connectedness in ideal topological spaces

The major aim of this paper is to present one operator utilizing the fuzzy ideal L, denoted and given as F·Ψ(L):IX→τ, where I denotes the closed unit interval [0,1] Other concepts such as τ-codensity of a fuzzy ideal, the fuzzy ideal-open sets and fuzzy ideally restrictions are obtained Particular attention is drawn to the case when L coincides with the fuzzy ideal of fuzzy τ-nowhere dense sets Moreover, several properties of the above-mentioned concepts are introduced Possible application to superstrings and E (∞) space-time is touched upon

Some topological applications via fuzzy ideals

In this paper, the concepts of I-regular, I-normal and completely I-normal spaces have been presented utilizing the I-open notion. Moreover, , T I − -spaces, 5 , 4 , 3 = i are also given. The similarities and dissimilarities between them and some other known corresponding types are discussed. Also, some of their characterizations and several of fundamental properties have been established.

http://emis.matem.unam.mx/journals/BMMSS/pdf/v24n2/v24n2p2.pdf

Regularity and Normality via Ideals

A space $ (X,\tau,I)$ consisting of a nonempty set $ X$ with a topology $ \tau$ and an ideal $ I$ of subsets of $ X$ which has heredity and finite additivity properties. In this paper the quasi $ I$-open and quasi $ I$-closed sets are presented. Utilizing these new concepts the class of quasi $ I$-continuous functions have been obtained. Both of quasi $ I$-openness and quasi $ I$-continuity is considered as a generalization of those $ I$-openness and $ I$-continuity. However, numerous topological properties of these new notions have been discussed as well as many of their known results have been improved.

On quasi I-openness and quasi I-continuity

Where as classical topology has been developed closely connected with classical analysis describing topological phenomena in analysis, fuzzy topology with its important application in quantum gravity indicated by Witten and Elnaschie, has only been introduced as an analogue of the classical topology. The development of fuzzy topology without close relations to analytical problems did not give the possibility of testing successfully the applicability of the new notions and results. Till now this situation did not change, essentially. Although, many types of fuzzy sets and fuzzy functions having the quasi-property in both of weak and strong than openness and continuity, respectively, have been studied in detail. Many properties on fuzzy topological spaces such as compactness are discussed via fuzzy notion. While others are far from being completely devoted in its foundation. So, this paper is devoted to present a new class of fuzzy quasi-continuous functions via fuzzy compactness has been defined. Some characterizations and several properties of this new concept were discussed. Possible application to high energy physics and quantum gravity are indicated.

On fuzzy quasi continuity and an application of fuzzy set theory

Functions between spaces are impotent tools for studing their properties and for constructing new spaces from previously exiting ones. So, several authors have been interested in this subject and hence more sorts of continuous, open and closed functions arise as one goes further in mathematics. Therefore, this paper devoted to introduce three types of functions called: strongly , strongly-open and strongly closed. Some of their characterizations are estabilished similarities and dissimilarities between these new types of functions and other corresponding ones are studied. The fundamental properties and effects of strongly on some topological spaces are investigated.

R. A. Mahmoud

Papers

Some topological applications via fuzzy ideals

Regularity and Normality via Ideals

On quasi I-openness and quasi I-continuity

On fuzzy quasi continuity and an application of fuzzy set theory

Some forms of strongly ${\mu}-functions,\;{\mu}{\in}\{{\alpha}-irresolute,\;open,\;closed\}$