| รหัสโครงการ : | R000000544 |
| ชื่อโครงการ (ภาษาไทย) : | แบบจำลองการประมาณวางนัยทั่วไปแบบอิงความสัมพันธ์ทวิภาคของเซตซอฟต์ที่ประยุกต์ใช้กับระบบพีชคณิตของกึ่งกรุปและปัญหาการตัดสินใจที่สมนัย |
| ชื่อโครงการ (ภาษาอังกฤษ) : | Binary Relations-Based Generalized Approximation Models of Soft Sets Applied to Algebraic Systems of Semigroups and Corresponding Decision-Making Problems |
| คำสำคัญของโครงการ(Keyword) : | ความสัมพันธ์ทวิภาค, ไอดีล, เซตรัฟ, กึ่งกรุป, ฟังก์ชันสาทิสสัณฐาน, เซตซอฟต์ |
| หน่วยงานเจ้าของโครงการ : | สถาบันวิจัยและพัฒนา |
| ลักษณะโครงการวิจัย : | โครงการวิจัยเดี่ยว |
| ลักษณะย่อยโครงการวิจัย : | ไม่อยู่ภายใต้แผนงานวิจัย/ชุดโครงการวิจัย |
| ประเภทโครงการ : | โครงการวิจัยใหม่ |
| สถานะของโครงการ : | propersal |
| งบประมาณที่เสนอขอ : | 70000 |
| งบประมาณทั้งโครงการ : | 70,000.00 บาท |
| วันเริ่มต้นโครงการ : | 30 พฤศจิกายน 2563 |
| วันสิ้นสุดโครงการ : | 29 พฤศจิกายน 2564 |
| ประเภทของโครงการ : | งานวิจัยพื้นฐาน(ทฤษฎี)/บริสุทธิ์ |
| กลุ่มสาขาวิชาการ : | วิทยาศาสตร์ธรรมชาติ |
| สาขาวิชาการ : | สาขาวิทยาศาสตร์กายภาพและคณิตสาศตร์ |
| กลุ่มวิชาการ : | คณิตศาสตร์ |
| ลักษณะโครงการวิจัย : | ระดับนานาชาติ |
| สะท้อนถึงการใช้ความรู้เชิงอัตลักษณ์ : | สะท้อนถึงการใช้ความรู้เชิงอัตลักษณ์ |
| สร้างความร่วมมือประหว่างประเทศ GMS : | สร้างความร่วมมือทางการวิจัยระหว่างประเทศ |
| นำไปใช้ในการพัฒนาคุณภาพการศึกษา : | นำไปใช้ประโยชน์ในการพัฒนาณภาพการศึกษา |
| เกิดจากความร่วมมือกับภาคการผลิต : | ไม่เกิดจากความร่วมมือกับภาคการผลิต |
| ความสำคัญและที่มาของปัญหา : | In order to solve problems in information science and big data, methods in fundamental mathematics are not always successfully used because incompleteness, granularity, and uncertainty of information and knowledge are typical for these problems. Pawlak’s rough set theory, proposed by Pawlak [1] in 1982, offers an alternative toolset to deal with imprecise, inconsistent, incomplete information and knowledge. Such a mathematical tool has been being used in information system, fuzzy system, decision support system and so on; see [2, 3, 4, 5, 6, 7]. One of the main research problems of Pawlak’s rough set theory is the approximation processing of sets by using equivalence relations in basis. In terms of a Pawlak’s approximation space induced by an equivalence relation, that is, a pair of a non-empty universal set with an equivalence relation, a non-empty subset of the given universe is approximated by the following sets.
The Pawlak’s upper approximation is the union of equivalent classes which have a non-empty intersection with the given non-empty subset (The set of all possibly elements with respect to a property of the given non-empty subset).
The Pawlak’s lower approximation is the union of equivalent classes which are subsets of the given non-empty subset (The set of all certainly elements with respect to a property of the given non-empty subset).
The Pawlak’s boundary region is a difference of the upper approximation and the lower approximation (The set of all uncertain elements with respect to a property of the given non-empty subset).
