Pub Date : 2021-01-02DOI: 10.1080/16168658.2021.1915453
Faruk Karaaslan, A. Ullah, Imtiaz Ahmad
In this study, we introduce the concept of normal bipolar soft subgroup and investigate some properties of normal bipolar soft subgroups. We also define notions of bipolar soft left and right cosets of a bipolar soft group and the concept of conjugate bipolar soft subgroup, and obtain some of their properties.
{"title":"Normal Bipolar Soft Subgroups","authors":"Faruk Karaaslan, A. Ullah, Imtiaz Ahmad","doi":"10.1080/16168658.2021.1915453","DOIUrl":"https://doi.org/10.1080/16168658.2021.1915453","url":null,"abstract":"In this study, we introduce the concept of normal bipolar soft subgroup and investigate some properties of normal bipolar soft subgroups. We also define notions of bipolar soft left and right cosets of a bipolar soft group and the concept of conjugate bipolar soft subgroup, and obtain some of their properties.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"8 1","pages":"79 - 98"},"PeriodicalIF":1.2,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78558474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-02DOI: 10.1080/16168658.2021.1929744
Sandhya S. Pai, T. Baiju
In this paper, we introduce Soft Lattice topological spaces which are defined over a soft lattice L with a fixed set of parameter P and it is also a generalisation of soft topological spaces. The notion of soft L-open sets, soft L-closed sets, soft L-closure, soft L-interior point and soft L-neighbourhood are introduced. Further some basic properties of Soft L-Topology are also investigated.
{"title":"On Soft Lattice Topological Spaces","authors":"Sandhya S. Pai, T. Baiju","doi":"10.1080/16168658.2021.1929744","DOIUrl":"https://doi.org/10.1080/16168658.2021.1929744","url":null,"abstract":"In this paper, we introduce Soft Lattice topological spaces which are defined over a soft lattice L with a fixed set of parameter P and it is also a generalisation of soft topological spaces. The notion of soft L-open sets, soft L-closed sets, soft L-closure, soft L-interior point and soft L-neighbourhood are introduced. Further some basic properties of Soft L-Topology are also investigated.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"11 1","pages":"1 - 16"},"PeriodicalIF":1.2,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81125197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-02DOI: 10.1080/16168658.2021.1915569
M. Touqeer, Atiqa Maryam, Muhammad Saeed
In p-hemiregular hemirings, some properties of ‘prime fuzzy p-ideals’ are examined. In the case of fuzzy p-ideal, p-hemiregular hemiring is also characterised. It is showed that in the case of hemiring , fuzzy subset φ is a ‘prime fuzzy left p-ideal’ in if and only if φ is having two values, set having all values of i?> in so that φ(p) equals to one is a ‘prime left(right) p-ideal’ in , φ(0) = 1. In hemirings for ‘maximal fuzzy left(right) p-ideals’, some related properties are also studied.
{"title":"Characterisation of p-ideals in Hemirings on the Basis of Hemiregularity, Prime and Normal Fuzzy Ideals","authors":"M. Touqeer, Atiqa Maryam, Muhammad Saeed","doi":"10.1080/16168658.2021.1915569","DOIUrl":"https://doi.org/10.1080/16168658.2021.1915569","url":null,"abstract":"In p-hemiregular hemirings, some properties of ‘prime fuzzy p-ideals’ are examined. In the case of fuzzy p-ideal, p-hemiregular hemiring is also characterised. It is showed that in the case of hemiring , fuzzy subset φ is a ‘prime fuzzy left p-ideal’ in if and only if φ is having two values, set having all values of i?> in so that φ(p) equals to one is a ‘prime left(right) p-ideal’ in , φ(0) = 1. In hemirings for ‘maximal fuzzy left(right) p-ideals’, some related properties are also studied.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"7 1","pages":"99 - 110"},"PeriodicalIF":1.2,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84205196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-02DOI: 10.1080/16168658.2021.1915456
A. Karbasioun, R. Ameri
Fuzzy sets and soft sets are two different soft computing models for representing vagueness and uncertainty. On the other domination is a rapidly developing area of research in graph theory, and its various applications to ad hoc networks, distributed computing, social networks and web graphs partly explain the increased interest. This concept was introduced by [Benecke S, Cockayne EJ, Mynhardt CM. Secure total domination in graphs. Util Math. 2007;74:247–259.] in 2007 and Go and Canoy continue the study of these notions [Canoy RS, Go CE. Domination in the corona and join of graphs. Int Math Forum. 2011;6(16):763–771.] and afterward introduce total dominating and secure total dominating sets. Also graph operations like corona product play a very important role in mathematical chemistry, since some chemically interesting graphs can be obtained from some simpler graphs by different graph operations. In this paper, we characterised the dominating, total dominating, and secure total dominating sets in the corona of two fuzzy soft connected.
