Multiple Definite Integrals of Intuitionistic Fuzzy Calculus and Isomorphic Mappings

Ai, Zhenghai; Zhang, Xu

doi:10.1109/tfuzz.2017.2687885

Cited by 20 publications

(19 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More recently, the scholars have investigated a series of fundamental properties with respect to the intuitionistic fuzzy calculus (IFC) [16][17][18][19][20][21][22]; the key characteristic of the IFC is that it is based on the basic operational laws of intuitionistic fuzzy numbers (IFNs). With these operational laws, Lei and Xu [16] introduced the limits, the derivatives, and the differentials in intuitionistic fuzzy circumstance and gave their basic properties.…”

Section: Introductionmentioning

confidence: 99%

“…Later on, the completeness of intuitionistic fuzzy partially ordered set [18] was discussed. As for the definite integrals in the IFC, the scholars constructed several kinds of definite integrals [19][20][21][22] from different points of view. Nevertheless, interval-valued IFC (IVIFC), which is based on the operational laws of the interval-valued IFNs (IVIFNs), is only in the original stage.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Foundation of Interval‐Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data

Shu

Zhang

2019

Complexity

Self Cite

View full text Add to dashboard Cite

The intuitionistic fuzzy calculus (IFC), based on the basic operational laws of intuitionistic fuzzy numbers (IFNs), has been put forward. However, the interval-valued IFC (IVIFC), based on the basic operational laws of interval-valued IFNs (IVIFNs), is only in the original stage. To further develop the theory of the IVIFC and make it be rigorous, the primary task is to systematically investigate the characteristics of the limits and differentials, which is a foundation of the IVIFC. Moreover, there is quite a lot of literature on IVIFNs; however, the scholars did not reveal the relationships between IFNs and the IVIFNs. To do that, we first investigate the limit of interval-valued intuitionistic fuzzy sequences, and then, we focus on investigating the limit, the continuity, and the differential of IVIFFs in detail and reveal their relationships. After that, due to the fact that the IFC and the IVIFC are based on the basic operational laws of IFNs and IVIFNs, respectively, we reveal the relationships between the IFNs and the IVIFNs via some homomorphic mappings. Finally, a case study about continuous data of IVIFNs is provided to illustrate the advantages of continuous data.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Foundation of Interval‐Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data

Shu

Zhang

2019

Complexity

Self Cite

View full text Add to dashboard Cite

show abstract

“…Otay et al [22] studied the multi-expert performance evaluation of healthcare institutions with intuitionistic fuzzy Analytic Hierarchy Process (AHP) and Data Envelopment Analysis (DEA) methodology. Ai and Xu [23] proposed the multiple definite integrals of intuitionistic fuzzy calculus and isomorphic mappings. Montes et al [24] defined the entropy measures for IFNs based on divergence.…”

Section: Introductionmentioning

confidence: 99%

Methods for Multiple Attribute Group Decision Making Based on Intuitionistic Fuzzy Dombi Hamy Mean Operators

2018

View full text Add to dashboard Cite

In this paper, we extended the Hamy mean (HM) operator, the Dombi Hamy mean (DHM) operator, the Dombi dual Hamy mean (DDHM), with the intuitionistic fuzzy numbers (IFNs) to propose the intuitionistic fuzzy Dombi Hamy mean (IFDHM) operator, intuitionistic fuzzy weighted Dombi Hamy mean (IFWDHM) operator, intuitionistic fuzzy Dombi dual Hamy mean (IFDDHM) operator, and intuitionistic fuzzy weighted Dombi dual Hamy mean (IFWDDHM) operator. Following this, the multiple attribute group decision-making (MAGDM) methods are proposed with these operators. To conclude, we utilized an applicable example for the selection of a car supplier to prove the proposed methods.

show abstract

“…This study provides important theoretical support for the development of an intuitionistic fuzzy limit theory that provides a necessary condition for the integrality and maturity of IFC. On the basis of which, many researchers have proposed the intuitionistic fuzzy infinite and finite integrals, the multiple definite integrals of IFFs, 20 some properties of intuitionistic fuzzy integrals, and the unification theory of subtraction and division derivatives of IFFs. 21 The above study improves and enriches the IFC theory.…”

mentioning

confidence: 99%

“…Then we get 1283 valid random samples. Afterward, on the basis of these samples, we obtain values of q-ROSVFF changes by Equations (19) and (20) when the increment is α Δ = (0.05, 0.95). To describe the veracity of differential approximate calculation formula more intuitively, we compute the distances f Δ −…”

mentioning

confidence: 99%

Single variable differential calculus under q ‐rung orthopair fuzzy environment: Limit, derivative, chain rules, and its application

Zhang

2019

Int J Intell Syst

Self Cite

View full text Add to dashboard Cite

The q‐rung orthopair fuzzy set ( q‐ROFS) that the sum of the qth power of the membership degree and the qth power of the nonmembership degree is restricted to one is a generalization of fuzzy set (FS). Recently, many researchers have given a series of aggregation operators to fuse q‐rung orthopair fuzzy discrete information. Subsequently, although some scholars have also focused on studying q‐rung orthopair fuzzy continuous information and give its continuity, derivative, differential, and integral, those studies are only considered from the perspective of multivariable fuzzy functions. Thus, the main aim of the paper is to study the q‐rung orthopair fuzzy continuous single variable information. In this paper, we first define the concept of q‐rung orthopair single variable fuzzy function ( q‐ROSVFF) to describe the fuzzy continuous information, and give its domain to make sure that this kind of function is meaningful. Afterward, we propose the limits, continuities, and infinitesimal of q‐ROSVFFs, and offer the relationship between the limit of q‐ROSVFF and that of q‐ROSVFF infinitesimal. On the basis of the definition of derivative in mathematical analysis, we define the subtraction and division derivatives and basic operational rules, and offer the simpler proofs for the derivatives of q‐ROSVFFs. What is more, we propose the subtraction and division differential invariances, and give the approximate calculation formulas of q‐ROSVFFs when the value of independent variable is changed small enough. In the real situation, fundamental functions cannot be used to express more complicated functions, thus we define the compound q‐ROSVFFs and give their chain rules of subtraction and division derivatives. Finally, we use numerical examples by simulation to verify the feasibility and veracity of the approximate calculation on q‐ROSVFFs.

show abstract

Multiple Definite Integrals of Intuitionistic Fuzzy Calculus and Isomorphic Mappings

Cited by 20 publications

References 23 publications

Foundation of Interval‐Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data

Foundation of Interval‐Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data

Methods for Multiple Attribute Group Decision Making Based on Intuitionistic Fuzzy Dombi Hamy Mean Operators

Single variable differential calculus under q ‐rung orthopair fuzzy environment: Limit, derivative, chain rules, and its application

Contact Info

Product

Resources

About