Pub Date : 1900-01-01DOI: 10.5899/2016/JFSVA-00303
F. Abbasi, S. Abbasbandy, J. Nieto
There are certain problems in the subtraction operator, division operator and obtaining the membership functions of operators and above all, dependence effect in the fuzzy arithmetic operations using the extension principle (in the domain of the membership function) or the interval arithmetics (in the domain of $alpha$ - cuts). In this regard, this paper provide a new method regarding the effective practical computation of elementary fuzzy arithmetic operations on pseudo-geometric fuzzy numbers. Therefore we eliminated such deficiency with the new proposed method and demonstrated that the new operators are more efficient. Finally, several illustrative examples were given to show the accomplishment and ability of the proposed method. The future prospect of this paper is a new attitude to fuzzy mathematics.
{"title":"A new and efficient method for elementary fuzzy arithmetic operations on pseudo-geometric fuzzy numbers","authors":"F. Abbasi, S. Abbasbandy, J. Nieto","doi":"10.5899/2016/JFSVA-00303","DOIUrl":"https://doi.org/10.5899/2016/JFSVA-00303","url":null,"abstract":"There are certain problems in the subtraction operator, division operator and obtaining the membership functions of operators and above all, dependence effect in the fuzzy arithmetic operations using the extension principle (in the domain of the membership function) or the interval arithmetics (in the domain of $alpha$ - cuts). In this regard, this paper provide a new method regarding the effective practical computation of elementary fuzzy arithmetic operations on pseudo-geometric fuzzy numbers. Therefore we eliminated such deficiency with the new proposed method and demonstrated that the new operators are more efficient. Finally, several illustrative examples were given to show the accomplishment and ability of the proposed method. The future prospect of this paper is a new attitude to fuzzy mathematics.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"28 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":"134288491","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-00163
T. Allahviranloo, A. Armand, Z. Gouyandeh, H. Ghadiri
In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.
{"title":"Existence and uniqueness of solutions for fuzzy fractional Volterra-Fredholm integro-differential equations","authors":"T. Allahviranloo, A. Armand, Z. Gouyandeh, H. Ghadiri","doi":"10.5899/2013/JFSVA-00163","DOIUrl":"https://doi.org/10.5899/2013/JFSVA-00163","url":null,"abstract":"In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"41 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":"133444461","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-00359
S. Islam, Partha Ray
In this paper, we propose a multi-objective transhipment problem where the source and destination parameters are chosen as triangular fuzzy numbers. There is an additional entropy objective function in the multi-objective transshipment problem.Using nearest interval approximation and total integral value of the fuzzy number, the problem is transformed into two types of crisp multi-objective problems. Finally, the transformed problems have been solved by fuzzy programming technique (using Bellman and Zadeh's (1970) minimum and additive operator). Numerical examples have been given to illustrate the original problem.
{"title":"Multi-objective Transhipment problem with an additional entropy objective function using fuzzy programming","authors":"S. Islam, Partha Ray","doi":"10.5899/2017/jfsva-00359","DOIUrl":"https://doi.org/10.5899/2017/jfsva-00359","url":null,"abstract":"In this paper, we propose a multi-objective transhipment problem where the source and destination parameters are chosen as triangular fuzzy numbers. There is an additional entropy objective function in the multi-objective transshipment problem.Using nearest interval approximation and total integral value of the fuzzy number, the problem is transformed into two types of crisp multi-objective problems. Finally, the transformed problems have been solved by fuzzy programming technique (using Bellman and Zadeh's (1970) minimum and additive operator). Numerical examples have been given to illustrate the original problem.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"501 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":"123896445","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-00258
H. Goudarzi
The main purpose of this paper, is to investigate the basic properties of t-proximinal sets. At first we prove some main results and then we see some classified cases, in finite dimensional fuzzy normed spaces.