The Pawlak’s rough set of the given non-empty subset is defned by meaning of a pair of upper and lower approximations, where the difference of upper and lower approximations is a non-empty set. Otherwise, the given non-empty subset is said to be a Pawlak’s defnable set. Because of novel thinking with respect to trend, Pawlak’s rough set theory has been becoming an attractive intelligent information processing tool in the feld of artifcial intelligence. As introduced above, Pawlak’s rough set theory is defned as approximation models of sets. Throughout this proposal, we use AMS to denote the brief text of the approximation model of sets in which AMS is a model consisting of upper and lower approximations, a boundary region, a rough set, and a definable set under an approximation space.
Pawlak’s AMS has possible uses in many algebraic systems, including groups; see [8, 9, 10], semigroups; see [11, 12, 13, 14], BCK-algebras [15], rings; see [16] and [17], modules [18], hemirings [19], quantales [20], LA-semigroups [21] and pseudo-BCI algebras [22]. Most of these utilizations have already been proved in the research of mathematical reasoning systems. One of the interesting aspects is the development of Pawlak’s AMS in semigroups. Because the semigroup [23] is a non-complex algebraic structure and it has been being employed in computer science and data technology, especially in algebraic automata theory and algebraic engineering theory [24], it attracts researchers much more. Patently, work on hybrid notions of Pawlak’s rough set theory and semigroup theory has been progressing continuously. In 1997, Kuroki [11] introduced the notions of upper and lower approximation semigroups (resp. ideals) in semigroups induced by congruence relations, and provided suffcient conditions of upper and lower approximation semigroups (resp. ideals). In 2006, Xiao and Zhang [12] proposed the notions of upper and lower approximation completely prime ideals in semigroups induced by congruence relations, and provided suffcient conditions of upper and lower approximation completely prime ideals. Also, they studied the relationship between upper and lower approximation completely prime ideals (resp. ideals) and the homomorphic image of upper and lower approximation completely prime ideals (resp. ideals) under homomorphism problems.
Binary relations play an important role in both mathematics and information sciences [25]. Then AMS based on an arbitrary binary relation on the single universe is one of the most important extensions of Pawlak’s AMS. This is an effective mathematical tool for dealing with uncertain knowledge and vagueness in data for the single universe; see [26, 27, 28, 29, 30, 31]. Recently, Rukchart and Manoj [32] introduced and studied Rukchart and Manoj’s AMS based on cores of successor classes induced by binary relations between two universal sets in 2019. Such generated class for Rukchart and Manoj’s AMS is defned as follows.
For a binary relation B from the universal set U to the universal set V and u is in U, a successor class of u induced by B is denoted by the set
SB(u) := {v is in V : (u, v) is in B}.
For a binary relation B on a universal set U and u is in U, a core of the successor class of u induced by B is denoted by
CSB(u) := {u is in U : SB(u) = SB(u)}.
Observe that Rukchart and Manoj’s AMS is a generalized AMS of Pawlak’s AMS whenever B is assigned in terms of an equivalence relation.
Molodtsov [33] initiated a novel concept called soft sets as a new mathematical tool for dealing with uncertainties. The soft set theory is free from many diffculties that have troubled the usual theoretical approaches; see [34] and [35]. Theory of soft sets has been successfully applied to decision?making under uncertainty; see [36]. Soft set theory is also closely related to many other soft computing models including rough sets. The notion of rough soft set theory motivated by Dubois and Prade’s [37] original idea about rough fuzzy sets, they consider the lower and upper approximations of a soft set in a Pawlak approximation space based on equivalence relations. Such theory is an interesting AMS for decision-making problems; see [38].
The goal of the research proposal, we shall introduce a generalized AMS of Dubois and Prade’s AMS under an approximation space induced by a binary relation between two universes with respect to the new class in [32]. We shall prove some fundamental algebraic properties for the new AMS. Next, we use such AMS to propose rough soft ideals, rough soft quasi-ideals, rough soft bi-ideals and rough soft prime ideals in semigroups under binary relations, including provide suffcient conditions for them, and give necessary and suffcient conditions for their homomorphic images. At the end, we shall construct the algorithm of a generalized decision-making method associated to soft sets with a corresponding real-world example.
