Dynamic Analysis of Customer Demand Based on Intuitionistic Fuzzy Number in Product Planning

To address the fuzziness and variability in determining customer demand importance,a dynamic analysis method based on intuitionistic fuzzy numbers is proposed.First,selected customers use intuitionistic fuzzy numbers to represent the importance of each demand.Then,the preference information is aggregated using customer weights and time period weights through the intuitionistic fuzzy ordered weighted average operator,yielding a dynamic vector of the subjective importance of the demand index.Finally,the feasibility of the proposed method is demonstrated through an application example of a vibrating sorting screen.

Fuzzy Semi-continuity of fuzzy number-valued function

In this paper we discuss the conecept and property of fuzzy semi continuous function.

Ideal Statistically Pre-Cauchy Triple Sequences of Fuzzy Number and Orlicz Functions

In this paper, we extend the notions of ideal statistically convergence for sequence of fuzzy number. We introduce the notions ideal statistically pre-Cauchy triple sequences of fuzzy number about Orlicz function, and give some correlation theorem. It is shown that x = {xijk} is ideal statistically pre-Cauchy if and only if D (xijk, xpqr) ≥ ε, i ≤ m, j ≤ n, t ≤ k}| ≥ δ} ∈I. At the same time, we have proved x = {xijk} is ideal statistically convergent to x0 if and only if . Also, some properties of these new sequence spaces are investigated.

Quantum phase distribution and the number-phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states：solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.

Properties of Some Kind of Number Theoretical Function(Ⅱ)

For any given positive integer n ≥ 1, the Euler function φ（n） is defined to be the number of positive integers not exceeding n, which is relatively prime to n. o：（n） is defined to be the number of different prime divisors of n. In order to know the solvability of the function of φ（φ（φ（n））） = 2^ω（n）, properties of the number theoretical function φ（φ（n）） is studied in the paper.

IS THE“DEGREE OF AGGREGATION”A FUNCTION OF THE AVERAGE AGGREGATE NUMBER,OR OF THE NUMBER OF AGGREGATES,OR BOTH?

Measurement of the average aggregate number of coaggregates(N_co)and evaluation Of the number of coaggregates([CoAg])in the region of increasing degree of aggregation shows that only N_co increases linearly with the concentration of the target molecules CE-In and BL-ol.

Travelling Waves: Interplay of Low to High Reynolds Number and Tan-Cot Function Method to Solve Burger’s Equations

We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.

On AP-Henstock Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.

Describing Fuzzy Membership Function and Detecting the Outlier by Using Five Number Summary of Data

One of the most important activities in data science is defining a membership function in fuzzy system. Although there are few ways to describe membership function like artificial neural networks, genetic algorithms etc.;they are very complex and time consuming. On the other hand, the presence of outlier in a data set produces deceptive results in the modeling. So it is important to detect and eliminate them to prevent their negative effect on the modeling. This paper describes a new and simple way of constructing fuzzy membership function by using five-number summary of a data set. Five states membership function can be created in this new method. At the same time, if there is any outlier in the data set, it can be detected with the help of this method. Usually box plot is used to identify the outliers of a data set. So along with the new approach, the box plot has also been drawn so that it is understood that the results obtained in the new method are accurate. Several real life examples and their analysis have been discussed with graph to demonstrate the potential of the proposed method. The results obtained show that the proposed method has given good results. In the case of outlier, the proposed method and the box plot method have shown similar results. Primary advantage of this new procedure is that it is not as expensive as neural networks, and genetic algorithms.

On Henstock-Stieltjes Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.

Physical Properties of the Function and Number of Empirical Macrohardness of the Material: Universal Physical Unit of Measurement of Macro Hardness (Part 2)

Results of analytical studies of the physical properties of the function and number of empirical macrohardness based on the standard experimental force diagram of kinetic macroindentation by a sphere.An analytical comparison method and a criterion for the similarity of the physical and empirical macrohardness of a material are proposed.The physical properties of the hardness measurement process using the Calvert-Johnson method are shown.The physical reasons for the size effect when measuring macrohardness are considered.The universal physical unit and standard of macrohardness of kinetic macroindentation by a sphere is substantiated.

A Number Theoretic Function and Its Mean Value Computation

Let p be a prime, n be any positiv e integer, α(n,p) denotes the power of p in the factorization of n! . In this paper, we give an exact computing formula of the mean value ∑ n<Nα(n,p).