模糊集和软集是表示模糊性和不确定性的两种不同的软计算模型。另一方面，图论是一个快速发展的研究领域，它在特设网络、分布式计算、社交网络和网络图中的各种应用部分地解释了人们日益增长的兴趣。这个概念是由Benecke S, Cockayne EJ, Mynhardt CM提出的。确保在图中的完全支配。数学学报。2007;74:247-259。]， Go和canoe继续研究这些概念[canoe RS, Go CE]。在图的日冕和连接中的支配。国际数学论坛。2011;6(16):763-771。]，然后介绍全控制集和安全全控制集。此外，像电晕积这样的图运算在数学化学中也起着非常重要的作用，因为一些化学上有趣的图可以通过不同的图运算从一些更简单的图中得到。本文对两个模糊软连通的晕上的控制集、总控制集和安全控制集进行了刻画。
{"title":"Total and Secure Domination for Corona Product of Two Fuzzy Soft Graphs","authors":"A. Karbasioun, R. Ameri","doi":"10.1080/16168658.2021.1915456","DOIUrl":"https://doi.org/10.1080/16168658.2021.1915456","url":null,"abstract":"Fuzzy sets and soft sets are two different soft computing models for representing vagueness and uncertainty. On the other domination is a rapidly developing area of research in graph theory, and its various applications to ad hoc networks, distributed computing, social networks and web graphs partly explain the increased interest. This concept was introduced by [Benecke S, Cockayne EJ, Mynhardt CM. Secure total domination in graphs. Util Math. 2007;74:247–259.] in 2007 and Go and Canoy continue the study of these notions [Canoy RS, Go CE. Domination in the corona and join of graphs. Int Math Forum. 2011;6(16):763–771.] and afterward introduce total dominating and secure total dominating sets. Also graph operations like corona product play a very important role in mathematical chemistry, since some chemically interesting graphs can be obtained from some simpler graphs by different graph operations. In this paper, we characterised the dominating, total dominating, and secure total dominating sets in the corona of two fuzzy soft connected.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"27 1","pages":"127 - 138"},"PeriodicalIF":1.2,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84290773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-02DOI: 10.1080/16168658.2021.1915454
S. Samanta, A. Ojha, B. Das, S. Mondal
In this paper, a solid transportation problem has been considered in which the transportation is accomplished in two stages – firstly, from the origin(s) to the near by station(s) of the destination(s) and secondly, from the near by station(s) to the exact destination(s). Here, a fuzzy AUD (all unit discount) policy has been introduced based upon the amount of transportation along with a fuzzy fixed charge. In addition, a budget constraint has been incorporated taking fuzzy unit transportation cost. Then the proposed model has been converted into a single objective optimisation problem using interval arithmetic method. To solve the model, Genetic Algorithm (GA) has been used depending on roulette wheel selection, crossover and mutation. Finally, a numerical example has been illustrated to study the feasibility of the model.
{"title":"A Profit Maximisation Solid Transportation Problem Using Genetic Algorithm in Fuzzy Environment","authors":"S. Samanta, A. Ojha, B. Das, S. Mondal","doi":"10.1080/16168658.2021.1915454","DOIUrl":"https://doi.org/10.1080/16168658.2021.1915454","url":null,"abstract":"In this paper, a solid transportation problem has been considered in which the transportation is accomplished in two stages – firstly, from the origin(s) to the near by station(s) of the destination(s) and secondly, from the near by station(s) to the exact destination(s). Here, a fuzzy AUD (all unit discount) policy has been introduced based upon the amount of transportation along with a fuzzy fixed charge. In addition, a budget constraint has been incorporated taking fuzzy unit transportation cost. Then the proposed model has been converted into a single objective optimisation problem using interval arithmetic method. To solve the model, Genetic Algorithm (GA) has been used depending on roulette wheel selection, crossover and mutation. Finally, a numerical example has been illustrated to study the feasibility of the model.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"61 1","pages":"40 - 57"},"PeriodicalIF":1.2,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80729702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-02DOI: 10.1080/16168658.2021.1936961
Sandeep Kumar, Shalu Rani, Mohit Kumar
Purpose: We introduce a multiple attribute group decision making (MAGDM) method under interval-valued intuitionistic fuzzy (IVIF) domain. In these MAGDM problems, attribute values and attribute weights are represented in terms of IVIF sets (IVIFSs). Methodology: The present methodology is divided into two parts. Firstly, an appropriate order function has been developed for IVIFSs. Secondly, an algorithm has been proposed for solving the MAGDM problems with IVIF decision information. Findings: To show the effectiveness of the proposed method, a theoretical comparative study with respect to some existing literature is provided. A real-life based numerical example is given to demonstrate the proposed solution procedure. The advantage of this method is also described. Values: Using proposed order function, interval-valued intuitionistic fuzzy hybrid geometric and ordered weighted averaging operators, the present method provides a most preferred alternative in six steps. On the basis of a comparative study, it can be observed that the present method simple and easy to implement for solving the IVIF MAGDM model occurrence in real-life decision making problems.
