Ranking Fuzzy Numbers Based on Ambiguity Degrees
|
|
- Esmond Cross
- 5 years ago
- Views:
Transcription
1 ustralian Journal of Basic and pplied Sciences, 5(): 6-69, ISSN Ranking Fuzzy Numbers Based on mbiguity Degrees Tayebeh Hajjari Department of Mathematics, Islamic zad University, Firuz Kuh Branch, Firuz Kuh, Iran bstract: Since much of human reasoning is based on imprecise, vague and subjective values, most of decision-making processing, in reality, requires handling and evaluation of fuzzy numbers. Zadeh s (Zadeh 965) fuzzy logic has given analysts a tool to present the human behavior more precisely, especially where relatively few data exist, and where the expert knowledge about the system is vague and linguistic (Hoogerdoorn et al. 999). Therefore, ranking fuzzy numbers is one of very important research topics in fuzzy set theory because it is a base of decision-making in applications. However, fuzzy numbers may not be easily ordered into one sequence according to their magnitudes because they represent uncertain values. lthough so far, many methods for ranking of fuzzy numbers have been discussed broadly, most of them contained some shortcomings, such as requirement of complicated calculations, inconstancy with human intuition and indiscrimination. However, these methods just can apply to rank some types of fuzzy numbers (i.e. normal, non-normal, positive, and negative fuzzy numbers), and many ranking cases can just rank by their graphs intuitively. Therefore, it is important to use proper methods in the right condition. The motivation of this study is to present a model for ranking fuzzy numbers based on their ambiguities. The advantages of the new proposed are that it can be applied for most of the defuzzification and the calculation is far simple and easy than previous methods. The effectiveness of the proposed method is finally demonstrated by including a comprehensive comparing different ranking method with the present one. Key words: mbiguity, Fuzzy numbers, membeship function, Ranking INTRODUCTION Many authors have introduced various ranking approaches of fuzzy numbers, these approaches are developed in the literature for multiple attribute decision-making problems, therefore in fuzzy environments, ranking fuzzy numbers is very important decision making procedure, because a good decision is necessary for achieving desired targets. This means that the quantity of a fuzzy number is not the only consideration in the ranking process for decision-making. In other words, the quality factor is suitably incorporated into the determination of the preference order of fuzzy numbers for the decision-making purpose in the fuzzy conditions. ny ranking existing method has a shortcoming that cannot rank special cases of fuzzy numbers. number of ranking methods focus on the centroid point and its distance from origin or the area measurement for a fuzzy numbers (bbasbandy, S. and T. Hajjari, 9; Hajjari, T., ; Hajjari, T., 8; Hajjari, T., 8; Cheng, C.H., 998; Chu, T. and C. Tsao, ), some have used from dispersion and distance indexes (bbasbandy, S. and B. sady, 6; Chen, S., 985; Tran, L., L. Duckstein, ), other some applied simulation and statistics methods for ranking fuzzy numbers (Wang Liu, X. and S. Lina Han, 5; Huijun, S. and W. Jianjun, 6; Lee, E.S., R.J. Li, 988). lmost each method, however has pitfalls in some aspect or have led to some misapplications, such as inconsistency with human intuition, indiscrimination, and difficulty. Consequently seems that uniquely the best method there does not exist for comparing fuzzy numbers, and different methods may satisfy different desirable criteria. The present study has been motivated by the author interest in making decisions in fuzzy environment. In this work, we attempt to combine some commonly used defuzzification methods to define some new definition into a certain uniform. The reminder of this paper is organized as follows: Section contains some basic notation, the definitions and some existing ranking methods, which used in this work. Section includes the developed method of Mag ranking (bbasbandy, S. and T. Hajjari, 9) and a new approach that can apply for most of the defuzzification methods. Some numerical examples demonstrate this idea to compare with previous methods. Corresponding uthor: Tayebeh Hajjari, Department of Mathematics, Islamic zad University, Firuz Kuh Branch, Firuz Kuh, Iran tayebehajjari@iaufb.ac.ir 6
2 ust. J. Basic & ppl. Sci., 5(): 6-69, Finally, concluding remarks are given in Section 4. Background Information: In general, a generalized fuzzy number is described as any fuzzy subset of real line R, whose membership ( x ) can be defined as (Dubios, D. and H. Prade, 987). L( x) a x b b x c ( x) R( x) c x d otherwise, () where is a constant, and L : a, b, and R : c, d, are two strictly monotonical and continuous mapping from R to closed interval [,ω]. If ω =, then is a normal fuzzy number; otherwise, it is a trapezoidal fuzzy number and is usually denoted by = (a, b, c, d, ω) or = (a, b, c, d) if ω =. In particular, when b = c, the trapezoidal fuzzy number is reduced to a triangular fuzzy number denoted by = (a, b, c, d, ω) or = (a, b, c, d) if ω =. Therefore, triangular fuzzy numbers are special cases of trapezoidal fuzzy numbers. Since L ( x ) and R( x) are both strictly monotonically and continuous functions, their inverse functions exist and should be continuous and strictly monotonically. Let L :, ab, and R :, c, d be the inverse functions of L ( x ) and R( x), respectively. Then L () r and R () r should be integrable on the close interval [. ω]. In other words, both and R () rdrshould exist. In the case L () r dr of trapezoidal fuzzy number, the inverse functions L r and R () r can be analytically expressed as () L () r a( ba) r/, () R () r d ( d c) r/, () The set of all elements that have a nonzero degree of membership in, it is called the support of, i.e. Supp ( ) xx ( x) (4) The set of elements having the largest degree of membership in, it is called the core of, i.e. Core ( ) xx ( x ) sup L ( x ). xx (5) In the following, we will always assume that is continuous and bounded support supp () = (a, d). The strong support of should be supp () = [a, d]. Definition.. function s:[.]º[,] is a reducing function if is s increasing and s() = and s() =. We say that s is a regular function if sxdx ( ). 6