{"title":"t-proximinal sets in fuzzy normed spaces","authors":"H. Goudarzi","doi":"10.5899/2016/JFSVA-00258","DOIUrl":"https://doi.org/10.5899/2016/JFSVA-00258","url":null,"abstract":"The main purpose of this paper, is to investigate the basic properties of t-proximinal sets. At first we prove some main results and then we see some classified cases, in finite dimensional fuzzy normed spaces.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"117 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":"125824003","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: 10.5899/2015/JFSVA-00224
K. A. Germina, K. Nageswararao
A 1-uniform dcsl of a graph $G$ is an injective set-valued function $f : V(G)rightarrow 2^{X}, X$ be a non-empty ground set, such that the corresponding induced function $f^{oplus} :V(G) times V(G) rightarrow 2^{X}setminus {phi}$ satisfies $vert f^{oplus}(u, v)vert = 1.d(u, v)$ for all distinct $u, v in V(G)$, where $d(u, v)$ is the distance between $u$ and $v$. Let ${mathscr{F}}$ be a family of subsets of a set $X$. A {it tight path} between two distinct sets $P$ and $Q$ (or from $P$ to $Q$) in ${mathscr{F}}$ is a sequence $P_0 = P, P_1, P_2 dots P_n = Q$ in ${mathscr{F}}$ such that $d(P,Q)= mid P bigtriangleup Q mid = n$ and $d(P_i, P_{i+1}) = 1$ for $0 leq ileq n-1$. The family ${mathscr{F}}$ is {it well-graded} (or {it wg-family}), if there is a {it tight path} between any two of its distinct sets. Any family ${mathscr{F}}$ of subsets of $X$ defines a graph $G_{mathscr{F}} = ( {mathscr{F}} , E_{mathscr{F}})$, where $E_{mathscr{F}} = { {P,Q } subseteq {mathscr{F}}:mid P bigtriangleup Q mid = 1 } $, and we call $G_{mathscr{F}$, an ${mathscr{F}}$-induced graph. In this paper, we study 1-uniform dcsl graphs whose vertex labelings whether or not forms a lattice and prove that the cover graph $C_{{mathscr{F}}}$ of a poset ${mathscr{F}}$ with respect to set inclusion ` $subseteq$' is isomorphic to the ${mathscr{F}}$-induced graph $G_{{mathscr{F}}}$.
{"title":"Characterization of Vertex labeling of 1-uniform dcsl graph which form a lattice","authors":"K. A. Germina, K. Nageswararao","doi":"10.5899/2015/JFSVA-00224","DOIUrl":"https://doi.org/10.5899/2015/JFSVA-00224","url":null,"abstract":"A 1-uniform dcsl of a graph $G$ is an injective set-valued function $f : V(G)rightarrow 2^{X}, X$ be a non-empty ground set, such that the corresponding induced function $f^{oplus} :V(G) times V(G) rightarrow 2^{X}setminus {phi}$ satisfies $vert f^{oplus}(u, v)vert = 1.d(u, v)$ for all distinct $u, v in V(G)$, where $d(u, v)$ is the distance between $u$ and $v$. Let ${mathscr{F}}$ be a family of subsets of a set $X$. A {it tight path} between two distinct sets $P$ and $Q$ (or from $P$ to $Q$) in ${mathscr{F}}$ is a sequence $P_0 = P, P_1, P_2 dots P_n = Q$ in ${mathscr{F}}$ such that $d(P,Q)= mid P bigtriangleup Q mid = n$ and $d(P_i, P_{i+1}) = 1$ for $0 leq ileq n-1$. The family ${mathscr{F}}$ is {it well-graded} (or {it wg-family}), if there is a {it tight path} between any two of its distinct sets. Any family ${mathscr{F}}$ of subsets of $X$ defines a graph $G_{mathscr{F}} = ( {mathscr{F}} , E_{mathscr{F}})$, where $E_{mathscr{F}} = { {P,Q } subseteq {mathscr{F}}:mid P bigtriangleup Q mid = 1 } $, and we call $G_{mathscr{F}$, an ${mathscr{F}}$-induced graph. In this paper, we study 1-uniform dcsl graphs whose vertex labelings whether or not forms a lattice and prove that the cover graph $C_{{mathscr{F}}}$ of a poset ${mathscr{F}}$ with respect to set inclusion ` $subseteq$' is isomorphic to the ${mathscr{F}}$-induced graph $G_{{mathscr{F}}}$.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"24 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":"125946356","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-00133
P. Gain, R. P. Chakraborty, M. Pal
