Covering-Based Variable Precision $(\mathcal {I},\mathcal {T})$-Fuzzy Rough Sets With Applications to Multiattribute Decision-Making

Jiang, Haibo; Zhan, Jianming; Chen, Degang

doi:10.1109/tfuzz.2018.2883023

Cited by 141 publications

(53 citation statements)

References 54 publications

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“…Our results can also be applied to other algebraic structures, such as an (α, β)-US hemiring, an (α, β)-US topology, (α, β)-US B-algebras, (α, β)-US KUS-algebras, (α, β)-US Vector algebras, and (α, β)-US lattices, and can be applied to other branches of pure mathematics. In addition, the recent development of fuzzy soft-covering-based [19,21,51] problems and β-covering-based rough fuzzy covering [23,52,53] problems have a huge scope of application to develop fuzzy soft covering BCK/BCI-algebras, fuzzy soft β-covering-based rough fuzzy BCK/BCI-algebras, as well as the construction of other fuzzy covering algebras.…”

Section: Discussionmentioning

confidence: 99%

On (α,β)-US Sets in BCK/BCI-Algebras

Jana

Pal

2019

Mathematics

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Molodtsov originated soft set theory, which followed a general mathematical framework for handling uncertainties, in which we encounter the data by affixing the parameterized factor during the information analysis. The aim of this paper is to establish a bridge to connect a soft set and the union operations on sets, then applying it to BCK/BCI-algebras. Firstly, we introduce the notion of the (α, β)-Union-Soft ((α, β)-US) set, with some supporting examples. Then, we discuss the soft BCK/BCI-algebras, which are called (α, β)-US algebras, (α, β)-US ideals, (α, β)-US closed ideals, and (α, β)-US commutative ideals. In particular, some related properties and relationships of the above algebraic structures are investigated. We also provide the condition of an (α, β)-US ideal to be an (α, β)-US closed ideal. Some conditions for a Union-Soft (US) ideal to be a US commutative ideal are given by means of (α, β)-unions. Moreover, several characterization theorems of (closed) US ideals and US commutative ideals are given in terms of (α, β)-unions. Finally, the extension property for an (α, β)-US commutative ideal is established.Mathematics 2019, 7, 252 2 of 18 (M, N)-SI-h-quasi-ideals in the environment of hemirings. At the same time, different soft algebraic structures have been developed on BCK/BCI-algebras, which was proposed by Imai and Iśeki [27,28]. Here, we briefly review some results of soft sets in the existing literature of BCK/BCI-algebras. Jana et al. [29][30][31], Ma and Zhan [32][33][34], and Senapati et al. [35,36] performed detailed investigations on BCK/BCI-algebras and related algebraic systems. In [37], Jun first constructed soft algebraic structure of BCK/BCI-algebras. Jun and Park [38] also pointed out applications of soft sets in the ideal theory of BCK/BCI-algebras. Jun et al. [39] also studied the soft p-ideal of soft BCI-algebras. Acar and Özürk [40] analytically studied maximal, irreducible, and prime soft ideals of BCK/BCI-algebras with supporting examples. First, Jun et al. [41,42] proposed a novel concept, namely union-soft sets and int-soft sets, and then implemented it to develop union-soft BCK/BCI-algebras and int-soft BCK/BCI-algebras. Sezgin [43] considered studying soft union interior ideals, quasi-ideals, and generalized bi-ideals of rings and gave their interrelationship. She also studied regular, intra-regular, regular-duo, and strongly-regular properties of rings in terms of soft-union ideals. Sezgin et al. [44] introduced a new soft classical ring theory, namely soft intersection rings, ideals, bi-ideals, interior ideals, and quasi-ideals. Furthermore, they defined their soft-union intersection product and their corresponding relationships. Jana and Pal [45] defined the concept of (α, β)-soft intersection sets and then introduced this ideal to develop (α, β)-soft intersectional groups structures and their various properties. Jana and Pal [46] also motivated using the same concept for the development of (α, β)-soft intersectional BCK/BCI algebraic structures. Again, Jana et al. [47] pr...

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Section: Discussionmentioning

confidence: 99%

On (α,β)-US Sets in BCK/BCI-Algebras

Jana

Pal

2019

Mathematics

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“…The method is in line with the purpose of this study to explore high-performance IC combination methods and make effective IC combination decision. This method has been widely applied to areas such as knowledge discovery, feature selection, data analysis, granular computing and pattern recognition [50], [51] However, only a few studies have utilised the method in economic management and IC management [52].…”

Section: A the Rough Set Methodsmentioning

confidence: 99%

How Intellectual Capital Combination Method Can Improve Corporate Performance in China’s Information Technology Industry

et al. 2020

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This study aims to illustrate how intellectual capital (IC) dimensions can improve corporate performance, and explore ideal IC combination methods in diversified firm situations to distribute IC dimensions effectively with limited resources. A universal theoretical framework based on Balanced Scorecard (BSC) theory is proposed to illustrate the way in which IC dimensions can enhance corporate performance from the perspective of stakeholders. Then, the rough set method is introduced to empirically explore ideal IC combination methods in diversified situations using 539 valid samples from China's information technology industry. The theoretical analysis shows that IC dimensions work as a combination rather than as isolated parts to affect corporate performance, and different levels of corporate performance can be achieved by different IC combination methods under diverse firm factors. Ideal IC combination method is obtained through empirical study. Relational capital is the most important IC dimension, whereas leverage is the most important influence factor. This study extends IC management theory by profoundly illustrating the internal logical between IC dimensions and corporate performance through the theoretical framework. Additionally, this study introduces the rough set method to IC empirical research to explore ideal IC combination methods. Findings will deepen insight of practitioners about the essence of IC dimension combinations to corporate performance, and how they can apply the IC combination results to effectively distribute IC resources in diversified firm situations. The theoretical and practical research of this study extends both the third and fourth stages of IC research. INDEX TERMS Intellectual capital (IC), IC combination method, balance scorecard (BSC), IC dimension and corporate performance theoretical framework, the rough set method.

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“…There has been fast-growing interest in this new emerging theory. The successful applications of rough set models in a variety of problems have their usefulness and versatility (Ma et al 2017;Pawlak 1991;Zhan et al 2017a, b;Zhan and Zhu 2017;Jiang et al 2018;Ma et al 2018;Zhang et al 2019;Zhan and Xu 2018;Zhan and Wang 2018;Zhan and Alcantud 2018a, b).…”

Section: Introductionmentioning

confidence: 99%

Rough approximation of a fuzzy set in semigroups based on soft relations

Kanwal

Shabir

2019

Comp. Appl. Math.

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Binary relations play an important role in both mathematics and information sciences. In this paper, we focus our discussion on a fuzzy set which is approximated in the sense of the aftersets and foresets. To this end, a soft binary relation has been used. A new approach is being introduced to get two sets of fuzzy soft sets, called the lower approximation and upper approximation regarding the aftersets and foresets. We applied these concepts on semigroups and approximations of fuzzy subsemigroups, fuzzy left (right) ideals, fuzzy interior ideals and fuzzy bi-ideals of semigroups are studied.

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Covering-Based Variable Precision $(\mathcal {I},\mathcal {T})$-Fuzzy Rough Sets With Applications to Multiattribute Decision-Making

Cited by 141 publications

References 54 publications

On (α,β)-US Sets in BCK/BCI-Algebras

On (α,β)-US Sets in BCK/BCI-Algebras

How Intellectual Capital Combination Method Can Improve Corporate Performance in China’s Information Technology Industry

Rough approximation of a fuzzy set in semigroups based on soft relations

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