3 ust. J. Basic & ppl. Sci., 5(): 6-69, Definition. If is a fuzzy number with r-cut representation, function, then the value of (with respect to s); it is defined by ( L( r), R ( r)) and s is a reducing ( ) ( )[ ( ) ( )] Val s r L r R r dr Definition. If is a fuzzy number with r-cut representation function then the ambiguity of (with respect to s) is defined by ( ) ( )[ ( ) ( )]. mb s r R r L r dr ( L( r), R ( r)) (6), and s is a reducing (7) Definition.4 The first of maxima (FOM) is the smallest element of core () i.e.. FOM min core( ) Definition.5 The last of maxima (LOM) is the greatest element of core() i.e. LOM max core( ). Some Existing Ranking Methods: In this part briefly, we review nine existing defuzzificationmethods: centroid point (Cheng, C.H., 998), Chu and Tsao s method ()Chu, T. and C. Tsao,, sign distance (bbasbandy, S. and B. sady, 6) and Mag Ranking method (bbasbandy, S. and T. Hajjari, 9) respectively. Centroid Point: In order to determine the centroid point ( x, y ) of a fuzzy number, Cheng (998) provided a formulae. Wang et al. (985) found from the point of view of analytical geometry and showed the corrected centroid point as follows: x y b c d xl ( x) dx xdx xr ( x) dx a b c b c d L ( x) dx dx R ( x) dx a b c yr ( y) dy yl ( y) dy. R ( y) dy L ( y) dy (8) For non-normal trapezoidal fuzzy number = (a, b, c, d, ω) formulas (8) lead to following results respectively. dc ab x a b c d ( d c) ( ab) y c d. ( d c) ( ab) (9) 64
4 ust. J. Basic & ppl. Sci., 5(): 6-69, Since non-normal triangular fuzzy numbers are special cases of normal trapezoidal fuzzy numbers with b = c, formulas (9) can be simplified as x abcd y. () In this case, normal triangular fuzzy numbers can be compared or ranked directly in terms of their centroid coordinates on horizontal axis. Cheng (998) formulated his idea as follows: R ( ) x( ) y( ) () Chu and Tsao s Method: Chu and Tsao ()Chu, T. and C. Tsao, computed the area between the centroid and original points to rank fuzzy numbers as: S( ) x ( ). y ( ) Sign Distance Method: Sign distance method (bbasbandy, S. and B. sady, 6) denoted by as follows d D (, ) p ( ) (, ) d ( p, ) (), which is computed () such that ( ): E {,}, (E stands for fuzzy numbers) and ( ) [ ( ) ( )] sign L x R x dx where (4) ( ) sign L x R x dx sign L x R x dx [ ( ) ( )] [ ( ) ( )] (5) also, if x ( ) if x (6) and p p p (, ) ( ( ) ( ) ). D L x R x dx (7) 65
5 ust. J. Basic & ppl. Sci., 5(): 6-69, Mag Ranking Method: For an arbitrary trapezoidal fuzzy number ( x, y,, ), with parametric form L x R x ( ( ), ( )), bbasbandy and Hajjari presented the magnitude of the trapezoidal fuzzy number as Mag L x R x x y s x dx ( ) ( ) ( ) ( ), (8) Where the function s(x) is a non-negative and increasing function on [, ] with s()=, s()= and sxdx ( ). Obviously, function s(x) can be considered as a weighting function. For more details, we refer the reader to (bbasbandy, S. and T. Hajjari, 9). New Method for General Fuzzy Numbers: In this part, we first develop Mag ranking method (bbasbandy, S. and T. Hajjari, 9) for all fuzzy numbers. Let be a fuzzy number with parametric form ( L ( x), R ( x)), which L (), R () are FOM and LOM respectively. Then the developed Mag ranking method can be written as L( x) R ( x) Mag( ) s( x) dx, L() R () (9) It is clear that the developed method has all properties, which the previous one has. For more detail, we refer the reader to (bbasbandy, S. and T. Hajjari, 9). Example.6. Consider two fuzzy numbers from (Wang, Z.X., 9) i.e. the triangular fuzzy number =(,,5) and fuzzy number B, shown in Fig., which the membership function of B is defined by x when x B x when x 4 when ( ), ( ) ( ),4. otherwise Fig. : 66
6 ust. J. Basic & ppl. Sci., 5(): 6-69, In Lious and Wang s ranking method (Wang, Z.X., 9), different ranking are produced for the same problem when applying different indices of optimism. Distance method with p, d (, ) 5, d ( B, ) 4.78 and p p p, d (, ) 5.957, d ( B, ).845, p p the ranking order is B. In Chu and Tsao s ranking method S() =.445 and S(B) =.8, therefore B From Mag ranking method Mag() = 4.5 and Mag() = 4 the ranking order is B. The results by Z-x Wang et al. s are the same. Moreover, if the approach in (Wang, Y.J. and H. Sh. Lee, 8) is used, the ranking order is B. We can concluded that B is more consistent with human intuition. s we know in most of fuzzy ranking methods, all symmetric fuzzy numbers with the same core and fuzzy numbers with the identical centroid points have the equal ranking order. This case will be more explained this by the next example. Example.7 Consider to triangular fuzzy number =(-.5,,.5) and B= (-,, ). By using Cheng s distance R() = R(), Chu and Tsao s S() = S(B) = and Mag ranking method Mag()=Mag(B)=. Hence and B have the same ranking order i.e..b. See Fig.. Fig. : Now we would like to introduce a new approach to apply our method and some other methods more precisely. In point of our view, more close to crisp number, less ambiguity because a crisp number or a certain number has no ambiguity. Consequently, the more ambiguity, the fuzzy number will be smaller. So we apply the value of ambiguity of fuzzy number as the degree of ordering in case that two fuzzy numbers are equal. The aforementioned method can apply for all defuzzification methods. In general, consider the defuzzification method DM(.) and for two fuzzy numbers and B the ranking order be based on the following situations:. If DM( ) DM( B) then B,. If DM( ) DM( B) then B,. If DM( ) DM( B) then B. In the third case, we can compare two fuzzy numbers precisely. In other words, first it should be computed the ambiguity of two fuzzy numbers then we will have one of the next conditions: 67