It is widely accepted that one of the most satisfactory generalization of the concept of compactness to fuzzy topological spaces is $alpha$-compactness, first introduced by Gantner et al. in 1978, followed by further investigations by many others. Chakraborty et al. introduced fuzzy semicompact set and investigated and characterized fuzzy semicompact spaces in terms of fuzzy nets and fuzzy prefilterbases in 2005. In this paper, we propose to introduce a new approach to characterize the notion of $alpha$-semicompactness in terms of ordinary nets and filters. This paper deals also with the concept of $alpha$-semilimit points of crisp subsets of a fuzzy topological space X and the concept of $alpha$-semiclosed sets in X and these concepts are used to define and characterize $alpha$-semicompact crisp subsets of X.
{"title":"A new approach towards characterization of semicompactness of fuzzy topological space and its crisp subsets","authors":"P. Gain, R. P. Chakraborty, M. Pal","doi":"10.5899/2013/JFSVA-00133","DOIUrl":"https://doi.org/10.5899/2013/JFSVA-00133","url":null,"abstract":"It is widely accepted that one of the most satisfactory generalization of the concept of compactness to fuzzy topological spaces is $alpha$-compactness, first introduced by Gantner et al. in 1978, followed by further investigations by many others. Chakraborty et al. introduced fuzzy semicompact set and investigated and characterized fuzzy semicompact spaces in terms of fuzzy nets and fuzzy prefilterbases in 2005. In this paper, we propose to introduce a new approach to characterize the notion of $alpha$-semicompactness in terms of ordinary nets and filters. This paper deals also with the concept of $alpha$-semilimit points of crisp subsets of a fuzzy topological space X and the concept of $alpha$-semiclosed sets in X and these concepts are used to define and characterize $alpha$-semicompact crisp subsets of X.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"92 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":"125980216","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-00188
M. Jahantigh, S. Hajighasemi
This study presents an approximate approach for ranking fuzzy numbers based on the centroid point of a fuzzy number and its area. The total approximate is determined by convex combining of fuzzy number’s relative and its area that based on decision maker’s optimistic perspectives. The proposed approach is simple in terms of computational efforts and is efficient in ranking a large quantity of fuzzy numbers. By a group of examples in [3] demonstrate the accuracy and applicability of the proposed approach. Finally by this approach, a new distance is introduced between two fuzzy numbers.
{"title":"A new distance and ranking method for trapezoidal fuzzy numbers","authors":"M. Jahantigh, S. Hajighasemi","doi":"10.5899/2014/JFSVA-00188","DOIUrl":"https://doi.org/10.5899/2014/JFSVA-00188","url":null,"abstract":"This study presents an approximate approach for ranking fuzzy numbers based on the centroid point of a fuzzy number and its area. The total approximate is determined by convex combining of fuzzy number’s relative and its area that based on decision maker’s optimistic perspectives. The proposed approach is simple in terms of computational efforts and is efficient in ranking a large quantity of fuzzy numbers. By a group of examples in [3] demonstrate the accuracy and applicability of the proposed approach. Finally by this approach, a new distance is introduced between two fuzzy numbers.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"7 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":"127036829","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-00355
A. Amroune, Ali Oumhani
In this paper, we extend some results obtained by A. Amroune and B. Davvaz in [1]. More precisely, we will develop a representation theory of intuitionistic fuzzy perfect distributive lattices in the finite case. To that end, we introduce the notion of intuitionistic fuzzy perfect distributive lattices and the one of fuzzy perfect Priestley spaces. In this way, the results of A. Amroune and B. Davvaz are extended to the intuitionistic fuzzy perfect case and the equivalence between the category of finite intuitionistic fuzzy perfect Priestley spaces the dual of the category of finite intuitionistic fuzzy perfect distributive lattices is proved.
