The Calculation and Estimate of Interval-Valued and Fuzzy Dirichlet Series Coefficient

2013 ◽  
Vol 325-326 ◽  
pp. 1515-1518
Author(s):  
Yu Duan ◽  
Hong Jian Luo
Keyword(s):  
Dirichlet Series ◽  
Series Coefficient ◽  
Definition Of ◽  
Interval Valued

This article gives the definition of interval-valued Dirichlet series. Based on [1, , this article discusses some properties about the coefficient of interval-valued and fuzzy Dirichlet series. Ihe calculation of coefficient , of interval-valued Dirichlet series and the coefficient of fuzzy Dirichelt series are also discussed. Moreover, some relative theorems and properties are presented.

Generalized interval-valued hesitant intuitionistic fuzzy soft sets

2021 ◽  
pp. 1-12
Author(s):  
Admi Nazra ◽  
Yudiantri Asdi ◽  
Sisri Wahyuni ◽  
Hafizah Ramadhani ◽  
Zulvera
Keyword(s):  
Hesitant Fuzzy Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Binary Operations ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Soft Sets ◽  
Comparison Table ◽  
Definition Of ◽  
Interval Valued ◽  
Intuitionistic Fuzzy Soft Sets

This paper aims to extend the Interval-valued Intuitionistic Hesitant Fuzzy Set to a Generalized Interval-valued Hesitant Intuitionistic Fuzzy Soft Set (GIVHIFSS). Definition of a GIVHIFSS and some of their operations are defined, and some of their properties are studied. In these GIVHIFSSs, the authors have defined complement, null, and absolute. Soft binary operations like operations union, intersection, a subset are also defined. Here is also verified De Morgan’s laws and the algebraic structure of GIVHIFSSs. Finally, by using the comparison table, a different approach to GIVHIFSS based decision-making is presented.

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

Cancellation in algebraic twisted sums on GL_ m

2021 ◽  
Vol 33 (4) ◽  
pp. 1061-1082
Author(s):  
Yujiao Jiang ◽  
Guangshi Lü
Keyword(s):  
Dirichlet Series ◽  
Central Character ◽  
Multiplicative Functions ◽  
Cuspidal Representation ◽  
Series Coefficient

Abstract Let π be an automorphic irreducible cuspidal representation of GL m {\operatorname{GL}_{m}} over ℚ {\mathbb{Q}} with unitary central character, and let λ π ⁢ ( n ) {\lambda_{\pi}(n)} be its n-th Dirichlet series coefficient. We study short sums of isotypic trace functions associated to some sheaves modulo primes q of bounded conductor, twisted by multiplicative functions λ π ⁢ ( n ) {\lambda_{\pi}(n)} and μ ⁢ ( n ) ⁢ λ π ⁢ ( n ) {\mu(n)\lambda_{\pi}(n)} . We are able to establish non-trivial bounds for these algebraic twisted sums with intervals of length of at least q 1 / 2 + ε {q^{1/2+\varepsilon}} for an arbitrary fixed ε > 0 {\varepsilon>0} .

scholarly journals Some Inequalities for LR-$$\left({h}_{1}, {h}_{2}\right)$$-Convex Interval-Valued Functions by Means of Pseudo Order Relation

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Muhammad Bilal Khan ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Kottakkaran Sooppy Nisar ◽  
Khadiga Ahmed Ismail ◽  
...  
Keyword(s):  
Applied Mathematics ◽  
Critical Role ◽  
Order Relation ◽  
Strong Relationship ◽  
New Class ◽  
Starting Point ◽  
Interval Valued Function ◽  
Fejér Inequality ◽  
Definition Of ◽  
Interval Valued

AbstractIn both theoretical and applied mathematics fields, integral inequalities play a critical role. Due to the behavior of the definition of convexity, both concepts convexity and integral inequality depend on each other. Therefore, the relationship between convexity and symmetry is strong. Whichever one we work on, we introduced the new class of generalized convex function is known as LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -convex interval-valued function (LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -IVF) by means of pseudo order relation. Then, we established its strong relationship between Hermite–Hadamard inequality (HH-inequality)) and their variant forms. Besides, we derive the Hermite–Hadamard–Fejér inequality (HH–Fejér inequality)) for LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -convex interval-valued functions. Several exceptional cases are also obtained which can be viewed as its applications of this new concept of convexity. Useful examples are given that verify the validity of the theory established in this research. This paper’s concepts and techniques may be the starting point for further research in this field.

Semiring of Generalized Interval-Valued Intuitionistic Fuzzy Matrices

2017 ◽  
pp. 132-152
Author(s):  
Debashree Manna
Keyword(s):  
Vector Space ◽  
Distributive Lattice ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Algebra ◽  
Definition Of ◽  
Interval Valued

In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over [0, 1]. Some properties of GIVIFMs are studied using the definition of comparability of GIVIFMs.

scholarly journals GRANULAR-INFORMATION-BASED RISK ANALYSIS IN UNCERTAIN SITUATIONS

2006 ◽  
Vol 1 ◽  
pp. 385
Author(s):  
A. Vališevskis
Keyword(s):  
Negative Impact ◽  
Real Life ◽  
Problem Area ◽  
Environmental Risks ◽  
Probabilistic Information ◽  
Future Events ◽  
Definition Of ◽  
Almost All ◽  
Measure Of Uncertainty ◽  
Interval Valued