7 ust. J. Basic & ppl. Sci., 5(): 6-69,. If amb( ) amb( B) then B,. If amb( ) amb( B) then B,. If amb( ) amb( B) then B. For example consider two fuzzy number and B from Example.7 that have the same ranking order. Now we compute the ambiguity of and B by using Eq. (7) amb( ) 6 and amb( B). since amb( ) amb( B) then B. Example.8 Consider the data used in (Chen, L.H., H.W. Lu, ), i.e. two fuzzy numbers =(, 6, 9) and B=(5, 6, 7), as shown in Fig.. Fig. : Through the proposed approach in this paper, since Mag()=Mag(B)= and amb()=and amb( B), the ranking order is B. This result is the same as Z-X Wang s method (Wang, Z.X., 9). Because fuzzy numbers and B have the same mode and symmetric spread, most of existing approaches fail. For instance by bbasbandy and sady approach (bbasbandy, S. and B. sady, 6), different ranking orders are optained when different index values (p) are taken. When p= and p=, the ranking order of fuzzy numbers is.b and B respectively. Meanwhile, using the approaches in (Chu, T. and C. Tsao, ; Wang, Y.J. and H. Sh. Lee, 8; Yao, J.S., K. WU, 996), the ranking order is the same, i.e..b. Nevertheless, inconsistent results produced when distance index and CV index of cheng s approach (Cheng, C.H., 998) are respectively used. Moreover, the ranking order obtained by Wang et al. s approach (Wang, M.L., 5) is B. dditionally, by the approaches provided in (Liu, X., ; Matarazzo, B., G. Munda, ; Yao, J.S. and F.T. Lin, ) different ranking order is obtained when different indices of optimism are taken. However, decision makers prefer to result B in tuition ally. Conclusion: In spite of many ranking methods, no one can rank fuzzy numbers with human intuition consistently in all cases. Here, we first developed Mag ranking method, we then introduced an approach to ranking fuzzy numbers based on their ambiguity. The proposed approach can be utilized for most of defuzzification precisely and may be corrected them in some situations. The new method does not imply much computational effort and does not require a priori knowledge of the set of all alternatives. We also used comparative examples to illustrate the advantages of the proposed method. 68
8 ust. J. Basic & ppl. Sci., 5(): 6-69, CKNOWLEDGMENT This work was partly supported by Islamic zad University-Firuz-Kuh Branch. REFERENCES bbasbandy, S. and T. Hajjari, 9. new approach for ranking of trapezoidal fuzzy numbers, Comput. Math. ppl., 57(4): bbasbandy, S. and B. sady, 6. Ranking of fuzzy numbers by sign distance, Inform. Sci., 76: Chen, L.H., H.W. Lu,. The preference order of fuzzy numbers, Comput. Math. ppl., 44: Chen, S., 985. Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems, 7: -9. Cheng, C.H., 998. new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, 95: 7-7. Chu, T. and C. Tsao,. Ranking fuzzy numbers with an area between the centroid point and orginal point, Comput. Math. ppl., 4: -7. Hajjari, T.,. Ranking of Fuzzy Numbers by Middle of Expected Interval, In: First International Conference in Mathematics and Statistics, Sharjah. Hajjari, T., 8. Comparison of Fuzzy numbers by Modified Centroid Point Method. In: Third International Conference in Mathematical Sciences Dubai, pp: Hajjari, T., 8. Fuzzy Euclidean Distance for Fuzzy Data, In: 8th Iranian Conference on Fuzzy Systems, Iran, pp: 7-. Hajjari, T., 7. Ranking Fuzzy Numbers by Sign Length, In: 7th Iranian Conference on Fuzzy Systems, Iran, pp: 97-. Huijun, S. and W. Jianjun, 6. new approach for ranking fuzzy numbers based on fuzzy simulation analysis method, pplied Mathematics and Computation, 74: Dubios, D. and H. Prade, 987. Operations on fuzzy numbers, Internat. J. System Sci., 9: Lee, E.S., R.J. Li, 988. Comparestion of fuzzy numbers based on the prob- ability measure of fuzzy event, Computer and Mathematics with pplication, 5: Matarazzo, B., G. Munda,. New approaches for the comparisonof L-R fuzzy numbers: a theoritical and operationalanalysis, Fuzzy Sets and Systems, 8: Liu, X.,. Measuring the satisfaction of constrains in fuzzy linear programming, Fuzzy Sets and Systems, : Tran, L., L. Duckstein,. Comparison of fuzzy numbers using a fuzzy distance measure, Fuzzy Sets and Systems, : -4. Wang, M.L., H.F. Wang and L.C. Lung, 5. Ranking fuzzy numbers based on lexicographic screening procedure, International Journal of Information Technology and Decision Making, 4: Wang Liu, X. and S. Lina Han, 5. Ranking fuzzy numbers with preference weighting function expectations, Computer and Mathematics with ppications, 49: Wang, Z.X., Y.J. Lio, Z.P. Fan and B. Feng, 9. Rnking LR fuzzy number based on deviation degree, Info. Sciences, 79: Wang, Y.J. and H. Sh. Lee, 8. The revised method of ranking fuzzy numbers with an area between the centroid and original points, Comput. Math. ppl., 55: -4. Yao, J.S., K. WU, 996. Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy Sets and Systems, 8: Yao, J.S. and F.T. Lin,. Fuzzy critical path method based on decomposition principle and signed distance, Fuzzy Sets and Systems, 6:
AN APPROXIMATION APPROACH FOR RANKING FUZZY NUMBERS BASED ON WEIGHTED INTERVAL - VALUE 1.INTRODUCTION
Mathematical and Computational Applications, Vol. 16, No. 3, pp. 588-597, 2011. Association for Scientific Research AN APPROXIMATION APPROACH FOR RANKING FUZZY NUMBERS BASED ON WEIGHTED INTERVAL - VALUE
More informationOrdering of fuzzy quantities based on upper and lower bounds
Ordering of fuzzy quantities based on upper and lower bounds Mahdi Karimirad Department of Industrial Engineering, University of Tehran, Tehran, Iran Fariborz Jolai Department of Industrial Engineering,
More informationEVALUATION FUZZY NUMBERS BASED ON RMS
EVALUATION FUZZY NUMBERS BASED ON RMS *Adel Asgari Safdar Young Researchers and Elite Club, Baft Branch, Islamic Azad University, Baft, Iran *Author for Correspondence ABSTRACT We suggest a new approach
More informationDEFUZZIFICATION METHOD FOR RANKING FUZZY NUMBERS BASED ON CENTER OF GRAVITY
Iranian Journal of Fuzzy Systems Vol. 9, No. 6, (2012) pp. 57-67 57 DEFUZZIFICATION METHOD FOR RANKING FUZZY NUMBERS BASED ON CENTER OF GRAVITY T. ALLAHVIRANLOO AND R. SANEIFARD Abstract. Ranking fuzzy
More informationRanking of fuzzy numbers, some recent and new formulas