{"title":"A New Order Function for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Group Decision Making","authors":"Sandeep Kumar, Shalu Rani, Mohit Kumar","doi":"10.1080/16168658.2021.1936961","DOIUrl":"https://doi.org/10.1080/16168658.2021.1936961","url":null,"abstract":"Purpose: We introduce a multiple attribute group decision making (MAGDM) method under interval-valued intuitionistic fuzzy (IVIF) domain. In these MAGDM problems, attribute values and attribute weights are represented in terms of IVIF sets (IVIFSs). Methodology: The present methodology is divided into two parts. Firstly, an appropriate order function has been developed for IVIFSs. Secondly, an algorithm has been proposed for solving the MAGDM problems with IVIF decision information. Findings: To show the effectiveness of the proposed method, a theoretical comparative study with respect to some existing literature is provided. A real-life based numerical example is given to demonstrate the proposed solution procedure. The advantage of this method is also described. Values: Using proposed order function, interval-valued intuitionistic fuzzy hybrid geometric and ordered weighted averaging operators, the present method provides a most preferred alternative in six steps. On the basis of a comparative study, it can be observed that the present method simple and easy to implement for solving the IVIF MAGDM model occurrence in real-life decision making problems.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"8 3 1","pages":"111 - 126"},"PeriodicalIF":1.2,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75493870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1080/16168658.2021.1924528
T. Al-shami, E. A. Abo-Tabl, Baravan A. Asaad
Realizing the importance of separation axioms in classifications of topological spaces and studying certain properties of fixed points, we formulate new soft separation axioms, namely tt-soft and tt-soft b-regular spaces. Their definitions depend on three factors: soft b-open sets, total belong and total non-belong relations. In fact, they are genuine generalizations of p-soft -spaces in the cases of i = 0, 1, 2. With the help of examples, we study the relationships between them as well as with soft and soft b-regular spaces. Some interesting properties of them are obtained under the conditions of soft hyperconnected and extended soft topological spaces. Also, we show that they are preserved under finite product soft spaces and soft -homeomorphism mappings. Finally, we introduce a concept of b-fixed soft points and investigate its main properties.
{"title":"Weak Forms of Soft Separation Axioms and Fixed Soft Points","authors":"T. Al-shami, E. A. Abo-Tabl, Baravan A. Asaad","doi":"10.1080/16168658.2021.1924528","DOIUrl":"https://doi.org/10.1080/16168658.2021.1924528","url":null,"abstract":"Realizing the importance of separation axioms in classifications of topological spaces and studying certain properties of fixed points, we formulate new soft separation axioms, namely tt-soft and tt-soft b-regular spaces. Their definitions depend on three factors: soft b-open sets, total belong and total non-belong relations. In fact, they are genuine generalizations of p-soft -spaces in the cases of i = 0, 1, 2. With the help of examples, we study the relationships between them as well as with soft and soft b-regular spaces. Some interesting properties of them are obtained under the conditions of soft hyperconnected and extended soft topological spaces. Also, we show that they are preserved under finite product soft spaces and soft -homeomorphism mappings. Finally, we introduce a concept of b-fixed soft points and investigate its main properties.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"35 1","pages":"509 - 528"},"PeriodicalIF":1.2,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76240257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1080/16168658.2021.1918039
Amit Kumar, P. Dhiman
This work presents an application of upgraded arithmetic operations on trapezoidal fuzzy number to extend the reliability from point estimation to interval estimation. A realistic example of an accidental case has been taken to show the desired results. As we know that uncertainty is a disregardable phenomenon and in this situation crisp reliability may not be exact. To get a better hold on this situation, we introduce a method of trapezoidal fuzzy number and upgraded arithmetic operations. In this paper, the reliability of each factor is represented by the trapezoidal fuzzy number and the final reliability is obtained in the form of trapezoidal fuzzy number. Hence, the dejection of fuzzy number is preserved and the crisp region is increased to illustrate the highest membership grade as an interval. So it can help the decision maker to analyse the behaviour of the system and take effective decision accordingly to reduce the chance of mishappening.