In the real life almost all of the decisions that we have to make incorporate uncertainty about the future events. Assessment of the uncertainty and, thus, the risk that is inherent in these decisions models can be critical. It is even truer if we are talking about the possibility of negative impact on the environment. It is very important to assess all the environmental risks in a project if there is any hazard to the environment. In this paper the possibility of using granular information is considered. The main advantage of the granular information is that it can be used to assess risks in situations when information about future events is incomplete and imprecise. Moreover, we can use natural language to describe the problem area, as granular information paradigm uses both fuzzy and probabilistic information. We propose to use entropy as the measure of uncertainty. However, the definition of entropy should be generalised, as values of probabilities, upon which the calculation of entropy is based on, are interval-valued. We propose several possibilities of generalizing the definition of entropy. Furthermore, we analyse these approaches to see whether the additivity feature holds for the generalized entropy.

scholarly journals Translation, modulation and dilation systems in set-valued signal processing

2018 ◽  
Vol 10 (1) ◽  
pp. 143-164 ◽  
Author(s):  
H. Levent ◽  
Y. Yilmaz
Keyword(s):  
Signal Processing ◽  
Linear Space ◽  
Algebraic Structure ◽  
Compact Convex ◽  
Inner Product ◽  
Complex Numbers ◽  
Real Numbers ◽  
Aumann Integral ◽  
Definition Of ◽  
Interval Valued

In this paper, we investigate a very important function space consists of set-valued functions defined on the set of real numbers with values on the space of all compact-convex subsets of complex numbers for which the $p$th power of their norm is integrable. In general, this space is denoted by $L^{p}% (\mathbb{R},\Omega(\mathbb{C}))$ for $1\leq p<\infty$ and it has an algebraic structure named as a quasilinear space which is a generalization of a classical linear space. Further, we introduce an inner-product (set-valued inner product) on $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$ and we think it is especially important to manage interval-valued data and interval-based signal processing. This also can be used in imprecise expectations. The definition of inner-product on $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$ is based on Aumann integral which is ready for use integration of set-valued functions and we show that the space $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$ is a Hilbert quasilinear space. Finally, we give translation, modulation and dilation operators which are three fundational set-valued operators on Hilbert quasilinear space $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$.

scholarly journals Multiple attribute group decision-making based on interval-valued q-rung orthopair uncertain linguistic power Muirhead mean operators and linguistic scale functions

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258772
Author(s):  
Yuan Xu ◽  
Shifeng Liu ◽  
Jun Wang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Comparison Method ◽  
Model Framework ◽  
Scale Functions ◽  
Multiple Attribute ◽  
Definition Of ◽  
Magdm Problems ◽  
Interval Valued

Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. Based on the previous studies, to find a better solution for fusing qualitative quantization information with fuzzy numbers, we propose a novel definition of interval-valued q-rung orthopair uncertain linguistic sets (IVq-ROULSs) based on the linguistic scale functions, as well as its corresponding properties, such as operational rules and the comparison method. Furthermore, we utilize the power Muirhead mean operators to construct the information fusion method, and provide a variety of aggregation operators based on the proposed information description environment. A model framework is constructed for solving the MAGDM problem utilizing the proposed method. Finally, we illustrate the performance of the new method and investigate its advantages and superiorities through comparative analysis.

A Novel Entropy Measure for Interval-Valued Intuitionistic Fuzzy Set and Its Application to Failure Mode and Effect Analysis

2021 ◽  
pp. 115-134
Author(s):  
Kamal Kumar ◽  
Naveen Mani ◽  
Amit Sharma ◽  
Reeta Bhardwaj
Keyword(s):  
Failure Mode ◽  
Fuzzy Set ◽  
Failure Modes ◽  
Intuitionistic Fuzzy Set ◽  
Entropy Measure ◽  
Effect Analysis ◽  
Intuitionistic Fuzzy ◽  
Safety And Reliability ◽  
Definition Of ◽  
Interval Valued

The failure mode and effect analysis (FMEA) is widely used an effective pre-accident risk assessment tool to identify, eliminate, and assess potential failure modes in different industries for enhancing the safety and reliability of systems, process, services, and products. Therefore, this chapter presents a new approach to rank the failure modes under the interval-valued intuitionistic fuzzy set (IVIFS). For this, a novel measure to measure the fuzziness known as entropy measure is proposed. Some properties and axiom definition of the proposed entropy measure have been presented to show the validity of it. Afterwards, the proposed entropy measure is utilized to obtain the weight of risk factor and developed an approach under the IVIFS environment to determine the risk priority order of failure modes. Finally, a real-life case of FMEA has been discussed to manifest the developed approach, and obtained results are compared with the results obtained by the existing methods for showing the feasibility and validity of the proposed approach.

A constructive method for the definition of interval-valued fuzzy implication operators

2005 ◽  
Vol 153 (2) ◽  
pp. 211-227 ◽  
Author(s):  
C. Alcalde ◽  
A. Burusco ◽  
R. Fuentes-González
Keyword(s):  
Constructive Method ◽  
Fuzzy Implication ◽  
Definition Of ◽  
Interval Valued
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