IFSA-EUSFLAT 29 Ranking of fuzzy numbers, some recent and new formulas Saeid Abbasbandy Department of Mathematics, Science and Research Branch Islamic Azad University, Tehran, 14778, Iran Email: abbasbandy@yahoo.com
More informationOrdering Generalized Hexagonal Fuzzy Numbers Using Rank, Mode, Divergence and Spread
IOSR Journal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn:319-765x. Volume 1, Issue 3 Ver. II (May-Jun. 14), PP 15-.iosrjournals.org Ordering Generalized Hexagonal Fuzzy Numbers Using Rank, Mode, Divergence
More informationRanking of Generalized Exponential Fuzzy Numbers using Integral Value Approach
Int. J. Advance. Soft Comput. Appl., Vol., No., July 010 ISSN 074-853; Copyright ICSRS Publication, 010.i-csrs.org Ranking of Generalized Exponential Fuzzy Numbers using Integral Value Approach Amit Kumar,
More informationComparison of Fuzzy Numbers with Ranking Fuzzy and Real Number
Journal of mathematics and computer Science 12 (2014) 65-72 Comparison of Fuzzy Numbers with Ranking Fuzzy and Real Number M. Yaghobi 1, M. Rabbani 2*, M. Adabitabar Firozja 3 J. Vahidi 4 1 Department
More informationInnovatively Ranking Fuzzy Numbers with Left-Right Areas and Centroids
Journal of Informatics and Mathematical Sciences Vol. 8, No. 3, pp. 167 174, 2016 ISSN 0975-5748 (online); 0974-875X (print) Published by RGN Publications http://www.rgnpublications.com Innovatively Ranking
More informationA NEW METHOD FOR RANKING FUZZY NUMBERS WITHOUT CONCERNING OF REAL NUMBERS
TWMS Jour. Pure Appl. Math., V.2, N.2, 2, pp.256-27 A NEW METHOD FOR RANKING FUZZY NUMBERS WITHOUT CONCERNING OF REAL NUMBERS R. EZZATI, R. ENAYATI, A. MOTTAGHI, R. SANEIFARD 2 Abstract. In this paper,
More informationScholars Journal of Physics, Mathematics and Statistics
Scholars Journal of Physics, Mathematics and Statistics Sch. J. Phys. Math. Stat. 2014; 1(2):53-60 Scholars cademic and Scientific Publishers (SS Publishers) (n International Publisher for cademic and
More informationCHAPTER 5 FUZZY LOGIC CONTROL
64 CHAPTER 5 FUZZY LOGIC CONTROL 5.1 Introduction Fuzzy logic is a soft computing tool for embedding structured human knowledge into workable algorithms. The idea of fuzzy logic was introduced by Dr. Lofti
More informationRanking Fuzzy Numbers with an Area Method Using Circumcenter of Centroids
Fuzzy Inf. Eng. (2013 1: 3-18 DOI 10.1007/s12543-013-0129-1 ORIGINAL ARTICLE Ranking Fuzzy Numbers with an Area Method Using Circumcenter of Centroids P. Phani Bushan Rao N. Ravi Shankar Received: 7 July
More informationA Comparative Study of Defuzzification Through a Regular Weighted Function
Australian Journal of Basic Applied Sciences, 4(12): 6580-6589, 2010 ISSN 1991-8178 A Comparative Study of Defuzzification Through a Regular Weighted Function 1 Rahim Saneifard 2 Rasoul Saneifard 1 Department
More informationA New Improved Method for Comparing Fuzzy Numbers by Centroid Point
Journal of Mathematical Extension Vol. 10, No. 2, (2016), 1-23 ISSN: 1735-8299 URL: http://www.ijmex.com A New Improved Method for Comparing Fuzzy Numbers by Centroid Point T. Hajjari Firoozkooh Branch,
More informationResearch Article Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality
Fuzzy Systems Volume 2011, Article ID 178308, 7 pages doi:10.1155/2011/178308 Research Article Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality P. Phani
More informationOrdering of Generalised Trapezoidal Fuzzy Numbers Based on Area Method Using Euler Line of Centroids
Advances in Fuzzy Mathematics. ISSN 0973-533X Volume 12, Number 4 (2017), pp. 783-791 Research India Publications http://www.ripublication.com Ordering of Generalised Trapezoidal Fuzzy Numbers Based on
More informationApproximation of Multiplication of Trapezoidal Epsilon-delta Fuzzy Numbers
Advances in Fuzzy Mathematics ISSN 973-533X Volume, Number 3 (7, pp 75-735 Research India Publications http://wwwripublicationcom Approximation of Multiplication of Trapezoidal Epsilon-delta Fuzzy Numbers
More informationSupplier Selection Based on Two-Phased Fuzzy Decision Making
GADING BUINE AND MANAGEMENT JOURNAL Volume 7, Number, 55-7, 03 upplier election Based on Two-Phased Fuzzy Decision Making Fairuz hohaimay, Nazirah Ramli, 3 iti Rosiah Mohamed & Ainun Hafizah Mohd,,3, Faculty
More informationThe Median Value of Fuzzy Numbers and its Applications in Decision Making
Available online at www.ispacs.com/jfsva Volume 2012, Year 2012 Article ID jfsva-00051, 9 pages doi:10.5899/2012/jfsva-00051 Research Article The Median Value of Fuzzy Numbers and its Applications in Decision
More informationFuzzy Variable Linear Programming with Fuzzy Technical Coefficients
Sanwar Uddin Ahmad Department of Mathematics, University of Dhaka Dhaka-1000, Bangladesh sanwar@univdhaka.edu Sadhan Kumar Sardar Department of Mathematics, University of Dhaka Dhaka-1000, Bangladesh sadhanmath@yahoo.com
More informationOptimization of fuzzy multi-company workers assignment problem with penalty using genetic algorithm
Optimization of fuzzy multi-company workers assignment problem with penalty using genetic algorithm N. Shahsavari Pour Department of Industrial Engineering, Science and Research Branch, Islamic Azad University,
More informationUNIVERSITY OF PORTSMOUTH INTUITION BASED DECISION MAKING METHODOLOGY FOR RANKING FUZZY NUMBERS USING CENTROID POINT AND SPREAD
UNIVERSITY OF PORTSMOUTH INTUITION BASED DECISION MAKING METHODOLOGY FOR RANKING FUY NUMBERS USING CENTROID POINT AND SPREAD AHMAD SYAFADHLI BIN ABU BAKAR The thesis is submitted in partial fulfillment
More informationA Centroid-Based Performance Evaluation Using Aggregated Fuzzy Numbers
Applied Mathematical Sciences, Vol., 2009, no. 48, 269-28 A Centroid-Based Performance Evaluation Using Aggregated Fuzzy Numbers Nazirah Ramli Department of Mathematics and Statistics Faculty of Information
More informationRanking Fuzzy Numbers Using Targets
Ranking Fuzzy Numbers Using Targets V.N. Huynh, Y. Nakamori School of Knowledge Science Japan Adv. Inst. of Sci. and Tech. e-mail: {huynh, nakamori}@jaist.ac.jp J. Lawry Dept. of Engineering Mathematics
More information399 P a g e. Key words: Fuzzy sets, fuzzy assignment problem, Triangular fuzzy number, Trapezoidal fuzzy number ranking function.