References
[1] Pawlak Z. Rough sets. International Journal of Information and Computer Security. 1982;11:341?-356.
[2] Li J, Mei C, Yuejin L. Incomplete decision contexts: Approximate concept construction, rule acquisition and knowledge reduction. International Journal of Approximate Reasoning. 2013;54(1):149-165.
[3] Yao YY. Interval sets and three-way concept analysis in incomplete contexts. International Journal of Machine Learning and Cybernetics. 2017;8(1):3-20.
[4] Giampiero C, Davide C, Tommaso G, Federico I. Rough set theory and digraphs. Journal of Intelligent and Fuzzy Systems. 2017;159(4):291-325.
[5] Maini T, Kumar A, Misra R. Rough set based feature selection using swarm intelligence with distributed sampled initialisation. Proceedings of the 6th IEEE International Conference on Computer Applications In Electrical Engineering Recent Advances; 2017 Oct 5-7; Roorkee, India. India: IEEE; 2018.
[6] Yu H, Yang G, Lin M, Meng F, Wu Q. Application of rough set theory for NVNA phase reference uncertainty analysis in hybrid information system. Computers and Electrical Engineering. 2018;69:893-906.
[7] Zouache D, Abdelaziz FB. A cooperative swarm intelligence algorithm based on quantum? inspired and rough sets for feature selection. Computers and Industrial Engineering. 2018;115:26-36.
[8] Biswas R, Nanda S. Rough groups and rough subgroups. Bulletin of the Polish Academy Sciences Mathematics.
1994;42:251-254.
[9] Kuroki N, Mordeson JN. Structure |
| จุดเด่นของโครงการ : | - |
| วัตถุประสงค์ของโครงการ : | 1. To introduce the concepts of generalized upper approximations and generalized lower approximations of soft sets by using binary relations between two universal sets, and investigate some interesting properties.
2. To introduce the concepts of rough soft ideals, rough soft quasi-ideals, rough soft bi-ideals and rough soft prime ideals by using binary relations on semigroups, and provide the suffcient conditions of rough soft ideals, rough soft quasi-ideals, rough soft bi-ideals and rough soft prime ideals.
3. To provide the necessary and suffcient conditions of homomorphic images of rough soft ideals, rough soft quasi-ideals, rough soft bi-ideals and rough soft prime ideals.
4. To introduce the concepts of a generalized decision-making method associated to soft sets with a corresponding real-world example.
5. To support research-based learning in Nakhon Sawan Rajabhat University. |
| ขอบเขตของโครงการ : | We research the approximation models of soft sets under binary relations between two universal sets. |
| ผลที่คาดว่าจะได้รับ : | 1. To obtain the concepts of generalized upper approximations and generalized lower approximations of soft sets by using binary relations between two universal sets, and some interesting properties.
2. To obtain the concepts of rough soft ideals, rough soft quasi-ideals, rough soft bi-ideals and rough soft prime ideals by using binary relations on semigroups, and obtain the suffcient conditions of rough soft ideals, rough soft quasi-ideals, rough soft bi-ideals and rough soft prime ideals.
3. To obtain the necessary and suffcient conditions of homomorphic images of rough soft ideals, rough soft quasi-ideals, rough soft bi-ideals and rough soft prime ideals.
4. To obtain the concepts of a generalized decision-making method associated to soft sets with a corresponding real-world example.
5. To obtain research-based learning in Nakhon Sawan Rajabhat University. |
| การทบทวนวรรณกรรม/สารสนเทศ : | - |
| ทฤษฎี สมมุติฐาน กรอบแนวความคิด : | - |
| วิธีการดำเนินการวิจัย และสถานที่ทำการทดลอง/เก็บข้อมูล : | We employ the method of direct proof for writing a mathematical proof of all theorems from the hypothesis to the conclusion. |
| คำอธิบายโครงการวิจัย (อย่างย่อ) : | - |
| จำนวนเข้าชมโครงการ : | 83 ครั้ง |
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