for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

Many geographical applications deal with spatial objects that cannot be adequately described by determinate, crisp concepts because of their intrinsically indeterminate and vague nature. Current geographical information systems and spatial database systems are unable to cope with this kind of data. To support such data and applications, we introduce vague spatial data types for vague points, va...

Based on the in-depth analysis of the essence and features of vague phenomena, this paper focuses on establishing the axiomatical foundation of membership degree theory for vague phenomena, presents an axiomatic system to govern membership degrees and their interconnections. On this basis, the concept of vague partition is introduced, further, the concept of fuzzy set introduced by Zadeh in 196...

The vague sum (product) of a finite number of real numbers and the vague integral multiples (powers) of real numbers based on a perfect vague addition (multiplication) operation are introduced, and some of their fundamental properties are pointed out. Furthermore, some examples are designed to show how they can be practically implemented. Keyword: Fuzzy arithmetic, Vague arithmetic, Vague arith...

Vagueness is something everyone is familiar with. In fact, most people think that vagueness is closely related to language and exists only there. However, vagueness is a property of the physical world. Quantum computers harness superposition and entanglement to perform their computational tasks. Both superposition and entanglement are vague processes. Thus quantum computers, which process exact...

in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...