Method For Solving Hungarian Assignment Problems Using Triangular And Trapezoidal Fuzzy Number Kadhirvel.K, Balamurugan.K Assistant Professor in Mathematics, T.K.Govt. Arts ollege, Vriddhachalam 606 001.
More informationIntegration of Fuzzy Shannon s Entropy with fuzzy TOPSIS for industrial robotic system selection
JIEM, 2012 5(1):102-114 Online ISSN: 2013-0953 Print ISSN: 2013-8423 http://dx.doi.org/10.3926/jiem.397 Integration of Fuzzy Shannon s Entropy with fuzzy TOPSIS for industrial robotic system selection
More informationIntroduction to Fuzzy Logic and Fuzzy Systems Adel Nadjaran Toosi
Introduction to Fuzzy Logic and Fuzzy Systems Adel Nadjaran Toosi Fuzzy Slide 1 Objectives What Is Fuzzy Logic? Fuzzy sets Membership function Differences between Fuzzy and Probability? Fuzzy Inference.
More informationZero Average Method to Finding an Optimal Solution of Fuzzy Transportation Problems
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-728, p-issn: 2319-76X. Volume 13, Issue 6 Ver. I (Nov. - Dec. 2017), PP 6-63 www.iosrjournals.org Zero verage Method to Finding an Optimal Solution of
More informationA Compromise Solution to Multi Objective Fuzzy Assignment Problem
Volume 113 No. 13 2017, 226 235 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu A Compromise Solution to Multi Objective Fuzzy Assignment Problem
More informationAn Appropriate Method for Real Life Fuzzy Transportation Problems
International Journal of Information Sciences and Application. ISSN 097-55 Volume 3, Number (0), pp. 7-3 International Research Publication House http://www.irphouse.com An Appropriate Method for Real
More informationTOPSIS Modification with Interval Type-2 Fuzzy Numbers
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 6, No 2 Sofia 26 Print ISSN: 3-972; Online ISSN: 34-48 DOI:.55/cait-26-2 TOPSIS Modification with Interval Type-2 Fuzzy Numbers
More informationFuzzy Transportation Problem of Trapezoidal Numbers with Cut and Ranking Technique
International Journal of Fuzzy Mathematics and Systems. ISSN 2248-9940 Volume 2, Number 3 (2012), pp. 263-267 Research India Publications http://www.ripublication.com Fuzzy Transportation Problem of Trapezoidal
More informationFuzzy Inventory Model without Shortage Using Trapezoidal Fuzzy Number with Sensitivity Analysis
IOSR Journal of Mathematics (IOSR-JM) ISSN: 78-578. Volume 4, Issue 3 (Nov. - Dec. 0), PP 3-37 Fuzzy Inventory Model without Shortage Using Trapezoidal Fuzzy Number with Sensitivity Analysis D. Dutta,
More informationA Novel Method to Solve Assignment Problem in Fuzzy Environment
A Novel Method to Solve Assignment Problem in Fuzzy Environment Jatinder Pal Singh Neha Ishesh Thakur* Department of Mathematics, Desh Bhagat University, Mandi Gobindgarh (Pb.), India * E-mail of corresponding
More informationSimilarity Measures of Pentagonal Fuzzy Numbers
Volume 119 No. 9 2018, 165-175 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Similarity Measures of Pentagonal Fuzzy Numbers T. Pathinathan 1 and
More informationFuzzy multi objective linear programming problem with imprecise aspiration level and parameters
An International Journal of Optimization and Control: Theories & Applications Vol.5, No.2, pp.81-86 (2015) c IJOCTA ISSN:2146-0957 eissn:2146-5703 DOI:10.11121/ijocta.01.2015.00210 http://www.ijocta.com
More informationRanking Fuzzy Numbers with an Area Method using Radius of Gyration
ELSEVIER An International Journal Available online at www.sciencedirect.com computers &.,=.=. ~o,..=t. mathematics with applications Computers and Mathematics with Applications 51 (2006) 1127-1136 www.elsevier.com/locate/camwa
More informationExact Optimal Solution of Fuzzy Critical Path Problems
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 93-9466 Vol. 6, Issue (June 0) pp. 5 67 (Previously, Vol. 6, Issue, pp. 99 008) Applications and Applied Mathematics: An International Journal
More informationA New Method For Forecasting Enrolments Combining Time-Variant Fuzzy Logical Relationship Groups And K-Means Clustering
A New Method For Forecasting Enrolments Combining Time-Variant Fuzzy Logical Relationship Groups And K-Means Clustering Nghiem Van Tinh 1, Vu Viet Vu 1, Tran Thi Ngoc Linh 1 1 Thai Nguyen University of
More informationA Fuzzy Model for a Railway-Planning Problem
Applied Mathematical Sciences, Vol. 10, 2016, no. 27, 1333-1342 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.63106 A Fuzzy Model for a Railway-Planning Problem Giovanni Leonardi University
More informationEpistemic/Non-probabilistic Uncertainty Propagation Using Fuzzy Sets
Epistemic/Non-probabilistic Uncertainty Propagation Using Fuzzy Sets Dongbin Xiu Department of Mathematics, and Scientific Computing and Imaging (SCI) Institute University of Utah Outline Introduction
More informationIJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 1 Issue 3, May
Optimization of fuzzy assignment model with triangular fuzzy numbers using Robust Ranking technique Dr. K. Kalaiarasi 1,Prof. S.Sindhu 2, Dr. M. Arunadevi 3 1 Associate Professor Dept. of Mathematics 2
More informationSolving Fuzzy Linear Programming by Using Revised Tsao s Method
