Pub Date : 1900-01-01DOI: 10.5899/2012/JFSVA-00118
A. S. Salama, O. G. Elbarbary
Fuzzy rough sets are the generalization of traditional rough sets to deal with both fuzziness and vagueness in data. The existing researches on fuzzy rough sets mainly concentrate on the construction of approximation operators. Less effort has been put on the knowledge discovery in datasets with fuzzy rough sets. This paper mainly focuses on knowledge discovery in datasets with fuzzy rough sets. After analyzing the previous works on knowledge discovery with fuzzy rough sets, we introduce formal concepts of attribute reduction with fuzzy rough sets and completely study the structure of attribute reduction.
{"title":"Fuzzy-rough set and fuzzy ID3 decision approaches to knowledge discovery in datasets","authors":"A. S. Salama, O. G. Elbarbary","doi":"10.5899/2012/JFSVA-00118","DOIUrl":"https://doi.org/10.5899/2012/JFSVA-00118","url":null,"abstract":"Fuzzy rough sets are the generalization of traditional rough sets to deal with both fuzziness and vagueness in data. The existing researches on fuzzy rough sets mainly concentrate on the construction of approximation operators. Less effort has been put on the knowledge discovery in datasets with fuzzy rough sets. This paper mainly focuses on knowledge discovery in datasets with fuzzy rough sets. After analyzing the previous works on knowledge discovery with fuzzy rough sets, we introduce formal concepts of attribute reduction with fuzzy rough sets and completely study the structure of attribute reduction.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"252 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133391592","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 : 1900-01-01DOI: 10.5899/2016/jfsva-00275
S. Ziari, R. Ezzati
In this paper, a new approach to rank fuzzy numbers based on sign distance is proposed. Our proposed method is extension of sign distance method and to decrease the set of equivalence callas of fuzzy numbers. Illustrative examples are included to show the advantage of the proposed method.
{"title":"A new method for ranking of fuzzy numbers based on sign distance","authors":"S. Ziari, R. Ezzati","doi":"10.5899/2016/jfsva-00275","DOIUrl":"https://doi.org/10.5899/2016/jfsva-00275","url":null,"abstract":"In this paper, a new approach to rank fuzzy numbers based on sign distance is proposed. Our proposed method is extension of sign distance method and to decrease the set of equivalence callas of fuzzy numbers. Illustrative examples are included to show the advantage of the proposed method.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114231667","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 : 1900-01-01DOI: 10.5899/2016/JFSVA-00284
M. A. Araghi, Hasan Barzegar Kelishami
In this paper, a reliable scheme is proposed to solve fuzzy differential equations by fuzzy Runge-Kutta method of order $m$. For this purpose, the stochastic arithmetic and CESTAC method are applied to validate the results. In order to implement the C++ codes, the CADNA library is used. In this case, the optimal step size is found. The examples illustrate the efficiency and importance of using the stochastic arithmetic in place of the floating-point arithmetic.
{"title":"Dynamical control of accuracy in the fuzzy Runge-Kutta methods to estimate the solution of a fuzzy differential equation","authors":"M. A. Araghi, Hasan Barzegar Kelishami","doi":"10.5899/2016/JFSVA-00284","DOIUrl":"https://doi.org/10.5899/2016/JFSVA-00284","url":null,"abstract":"In this paper, a reliable scheme is proposed to solve fuzzy differential equations by fuzzy Runge-Kutta method of order $m$. For this purpose, the stochastic arithmetic and CESTAC method are applied to validate the results. In order to implement the C++ codes, the CADNA library is used. In this case, the optimal step size is found. The examples illustrate the efficiency and importance of using the stochastic arithmetic in place of the floating-point arithmetic.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115096898","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 : 1900-01-01DOI: 10.5899/2016/JFSVA-00274
M. A. Araghi, A. Fallahzadeh
In this paper, the inherited collocation method is introduced to solve the fuzzy differential equations. For this purpose, the so-called inherited LU factorization of matrices and inherited polynomials are used to decompose the extended crisp matrix obtained from the proposed method easily. The examples show the efficiency and importance of this method.