{"title":"Representation theorem for finite intuitionistic fuzzy perfect distributive lattices","authors":"A. Amroune, Ali Oumhani","doi":"10.5899/2016/jfsva-00355","DOIUrl":"https://doi.org/10.5899/2016/jfsva-00355","url":null,"abstract":"In this paper, we extend some results obtained by A. Amroune and B. Davvaz in [1]. More precisely, we will develop a representation theory of intuitionistic fuzzy perfect distributive lattices in the finite case. To that end, we introduce the notion of intuitionistic fuzzy perfect distributive lattices and the one of fuzzy perfect Priestley spaces. In this way, the results of A. Amroune and B. Davvaz are extended to the intuitionistic fuzzy perfect case and the equivalence between the category of finite intuitionistic fuzzy perfect Priestley spaces the dual of the category of finite intuitionistic fuzzy perfect distributive lattices is proved.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"54 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":"122358970","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: 10.5899/2012/JFSVA-00106
Manjit Verma, Amit Kumar, Y. Singh
This paper describes a fault tree technique based on generalized fuzzy numbers to a possibility distribution of reliability indices for power systems. Due to uncertainty in the collected data, all the failure probabilities are represented by generalized trapezoidal fuzzy number. In this paper, the fault-tree incorporated with the generalized trapezoidal fuzzy number and minimal cut sets approach is used for reliability assessment of power systems. An example of gas power plant is given to demonstrate the method. By using this approach fuzzy system reliability can be analyzed in a more flexible and more intelligent manner.
{"title":"Power System Reliability Evaluation Using Fault Tree Approach Based on Generalized Fuzzy Number","authors":"Manjit Verma, Amit Kumar, Y. Singh","doi":"10.5899/2012/JFSVA-00106","DOIUrl":"https://doi.org/10.5899/2012/JFSVA-00106","url":null,"abstract":"This paper describes a fault tree technique based on generalized fuzzy numbers to a possibility distribution of reliability indices for power systems. Due to uncertainty in the collected data, all the failure probabilities are represented by generalized trapezoidal fuzzy number. In this paper, the fault-tree incorporated with the generalized trapezoidal fuzzy number and minimal cut sets approach is used for reliability assessment of power systems. An example of gas power plant is given to demonstrate the method. By using this approach fuzzy system reliability can be analyzed in a more flexible and more intelligent manner.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"2012 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":"131344515","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-00405
R. Mesiar, F. Kouchakinejad, M. Mashinchi
A revised definition for fuzzy bags is reviewed, developing the concept of bags given by Delgado et al. 2009 from which each bag has two parts, function and summary information. Then, the definitions of fuzzy bag expected value, bag entropy and bag similarity are introduced. By some examples, the new concepts are illustrated.
{"title":"Parameters of Fuzzy Bags","authors":"R. Mesiar, F. Kouchakinejad, M. Mashinchi","doi":"10.5899/2017/jfsva-00405","DOIUrl":"https://doi.org/10.5899/2017/jfsva-00405","url":null,"abstract":"A revised definition for fuzzy bags is reviewed, developing the concept of bags given by Delgado et al. 2009 from which each bag has two parts, function and summary information. Then, the definitions of fuzzy bag expected value, bag entropy and bag similarity are introduced. By some examples, the new concepts are illustrated.","PeriodicalId":308518,"journal":{"name":"Journal of Fuzzy Set Valued Analysis","volume":"236 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":"121474767","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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