ustralian Journal of asic and pplied Sciences, 4(1): 4592-46, 21 ISS 1991-8178 Solving Fuzz inear Programming b Using evised Tsao s Method S.H. asseri, M. Sohrabi Department of Mathematical Sciences, Mazandaran
More informationDifferent Algorithmic Approach for Type 2 Fuzzy Shortest Path Problem on a Network
Intern. J. Fuzzy Mathematical rchive Vol. 7, No., 205, 27-33 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 22 January 205 www.researchmathsci.org International Journal of Different lgorithmic pproach
More informationCHAPTER 4 FREQUENCY STABILIZATION USING FUZZY LOGIC CONTROLLER
60 CHAPTER 4 FREQUENCY STABILIZATION USING FUZZY LOGIC CONTROLLER 4.1 INTRODUCTION Problems in the real world quite often turn out to be complex owing to an element of uncertainty either in the parameters
More informationBest proximation of fuzzy real numbers
214 (214) 1-6 Available online at www.ispacs.com/jfsva Volume 214, Year 214 Article ID jfsva-23, 6 Pages doi:1.5899/214/jfsva-23 Research Article Best proximation of fuzzy real numbers Z. Rohani 1, H.
More informationCost Minimization Fuzzy Assignment Problem applying Linguistic Variables
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 6 2017, 404 412 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Cost Minimization
More informationFuzzy Transportation Problems with New Kind of Ranking Function
The International Journal of Engineering and Science (IJES) Volume 6 Issue 11 Pages PP 15-19 2017 ISSN (e): 2319 1813 ISSN (p): 2319 1805 Fuzzy Transportation Problems with New Kind of Ranking Function
More informationAN ARITHMETIC OPERATION ON HEXADECAGONAL FUZZY NUMBER
AN ARITHMETIC OPERATION ON HEXADECAGONAL FUZZY NUMBER Dr.A.Sahaya Sudha 1 and R.Gokilamani 2 1 Department of Mathematics, Nirmala College for Women, Coimbatore 2 Department of Mathematics, Sri Ramakrishna
More informationIrregular Interval Valued Fuzzy Graphs
nnals of Pure and pplied Mathematics Vol 3, No, 03, 56-66 ISSN: 79-087X (P), 79-0888(online) Published on 0 May 03 wwwresearchmathsciorg nnals of Irregular Interval Valued Fuzzy Graphs Madhumangal Pal
More informationGeneral network with four nodes and four activities with triangular fuzzy number as activity times
International Journal of Engineering Research and General Science Volume 3, Issue, Part, March-April, 05 ISSN 09-730 General network with four nodes and four activities with triangular fuzzy number as
More informationApplication of fuzzy set theory in image analysis. Nataša Sladoje Centre for Image Analysis
Application of fuzzy set theory in image analysis Nataša Sladoje Centre for Image Analysis Our topics for today Crisp vs fuzzy Fuzzy sets and fuzzy membership functions Fuzzy set operators Approximate
More informationSOME OPERATIONS ON INTUITIONISTIC FUZZY SETS
IJMMS, Vol. 8, No. 1, (June 2012) : 103-107 Serials Publications ISSN: 0973-3329 SOME OPERTIONS ON INTUITIONISTIC FUZZY SETS Hakimuddin Khan bstract In This paper, uthor Discuss about some operations on
More informationInternational Journal of Scientific & Engineering Research, Volume 6, Issue 3, March ISSN
nternational Journal of Scientific & Engineering Research, Volume 6, ssue, March-5 SSN 9-558 Fuzzy Hungarian Method for Solving ntuitionistic Fuzzy Assignment Problems K. Prabakaran and K. Ganesan ABSTRACT-
More informationPENTAGON FUZZY NUMBER AND ITS APPLICATION TO FIND FUZZY CRITICAL PATH
Volume 114 No. 5 017, 183-185 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu PENTAGON FUZZY NUMBER AND ITS APPLICATION TO FIND FUZZY CRITICAL PATH SyedaNaziyaIkram
More informationSpeed regulation in fan rotation using fuzzy inference system
58 Scientific Journal of Maritime Research 29 (2015) 58-63 Faculty of Maritime Studies Rijeka, 2015 Multidisciplinary SCIENTIFIC JOURNAL OF MARITIME RESEARCH Multidisciplinarni znanstveni časopis POMORSTVO
More informationSingle-Period Inventory Models with Discrete Demand Under Fuzzy Environment
J. of Mult.-Valued Logic & Soft Computing, Vol. 18, pp. 371 386 Reprints available directly from the publisher Photocopying permitted by license only 2012 Old City Publishing, Inc. Published by license
More informationAn algorithmic method to extend TOPSIS for decision-making problems with interval data
Applied Mathematics and Computation 175 (2006) 1375 1384 www.elsevier.com/locate/amc An algorithmic method to extend TOPSIS for decision-making problems with interval data G.R. Jahanshahloo, F. Hosseinzadeh
More informationII. MULTI OBJECTIVE NON- LINEAR PROGRAMMING
Solving Fuzzy Multi Objective Non-linear Programming Problem Using Fuzzy Programming Technique P.Durga Prasad Dash, Rajani B. Dash Shishu Ananta Mahavidyalaya, Balipatna, Khurda,Odisha,India Department
More information2 Dept. of Computer Applications 3 Associate Professor Dept. of Computer Applications
International Journal of Computing Science and Information Technology, 2014, Vol.2(2), 15-19 ISSN: 2278-9669, April 2014 (http://ijcsit.org) Optimization of trapezoidal balanced Transportation problem
More informationUsing Goal Programming For Transportation Planning Decisions Problem In Imprecise Environment
Australian Journal of Basic and Applied Sciences, 6(2): 57-65, 2012 ISSN 1991-8178 Using Goal Programming For Transportation Planning Decisions Problem In Imprecise Environment 1 M. Ahmadpour and 2 S.