{"title":"Inherited collocation method for fuzzy differential equations","authors":"M. A. Araghi, A. Fallahzadeh","doi":"10.5899/2016/JFSVA-00274","DOIUrl":"https://doi.org/10.5899/2016/JFSVA-00274","url":null,"abstract":"In this paper, the inherited collocation method is introduced to solve the fuzzy differential equations. For this purpose, the so-called inherited LU factorization of matrices and inherited polynomials are used to decompose the extended crisp matrix obtained from the proposed method easily. The examples show the efficiency and importance of this method.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133731388","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 : 1900-01-01DOI: 10.5899/2014/JFSVA-00193
G. Malkawi, N. Ahmad, H. Ibrahim, Bander Alshmari
This study proposes a new method for finding a feasible fuzzy solution in positive Fully Fuzzy Linear System (FFLS), where the coefficients are unknown. The fully fuzzy system is transferred to linear system in order to obtain the solution using row reduced echelon form, thereafter; the crisp solution is restricted in obtaining the positive fuzzy solution. The fuzzy solution of FFLS is included crisp intervals, to assign alternative values of unknown entries of fuzzy numbers. To illustrate the proposed method, numerical examples are solved, where the entries of coefficients are unknown in right or left hand side, to demonstrate the contributions in this study.
{"title":"Row Reduced Echelon Form for Solving Fully Fuzzy System with Unknown Coefficients","authors":"G. Malkawi, N. Ahmad, H. Ibrahim, Bander Alshmari","doi":"10.5899/2014/JFSVA-00193","DOIUrl":"https://doi.org/10.5899/2014/JFSVA-00193","url":null,"abstract":"This study proposes a new method for finding a feasible fuzzy solution in positive Fully Fuzzy Linear System (FFLS), where the coefficients are unknown. The fully fuzzy system is transferred to linear system in order to obtain the solution using row reduced echelon form, thereafter; the crisp solution is restricted in obtaining the positive fuzzy solution. The fuzzy solution of FFLS is included crisp intervals, to assign alternative values of unknown entries of fuzzy numbers. To illustrate the proposed method, numerical examples are solved, where the entries of coefficients are unknown in right or left hand side, to demonstrate the contributions in this study.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133496948","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 : 1900-01-01DOI: 10.5899/2017/jfsva-00366
Anupam K. Singh, Saumya Pandey, S. Tiwari
Theories of fuzzy sets and type-2 fuzzy sets are powerful mathematical tools for modeling various types of uncertainty. In this paper we introduce the concept of type-2 fuzzy finite state automata and discuss the algebraic study of type-2 fuzzy finite state automata, i.e., to introduce the concept of homomorphisms between two type-2 fuzzy finite state automata, to associate a type-2 fuzzy transformation semigroup with a type-2 fuzzy finite state automata. Finally, we discuss several product of type-2 fuzzy finite state automata and shown that these product is a categorical product.
{"title":"On Algebraic Study of Type-2 Fuzzy Finite State Automata","authors":"Anupam K. Singh, Saumya Pandey, S. Tiwari","doi":"10.5899/2017/jfsva-00366","DOIUrl":"https://doi.org/10.5899/2017/jfsva-00366","url":null,"abstract":"Theories of fuzzy sets and type-2 fuzzy sets are powerful mathematical tools for modeling various types of uncertainty. In this paper we introduce the concept of type-2 fuzzy finite state automata and discuss the algebraic study of type-2 fuzzy finite state automata, i.e., to introduce the concept of homomorphisms between two type-2 fuzzy finite state automata, to associate a type-2 fuzzy transformation semigroup with a type-2 fuzzy finite state automata. Finally, we discuss several product of type-2 fuzzy finite state automata and shown that these product is a categorical product.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"271 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116619234","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 : 1900-01-01DOI: 10.5899/2013/JFSVA-00134
M. Ahmad, Salahuddin
This paper is devoted to the existence of solutions for generalized variational like inequalities with fuzzy mappings in topological vector spaces by using a particular form of the generalized KKM-Theorem.