Lower Bounds on the Majority Domination Number of Graphs

Let G=(V,E) be a simple graph. For any real valued function f∶V→R and SV, let f(S)=∑ u∈S?f(u). A majority dominating function is a function f∶V→{-1,1} such that f(N)≥1 for at least half the vertices v∈V. Then majority domination number of a graph G is γ maj(G)=min{f(V)|f is a majority dominating function on G}. We obtain lower bounds on this parameter and generalize some results of Henning.

Scan of the endogenous retrovirus sequences across the swine genome and survey of their copy number variation and sequence diversity among various Chinese and Western pig breeds

In pig-to-human xenotransplantation,the transmission risk of porcine endogenous retroviruses(PERVs)is of great concern.However,the distribution of PERVs in pig genomes,their genetic variation among Eurasian pigs,and their evolutionary history remain unclear.We scanned PERVs in the current pig reference genome(assembly Build 11.1),and identified 36 long complete or near-complete PERVs(lc PERVs)and 23 short incomplete PERVs(si PERVs).Besides three known PERVs(PERV-A,-B,and-C),four novel types(PERV-JX1,-JX2,-JX3,and-JX4)were detected in this study.According to evolutionary analyses,the newly discovered PERVs were more ancient,and PERV-Bs probably experienced a bottleneck~0.5 million years ago(Ma).By analyzing63 high-quality porcine whole-genome resequencing data,we found that the PERV copy numbers in Chinese pigs were lower(32.0±4.0)than in Western pigs(49.1±6.5).Additionally,the PERV sequence diversity was lower in Chinese pigs than in Western pigs.Regarding the lc PERV copy numbers,PERV-A and-JX2 in Western pigs were higher than in Chinese pigs.Notably,Bama Xiang(BMX)pigs had the lowest PERV copy number(27.8±5.1),and a BMX individual had no PERV-C and the lowest PERV copy number(23),suggesting that BMX pigs were more suitable for screening and/or modification as xenograft donors.Furthermore,we identified 451 PERV transposon insertion polymorphisms(TIPs),of which 86 were shared by all 10 Chinese and Western pig breeds.Our findings provide systematic insights into the genomic distribution,variation,evolution,and possible biological function of PERVs.

Signed total domatic number of a graph

Let G = （V, E） be a graph, and let f ： V →{-1, 1} be a two-valued function. If ∑x∈N（v） f（x） ≥ 1 for each v ∈ V, where N（v） is the open neighborhood of v, then f is a signed total dominating function on G. A set {fl, f2,… fd} of signed d total dominating functions on G with the property that ∑i=1^d fi（x） ≤ 1 for each x ∈ V, is called a signed total dominating family （of functions） on G. The maximum number of functions in a signed total dominating family on G is the signed total domatic number on G, denoted by dt^s（G）. The properties of the signed total domatic number dt^s（G） are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs.

Lychrel Numbers in Base 10: A Probabilistic Approach

For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical extraction of new Lychrel numbers from existing ones. This probabilistic approach has the advantage of being extendable to other bases. The results show that palindromes can also be Lychrel numbers.

Roman Domination Number and Domination Number of a Tree

A Roman dominating function on a graph G = （V, E） is a function f ： V→{0, 1, 2} satisfying the condition that every vertex u for which f（u） = 0 is adjacent to at least one vertex v for which f（v） = 2. The weight of a Roman dominating function is the value f（V） = Σu∈Vf（u）. The minimum weight of a Roman dominating function on a graph G, denoted by γR（G）, is called the Roman dominating number of G. In this paper, we will characterize a tree T with γR（T） = γ（T） ＋ 3.

The Signed Domination Number of Cartesian Product of Two Paths

Let G be a finite connected simple graph with vertex set V(G) and edge set E(G). A function f:V(G) → {1,1} is a signed dominating function if for every vertex v∈V(G), the closed neighborhood of v contains more vertices with function values 1 than with &#8722;1. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. In this paper, we calculate The signed domination numbers of the Cartesian product of two paths Pm and Pn for m = 3, 4, 5 and arbitrary n.

SOME CLASSES OF DIFFERENCE SEQUENCES OF FUZZY NUMBERS DEFINED BY A SEQUENCE OF MODULI

In this article, we introduce and examine some properties of new difference sequence spaces of fuzzy numbers defined using a sequence of modulus functions.

Special Numbers on Analytic Functions

The aim of this paper is to give some analytic functions which are related to the generating functions for the central factorial numbers. By using these functions and p-adic Volkenborn integral, we derive many new identities associated with the Bernoulli and Euler numbers, the central factorial numbers and the Stirling numbers. We also give some remarks and comments on these analytic functions, which are related to the generating functions for the special numbers.