{"title":"Reliability Range Through Upgraded Operation with Trapezoidal Fuzzy Number","authors":"Amit Kumar, P. Dhiman","doi":"10.1080/16168658.2021.1918039","DOIUrl":"https://doi.org/10.1080/16168658.2021.1918039","url":null,"abstract":"This work presents an application of upgraded arithmetic operations on trapezoidal fuzzy number to extend the reliability from point estimation to interval estimation. A realistic example of an accidental case has been taken to show the desired results. As we know that uncertainty is a disregardable phenomenon and in this situation crisp reliability may not be exact. To get a better hold on this situation, we introduce a method of trapezoidal fuzzy number and upgraded arithmetic operations. In this paper, the reliability of each factor is represented by the trapezoidal fuzzy number and the final reliability is obtained in the form of trapezoidal fuzzy number. Hence, the dejection of fuzzy number is preserved and the crisp region is increased to illustrate the highest membership grade as an interval. So it can help the decision maker to analyse the behaviour of the system and take effective decision accordingly to reduce the chance of mishappening.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"63 1","pages":"452 - 463"},"PeriodicalIF":1.2,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86655927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1080/16168658.2021.1923442
A. Bayoumi, M. Ramadan
ABSTRACT In this paper, five iterative methods for solving two coupled fuzzy Sylvester matrix equations are considered. The two coupled fuzzy Sylvester matrix equations are expressed by using the generalized inverse of the coefficient matrix, then iterative solutions are constructed by applying the hierarchical identification principle and by using the block-matrix inner product (the star product for short). A proposed modification to this algorithm to solve the first coupled fuzzy Sylvester matrix equations is suggested. This proposed modification is compared with the first algorithm where our modification exhibits fast convergence behavior. Also, we suggested two least-squares iterative algorithm by applying a hierarchical identification principle to solve the two coupled fuzzy Sylvester matrix equations. The proposed methods are illustrated by numerical examples.
{"title":"Solving Two Coupled Fuzzy Sylvester Matrix Equations Using Iterative Least-squares Solutions","authors":"A. Bayoumi, M. Ramadan","doi":"10.1080/16168658.2021.1923442","DOIUrl":"https://doi.org/10.1080/16168658.2021.1923442","url":null,"abstract":"ABSTRACT In this paper, five iterative methods for solving two coupled fuzzy Sylvester matrix equations are considered. The two coupled fuzzy Sylvester matrix equations are expressed by using the generalized inverse of the coefficient matrix, then iterative solutions are constructed by applying the hierarchical identification principle and by using the block-matrix inner product (the star product for short). A proposed modification to this algorithm to solve the first coupled fuzzy Sylvester matrix equations is suggested. This proposed modification is compared with the first algorithm where our modification exhibits fast convergence behavior. Also, we suggested two least-squares iterative algorithm by applying a hierarchical identification principle to solve the two coupled fuzzy Sylvester matrix equations. The proposed methods are illustrated by numerical examples.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"1 1","pages":"464 - 489"},"PeriodicalIF":1.2,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89404366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1080/16168658.2021.1924513
N. Kausar, M. Munir, S. Kousar, M. Gulistan, K. Anitha
In this article, we present brief description on R-OAG-gpd regular ordered AG-groupoid and IR-OAG-gpd intra-regular ordered AG-groupoid by using FL-ideal, FR-ideal, FQ-ideal, FB-ideal, FB-ideal, FGB-ideal.
{"title":"Characterization of Non-Associative Ordered Semigroups by the Properties of F-Ideals","authors":"N. Kausar, M. Munir, S. Kousar, M. Gulistan, K. Anitha","doi":"10.1080/16168658.2021.1924513","DOIUrl":"https://doi.org/10.1080/16168658.2021.1924513","url":null,"abstract":"In this article, we present brief description on R-OAG-gpd regular ordered AG-groupoid and IR-OAG-gpd intra-regular ordered AG-groupoid by using FL-ideal, FR-ideal, FQ-ideal, FB-ideal, FB-ideal, FGB-ideal.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"11 1","pages":"490 - 508"},"PeriodicalIF":1.2,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79644549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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