Novel decision-making algorithms based on intuitionistic fuzzy rough environment

Zhan, Jianming; Malik, Hafsa Masood; Akram, Muhammad

doi:10.1007/s13042-018-0827-4

Cited by 73 publications

(17 citation statements)

References 48 publications

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“…After that, Lei et al 19‐21 researched the indefinite integral, definite integral, chain rule, substitution rule, and so forth, in IFC, and construct the whole system of IFC. And for IF rough sets, Zhan et al 22 combined IFS and rough sets, introduced the intuitionistic fuzzy rough graphs, and developed efficient algorithms to solve decision‐making problems and compute time complexity of each algorithm. Also, Zhan and Sun 23 applied covering‐based intuitionistic fuzzy rough sets (CIFRS) models to MADM problem with evaluation of IF information.…”

Section: Introductionmentioning

confidence: 99%

Basic theory of line integrals under the q‐rung orthopair fuzzy environment and their applications

Shao

Zhuo

2020

Int J Intell Syst

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In the process of decision making (DM), to have more freedom in expressing DM experts' belief about membership and nonmembership grade, Yager presented the q-rung orthopair fuzzy sets (q-ROFSs) as an extension of fuzzy sets. Recently, for aggregating discrete and continuous q-ROF information, many scholars provided various aggregation operators.However, there are still some kinds of continuous q-ROF information cannot be aggregated through existing aggregation operators. In this paper, we present two novel kinds of line integrals under the q-rung orthopair fuzzy environment (q-ROFE), which supply a wider range on method choice for multiple attribute decision making (MADM) concerning discrete or continuous q-ROF information.We first construct the first form of line integral under the q-ROFE and study their properties, we prove the specific condition mean valued theorem but negate the general condition for it. Besides, several inequalities with regard to it are also provided. After that, we give two characterization forms of the second form of line integral under the q-ROFE, we study the relationship between two kinds of line integrals. What is more important, we show the Green formula under q-ROFE, which connect the existing q-rung orthopair fuzzy integration theory. Afterward, we provide two kinds of aggregation operators on the basis of two line integrals, respectively. As their applications, we give two novel MADM methods based on two kinds of line integral aggregation operators.And some examples are shown to demonstrate the aggregation process of line integral operators. We not only stress their availabilities and superiorities on aggregating continuous q-ROF information, but also comparing with other existing aggregation methods for emphasizing the novel methods' abilities when deal with abnormal q-ROF information. K E Y W O R D S multiple attribute decision making, nonstandard fuzzy set, q-rung orthopair fuzzy aggregation operator, q-rung orthopair fuzzy line integral | 1197 How to cite this article: Shao Y, Zhuo J. Basic theory of line integrals under the q-rung orthopair fuzzy environment and their applications.

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Section: Introductionmentioning

confidence: 99%

Basic theory of line integrals under the q‐rung orthopair fuzzy environment and their applications

Shao

Zhuo

2020

Int J Intell Syst

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“…The relation is an equivalent in Pawlak's rough set. After that, many researchers proposed other types of rough set theory (see the work by the following authors [1][2][3][4][5][6][7][8]).…”

Section: Introductionmentioning

confidence: 99%

Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications

Zhang

Shao

et al. 2018

Symmetry

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It is an interesting direction to study rough sets from a multi-granularity perspective. In rough set theory, the multi-particle structure was represented by a binary relation. This paper considers a new neutrosophic rough set model, multi-granulation neutrosophic rough set (MGNRS). First, the concept of MGNRS on a single domain and dual domains was proposed. Then, their properties and operators were considered. We obtained that MGNRS on dual domains will degenerate into MGNRS on a single domain when the two domains are the same. Finally, a kind of special multi-criteria group decision making (MCGDM) problem was solved based on MGNRS on dual domains, and an example was given to show its feasibility.

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“…Obviously, a bipolar neutrosophic graph structure can deal with more than one factors involved for particular type of relationship between any two vertices, which is properly explained in this research paper with some interesting real-life applications. For other notations, terminologies and applications are not mentioned in this research article; the readers are referred to Alcantud (2016), Ali et al (2016), Dinesh (2011), Greco and Kadzinski (2018), Luo et al (2018), Majumdar and Samanta (2014), Mordeson and Nair (2001), Myithili et al (2016), Pramanik et al (2016), Sayed et al (2018), Smarandache (1999), Turksen (1986), Wu et al (2017) and Zhan et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Novel decision-making method based on bipolar neutrosophic information

2018

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Novel decision-making algorithms based on intuitionistic fuzzy rough environment

Cited by 73 publications

References 48 publications

Basic theory of line integrals under the q‐rung orthopair fuzzy environment and their applications

Basic theory of line integrals under the q‐rung orthopair fuzzy environment and their applications

Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications

Novel decision-making method based on bipolar neutrosophic information

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