Rough approximations based on soft binary relations and knowledge bases

Multigranulation rough set (MGRS) based on soft relations is a very useful technique to describe the objectives of problem solving. This MGRS over two universes provides the combination of multiple granulation knowledge in a multigranulation space. This paper extends the concept of fuzzy set Shabir and Jamal in terms of an intuitionistic fuzzy set (IFS) based on multi-soft binary relations. This paper presents the multigranulation roughness of an IFS based on two soft relations over two universes with respect to the aftersets and foresets. As a result, two sets of IF soft sets with respect to the aftersets and foresets are obtained. These resulting sets are called lower approximations and upper approximations with respect to the aftersets and with respect to the foresets. Some properties of this model are studied. In a similar way, we approximate an IFS based on multi-soft relations and discuss their some algebraic properties. Finally, a decision-making algorithm has been presented with a suitable example.

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“…Li et al [69] presented the generalization of the soft binary relation over U 1 to U 2 , as follows.…”

Section: Definition 3 ([6]mentioning

confidence: 99%

Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision Making

et al. 2021

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“…Since RS theory has been developed, many robust generalizations of RS have been established in various directions. For instance, binary relations [24,25], tolerance relations [26], similarity relations [27], soft binary relations [28,29], soft equivalence relations [30], set valued maps [31], two equivalence relations [32], normal soft group [33], etc. Recently, Shiekh et al [34] proposed the solution of matrix games with rough interval pay-offs and its application in the telecom market share problem.…”

Section: Introductionmentioning

confidence: 99%

Linear Diophantine Fuzzy Rough Sets: A New Rough Set Approach with Decision Making

et al. 2022

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In this article, a new hybrid model named linear Diophantine fuzzy rough set (LDFRS) is proposed to magnify the notion of rough set (RS) and linear Diophantine fuzzy set (LDFS). Concerning the proposed model of LDFRS, it is more efficient to discuss the fuzziness and roughness in terms of linear Diophantine fuzzy approximation spaces (LDFA spaces); it plays a vital role in information analysis, data analysis, and computational intelligence. The concept of (<p,p′>,<q,q′>)-indiscernibility of a linear Diophantine fuzzy relation (LDF relation) is used for the construction of an LDFRS. Certain properties of LDFA spaces are explored and related results are developed. Moreover, a decision-making technique is developed for modeling uncertainties in decision-making (DM) problems and a practical application of fuzziness and roughness of the proposed model is established for medical diagnosis.

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“…To address these issues, tolerance relations, similarity relations, general binary relations, neighborhood systems, and others are used in place of partitions. Feng et al [16] combined SS with FS and RS, the RSS and SRS are investigated in [17][18][19], the rough set approximation based on SBr and knowledge bases was discussed by Li et al [20], Meng et al [21] discussed SRFS and SFRS, Zhang et al [22] presented novel FRS models and corresponding applications to MCDM. Many authors have blended the concepts of FS and RS in various ways, as demonstrated in [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Pessimistic Multigranulation Roughness of a Fuzzy Set Based on Soft Binary Relations over Dual Universes and Its Application

2022

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The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes. Firstly, we approximate fuzzy set w.r.t aftersets and foresets of the finite number of soft binary relations. As a result, we obtained two sets of fuzzy soft sets known as the pessimistic lower approximation of a fuzzy set and the pessimistic upper approximation of a fuzzy set—the w.r.t aftersets and the w.r.t foresets. The pessimistic lower and pessimistic upper approximations of the newly proposed multigranulation rough set model are then investigated for several interesting properties. This article also addresses accuracy measures and measures of roughness. Finally, we give a decision-making algorithm as well as examples from the perspective of application.

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Rough approximations based on soft binary relations and knowledge bases

Cited by 21 publications

References 21 publications

Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision Making

Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision Making

Linear Diophantine Fuzzy Rough Sets: A New Rough Set Approach with Decision Making

Pessimistic Multigranulation Roughness of a Fuzzy Set Based on Soft Binary Relations over Dual Universes and Its Application

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