More informationExtension of the TOPSIS method for decision-making problems with fuzzy data
Applied Mathematics and Computation 181 (2006) 1544 1551 www.elsevier.com/locate/amc Extension of the TOPSIS method for decision-making problems with fuzzy data G.R. Jahanshahloo a, F. Hosseinzadeh Lotfi
More informationOn JAM of Triangular Fuzzy Number Matrices
117 On JAM of Triangular Fuzzy Number Matrices C.Jaisankar 1 and R.Durgadevi 2 Department of Mathematics, A. V. C. College (Autonomous), Mannampandal 609305, India ABSTRACT The fuzzy set theory has been
More informationFuzzy Optimal Solution for Fully Fuzzy Linear Programming Problems Using Hexagonal Fuzzy Numbers
Intern. J. uzzy Mathematical Archive Vol. No. 2 26 7-23 ISSN: 232 3242 (P 232 325 (online Published on 29 April 26 www.researchmathsci.org International Journal of uzzy Optimal Solution for ully uzzy Linear
More informationANALYTICAL FORMULATIONS FOR THE LEVEL BASED WEIGHTED AVERAGE VALUE OF DISCRETE TRAPEZOIDAL FUZZY NUMBERS
ANALYTICAL FORMULATIONS FOR TH LVL BASD WIGHTD AVRAG VALU OF DISCRT TRAPZOIDAL FUZZY NUMBRS Resmiye Nasiboglu 1*, Rahila Abdullayeva 2 1 Department of Computer Science, Dokuz ylul University, Izmir, Turkey
More informationSub-Trident Ranking Using Fuzzy Numbers
International Journal of Mathematics nd its pplications Volume, Issue (016), 1 150 ISSN: 7-1557 vailable Online: http://ijmaain/ International Journal 7-1557 of Mathematics pplications nd its ISSN: International
More information1. Fuzzy sets, fuzzy relational calculus, linguistic approximation
1. Fuzzy sets, fuzzy relational calculus, linguistic approximation 1.1. Fuzzy sets Let us consider a classical set U (Universum) and a real function : U --- L. As a fuzzy set A we understand a set of pairs
More informationASIAN JOURNAL OF MANAGEMENT RESEARCH Online Open Access publishing platform for Management Research
ASIAN JOURNAL OF MANAGEMENT RESEARCH Online Open Access publishing platform for Management Research Copyright 2010 All rights reserved Integrated Publishing association Review Article ISSN 2229 3795 The
More informationA TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS
Iranian Journal of Fuzzy Systems Vol. 5, No. 7, 208 pp. 2-3 2 A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS A. C. CEVIKEL AND M. AHLATCIOGLU Abstract. In this paper,
More informationSaudi Journal of Business and Management Studies. DOI: /sjbms ISSN (Print)
DOI: 10.21276/sjbms.2017.2.2.5 Saudi Journal of Business and Management Studies Scholars Middle East Publishers Dubai, United Arab Emirates Website: http://scholarsmepub.com/ ISSN 2415-6663 (Print ISSN
More informationExponential Membership Functions in Fuzzy Goal Programming: A Computational Application to a Production Problem in the Textile Industry
American Journal of Computational and Applied Mathematics 2015, 5(1): 1-6 DOI: 10.5923/j.ajcam.20150501.01 Exponential Membership Functions in Fuzzy Goal Programming: A Computational Application to a Production
More informationCHAPTER 3 MAINTENANCE STRATEGY SELECTION USING AHP AND FAHP
31 CHAPTER 3 MAINTENANCE STRATEGY SELECTION USING AHP AND FAHP 3.1 INTRODUCTION Evaluation of maintenance strategies is a complex task. The typical factors that influence the selection of maintenance strategy
More informationSolving Fuzzy Travelling Salesman Problem Using Octagon Fuzzy Numbers with α-cut and Ranking Technique
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 239-765X. Volume 2, Issue 6 Ver. III (Nov. - Dec.26), PP 52-56 www.iosrjournals.org Solving Fuzzy Travelling Salesman Problem Using Octagon
More informationReview of Fuzzy Logical Database Models
IOSR Journal of Computer Engineering (IOSRJCE) ISSN: 2278-0661, ISBN: 2278-8727Volume 8, Issue 4 (Jan. - Feb. 2013), PP 24-30 Review of Fuzzy Logical Database Models Anupriya 1, Prof. Rahul Rishi 2 1 (Department
More informationA MODIFICATION OF FUZZY TOPSIS BASED ON DISTANCE MEASURE. Dept. of Mathematics, Saveetha Engineering College,
International Journal of Pure and pplied Mathematics Volume 116 No. 23 2017, 109-114 ISSN: 1311-8080 (printed version; ISSN: 1314-3395 (on-line version url: http://www.ijpam.eu ijpam.eu MODIFICTION OF
More informationRANKING OF HEPTAGONAL FUZZY NUMBERS USING INCENTRE OF CENTROIDS
RANKING OF HEPTAGONAL FUZZY NUMBERS USING INCENTRE OF CENTROIDS Namarta 1, Dr Neha Ishesh Thakur, Dr Umesh Chandra Gupta 3 1 Research Scholar, UTU, Dehradun and Assistant Professor,Khalsa College Patiala
More informationLecture notes. Com Page 1
Lecture notes Com Page 1 Contents Lectures 1. Introduction to Computational Intelligence 2. Traditional computation 2.1. Sorting algorithms 2.2. Graph search algorithms 3. Supervised neural computation
More informationα - CUT FUZZY CONTROL CHARTS FOR BOTTLE BURSTING STRENGTH DATA
International Journal of Electronics, Communication & Instrumentation Engineering Research and Development (IJECIERD ISSN 2249-684X Vol. 2 Issue 4 Dec 2012 17-30 TJPRC Pvt. Ltd., α - CUT FUZZY CONTROL
More informationLinguistic Values on Attribute Subdomains in Vague Database Querying
Linguistic Values on Attribute Subdomains in Vague Database Querying CORNELIA TUDORIE Department of Computer Science and Engineering University "Dunărea de Jos" Domnească, 82 Galaţi ROMANIA Abstract: -
More informationFuzzy Sets and Systems. Lecture 1 (Introduction) Bu- Ali Sina University Computer Engineering Dep. Spring 2010
Fuzzy Sets and Systems Lecture 1 (Introduction) Bu- Ali Sina University Computer Engineering Dep. Spring 2010 Fuzzy sets and system Introduction and syllabus References Grading Fuzzy sets and system Syllabus
More informationFuzzy Set, Fuzzy Logic, and its Applications
Sistem Cerdas (TE 4485) Fuzzy Set, Fuzzy Logic, and its pplications Instructor: Thiang Room: I.201 Phone: 031-2983115 Email: thiang@petra.ac.id Sistem Cerdas: Fuzzy Set and Fuzzy Logic - 1 Introduction
More informationStudy of Fuzzy Set Theory and Its Applications
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 12, Issue 4 Ver. II (Jul. - Aug.2016), PP 148-154 www.iosrjournals.org Study of Fuzzy Set Theory and Its Applications
More informationMath 302 Introduction to Proofs via Number Theory. Robert Jewett (with small modifications by B. Ćurgus)
Math 30 Introduction to Proofs via Number Theory Robert Jewett (with small modifications by B. Ćurgus) March 30, 009 Contents 1 The Integers 3 1.1 Axioms of Z...................................... 3 1.