利用广义kkm定理的一种特殊形式，研究了拓扑向量空间中具有模糊映射的广义类变分不等式解的存在性。
{"title":"Fuzzy Generalized Variational Like Inequality problems in Topological Vector Spaces","authors":"M. Ahmad, Salahuddin","doi":"10.5899/2013/JFSVA-00134","DOIUrl":"https://doi.org/10.5899/2013/JFSVA-00134","url":null,"abstract":"This paper is devoted to the existence of solutions for generalized variational like inequalities with fuzzy mappings in topological vector spaces by using a particular form of the generalized KKM-Theorem.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122086922","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 : 1900-01-01DOI: 10.5899/2016/JFSVA-00278
R. Ezzati, S. Sadatrasoul
In this paper, our aim is to provide two hybrid and non-hybrid efficient method based on non-orthogonal Bernoulli polynomials to approximate solution of linear fuzzy Fredholm integral equations. At first, using Bernoulli basis polynomials and also combining them with known block-pulse functions, we convert the fuzzy integral equations to two algebraic systems. The convergence and error estimates of the methods is also given. Finally, we present some illustrative examples and compare the numerical computational results to confirm the theoretical topics and demonstrate the convergence rate of the methods.
{"title":"Two hybrid and non-hybrid methods for solving fuzzy integral equations based on Bernoulli polynomials","authors":"R. Ezzati, S. Sadatrasoul","doi":"10.5899/2016/JFSVA-00278","DOIUrl":"https://doi.org/10.5899/2016/JFSVA-00278","url":null,"abstract":"In this paper, our aim is to provide two hybrid and non-hybrid efficient method based on non-orthogonal Bernoulli polynomials to approximate solution of linear fuzzy Fredholm integral equations. At first, using Bernoulli basis polynomials and also combining them with known block-pulse functions, we convert the fuzzy integral equations to two algebraic systems. The convergence and error estimates of the methods is also given. Finally, we present some illustrative examples and compare the numerical computational results to confirm the theoretical topics and demonstrate the convergence rate of the methods.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122260414","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 : 1900-01-01DOI: 10.5899/2014/JFSVA-00202
Masamichi Kon
For fuzzy mathematical models using general fuzzy sets rather than fuzzy numbers or fuzzy vectors, operations (addition and scalar multiplication) and orderings of fuzzy sets are needed, and the concept of fuzzy set-valued convex mappings is important. In the present paper, fundamental properties of operations, orderings, and fuzzy set-valued convex mappings for general fuzzy sets are investigated systematically.
{"title":"Operation and ordering of fuzzy sets, and fuzzy set-valued convex mappings","authors":"Masamichi Kon","doi":"10.5899/2014/JFSVA-00202","DOIUrl":"https://doi.org/10.5899/2014/JFSVA-00202","url":null,"abstract":"For fuzzy mathematical models using general fuzzy sets rather than fuzzy numbers or fuzzy vectors, operations (addition and scalar multiplication) and orderings of fuzzy sets are needed, and the concept of fuzzy set-valued convex mappings is important. In the present paper, fundamental properties of operations, orderings, and fuzzy set-valued convex mappings for general fuzzy sets are investigated systematically.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125201014","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 : 1900-01-01DOI: 10.5899/2016/jfsva-00347
D. Vivek, K. Kanagarajan, S. Harikrishnan
In this paper, we develop a framework to obtain approximate analytical solutions to hybrid fuzzy fractional initial value problem [HFFIVP] using fractional predictor-corrector method. Characterization theorem and convergent results are proved. We include some examples to verify the method applicability.
{"title":"A study on numerical solution to hybrid fuzzy fractional differential equations by predictor-corrector method","authors":"D. Vivek, K. Kanagarajan, S. Harikrishnan","doi":"10.5899/2016/jfsva-00347","DOIUrl":"https://doi.org/10.5899/2016/jfsva-00347","url":null,"abstract":"In this paper, we develop a framework to obtain approximate analytical solutions to hybrid fuzzy fractional initial value problem [HFFIVP] using fractional predictor-corrector method. Characterization theorem and convergent results are proved. We include some examples to verify the method applicability.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127395490","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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