More informationUnit V. Neural Fuzzy System
Unit V Neural Fuzzy System 1 Fuzzy Set In the classical set, its characteristic function assigns a value of either 1 or 0 to each individual in the universal set, There by discriminating between members
More informationOPTIMIZATION OF FUZZY INVENTORY MODEL WITHOUT SHORTAGE USING PENTAGONAL FUZZY NUMBER
International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue, November 08, pp. 7, Article ID: IJMET_09 8 Available online at http://www.ia aeme.com/ijmet/issues.asp?jtypeijmet&vtype
More informationNETWORK FLOW WITH FUZZY ARC LENGTHS USING HAAR RANKING
NETWORK FLOW WITH FUZZY ARC LENGTHS USING HAAR RANKING S. Dhanasekar 1, S. Hariharan, P. Sekar and Kalyani Desikan 3 1 Vellore Institute of Technology, Chennai Campus, Chennai, India CKN College for Men,
More informationComputing Performance Measures of Fuzzy Non-Preemptive Priority Queues Using Robust Ranking Technique
Applied Mathematical Sciences, Vol. 7, 2013, no. 102, 5095-5102 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2013.37378 Computing Performance Measures of Fuzzy Non-Preemptive Priority Queues
More informationA method for solving unbalanced intuitionistic fuzzy transportation problems
Notes on Intuitionistic Fuzzy Sets ISSN 1310 4926 Vol 21, 2015, No 3, 54 65 A method for solving unbalanced intuitionistic fuzzy transportation problems P Senthil Kumar 1 and R Jahir Hussain 2 1 PG and
More informationCHAPTER - 3 FUZZY SET THEORY AND MULTI CRITERIA DECISION MAKING
CHAPTER - 3 FUZZY SET THEORY AND MULTI CRITERIA DECISION MAKING 3.1 Introduction Construction industry consists of broad range of equipment and these are required at different points of the execution period.
More informationAn evaluation approach to engineering design in QFD processes using fuzzy goal programming models
European Journal of Operational Research 7 (006) 0 48 Production Manufacturing and Logistics An evaluation approach to engineering design in QFD processes using fuzzy goal programming models Liang-Hsuan
More informationAttributes Weight Determination for Fuzzy Soft Multiple Attribute Group Decision Making Problems
International Journal of Statistics and Systems ISSN 0973-2675 Volume 12, Number 3 2017), pp. 517-524 Research India Publications http://www.ripublication.com Attributes Weight Determination for Fuzzy
More informationAn Application of Fuzzy Matrices in Medical Diagnosis
Intern. J. Fuzzy Mathematical Archive Vol. 9, No. 2, 2015, 211-216 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 8 October 2015 www.researchmathsci.org International Journal of An Application of
More informationFuzzy Expert Systems Lecture 8 (Fuzzy Systems)
Fuzzy Expert Systems Lecture 8 (Fuzzy Systems) Soft Computing is an emerging approach to computing which parallels the remarkable ability of the human mind to reason and learn in an environment of uncertainty
More informationThe Travelling Salesman Problem. in Fuzzy Membership Functions 1. Abstract
Chapter 7 The Travelling Salesman Problem in Fuzzy Membership Functions 1 Abstract In this chapter, the fuzzification of travelling salesman problem in the way of trapezoidal fuzzy membership functions
More informationCHAPTER 2 LITERATURE REVIEW
22 CHAPTER 2 LITERATURE REVIEW 2.1 GENERAL The basic transportation problem was originally developed by Hitchcock (1941). Efficient methods of solution are derived from the simplex algorithm and were developed
More informationHAAR HUNGARIAN ALGORITHM TO SOLVE FUZZY ASSIGNMENT PROBLEM
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 7 2017, 58 66 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu HAAR HUNGARIAN
More information742 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 13, NO. 6, DECEMBER Dong Zhang, Luo-Feng Deng, Kai-Yuan Cai, and Albert So
742 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL 13, NO 6, DECEMBER 2005 Fuzzy Nonlinear Regression With Fuzzified Radial Basis Function Network Dong Zhang, Luo-Feng Deng, Kai-Yuan Cai, and Albert So Abstract
More informationSaturated Sets in Fuzzy Topological Spaces
Computational and Applied Mathematics Journal 2015; 1(4): 180-185 Published online July 10, 2015 (http://www.aascit.org/journal/camj) Saturated Sets in Fuzzy Topological Spaces K. A. Dib, G. A. Kamel Department
More informationDifferent strategies to solve fuzzy linear programming problems
ecent esearch in Science and Technology 2012, 4(5): 10-14 ISSN: 2076-5061 Available Online: http://recent-science.com/ Different strategies to solve fuzzy linear programming problems S. Sagaya oseline
More information