Aggregation of Pentagonal Fuzzy Numbers with Ordered Weighted Averaging Operator based VIKOR
|
|
- Jody Daniels
- 5 years ago
- Views:
Transcription
1 Volume 119 No , ISSN: (printed version); ISSN: (on-line version) url: ijpam.eu Aggregation of Pentagonal Fuzzy Numbers with Ordered Weighted Averaging Operator based VIKOR S. Johnson Savarimuthu 1 and T. Pathinathan 2 1 Department of Mathematics, St. Joseph s College of Arts and Science, Cuddalore-1, Tamil Nadu, India 1 johnson22970@gmail.com 2 P.G. and Research Department of Mathematics, Loyola College, Chennai - 34, Tamil Nadu, India 2 pathinathan@gmail.com Abstract Conflicting opinions arise while making decisions in groups. VIKOR is a technique to determine a compromise solution among the group decision makers to resolve the contradictions. In this paper, we introduce two different methodologies to aggregate the group decision makers opinion characterized by Pentagonal Fuzzy Numbers (PFNs). First, we utilize the generalized induced ordered weighted averaging (GIOWA) operator to aggregate the group decision makers opinion represented by PFNs. Then, we aggregate the group decision makers opinion by combining the linguistic GIOWA operator into pentagonal VIKOR method. The newly introduced two methodologies are compared with the previously used method using a case study. We have employed these methodologies to choose a most suitable crop for cultivation in Villupuram District, Tamil Nadu, India. AMS Subject Classification:03E
2 Keywords: Pentagonal fuzzy number, VIKOR, OWA operator, GIOWA operator, compromise solution. 1 Introduction The real life group decision making process encounters conflicting opinions, disagreements, and contradictions. Several decision making techniques [3] are proposed to resolve the disagreements among the decision makers. VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje) is one such technique, which primarily focus on the conflicting situations among the decision makers and largely employed to resolve the disagreements. The principal idea behind the VIKOR technique is to determine the compromise solution [26] among the group multiple solutions. Ronald Yager [2, 19 24] extensively studied and extended the work of Richard Bellman and Lotfi Zadeh [1] in decision making environments. Bellman and Zadeh developed a decision making theory and used fuzzy intersection (minimum) operation to combine the importance of the criteria. Ronald Yager [19] [23] extended the theory by developing the concept of quantifier guided aggregation to combine the importance of the criteria. Also, he suggested that the criteria weight importance calculated through quantifier guided aggregation [2] [16 18] [19 24] provides an overall group assessment over each criterion. T. Pathinathan and S. Johnson Savarimuthu [5] made a historical review on VIKOR multi-criteria decision making technique. Also, they extended the VIKOR method [12], where the decision makers opinion is characterized by pentagonal fuzzy numbers. Earlier, they had developed several decision making techniques such as TOPSIS combined with dual hesitant fuzzy set [6], TOPSIS with pentagonal hesitant fuzzy sets [7] and weight based intuitionistic fuzzy set (WBIFS) [9] into analytic hierarchy process (AHP). In all the earlier methods [6 9] [11] [12] [14] [15], the Experts opinion are collected and processed to establish an ideal solution. In early 2017, T. Pathinathan and S. Johnson Savarimuthu introduced a new fuzzy set named: weight based intuitionistic fuzzy set (WBIFS) [9] to study the impact of the external factors over the selection of best alternative. Then they applied the newly defined 2 296
3 weight based intuitionistic fuzzy set concept into analytic hierarchy process, where the entries of the decision matrix are characterized by WBIFS. In some cases, the conflicts arise among the decision makers in choosing a best alternative among the multiple alternatives. In such conflicting situations, the methods which we had developed earlier are found to be inconsistent to obtain the best alternative. In this paper, we propose two different methodologies which primarily order the importance of the opinion based on the importance of the criteria. We have employed the generalized ordered weighted averaging operator to order the importance of the criteria. Then we have proposed the generalized ordered weighted averaging operator combined with VIKOR for the multiple group decision analysis which is characterized by pentagonal fuzzy numbers. This paper is organized in the following manner. Section Two provides the proposed algorithm (1) which uses generalized ordered weighted averaging operator for the quantification. Section Three discusses the algorithmic approach of the newly proposed GIOWA- VIKOR decision making technique. Section Four gives the experimental verification of the proposed algorithms followed by comparison of the results obtained from both the algorithms in section five. Finally the paper is concluded in section Six. 2 Proposed algorithm on aggregating the multiple group decisions using GIOWA operator We propose an algorithm for newly extended multiple group decision making technique which uses GIOWA operator, where the decision entries are characterized by pentagonal fuzzy number. The newly proposed multi-criteria decision making technique aggregate the group subjective opinions by fixing the positions. Step 1: The subjective opinions from the group of decision makers (experts) are gathered. Step 2: The collected subjective opinions are of vague statements 3 297
4 characterized into a linguistic variables. Step 3: Construct a decision matrix (DM) where the decision entries of the matrix are characterized by a pentagonal fuzzy number and it is given by: DM = [f ij ] n m (1) Step 4: Construct an aggregated decision matrix from the group decision opinions (12). Step 5: The importance of the criteria and its respective weights has been calculated. Step 6: Construct aggregated subjective weights of each criterion (12). Step 7: The entries in the decision matrix are ordered from largest value to the smallest value. Then the respective criteria weights are ordered and the importance of the ordered criteria weights (i.e., the ordered weighted averaging weights) is calculated by the formula: w i (x) = Q ( ik=1 ) ( c i 1 k k=1 nk=1 Q c ) k c nk=1 k c k where i=1,2,3,...n represents n criteria s and T represents the total sum of the importance of criteria s and it is given by, and linguistic quantifier Q is defined as: (2) n T = c k (3) k=1 Q(x) = x 2 (4) 4 298
5 Step 8: Then the group overall assessment is calculated by the function, generalized induced ordered weighted averaging operator (GIOWA) is defined as follows: n GIOW A w ( A 1, C 1, x 11, A 1, C 2, x 12..., A 1, C n, x 1n ) = w i x 1i i=1 (5) Step 9: Ranking of a best alternative has been calculated as minimum gets first and maximum gets last. 3 Proposed algorithm on aggregating the multiple group decisions using VIKOR- GIOWA operator method We propose an algorithm which combines GIOWA operator into VIKOR decision making technique, where the decision entries are characterized by pentagonal fuzzy number. Step 1: The subjective opinions from the group of decision makers (Experts) are gathered. Step 2: The collected subjective opinions are of vague statements characterized into a linguistic variables. Step 3: Construct a decision matrix (DM) where the decision entries of the matrix are characterized by a pentagonal fuzzy number and it is given by: DM = [f ij ] n m (6) 5 299
6 Step 4: Construct an aggregated decision matrix from the group decision opinions (12). Step 5: The importance of the criteria and its respective weights has been calculated. Step 6: Construct aggregated subjective weights of each criterion using equations (12). Step 7: Construct a normalized decision matrix using the following equations x + ij5 = max {x ij5 }, C j B (7) i f ij = f ij = x ij1 = min {x ij1 }, C j C (8) i, x ij2 x +, x ij3 ij5 x +, x ij4 ij5 x +, x ) ij5 ij5 x +, C j B (9) ij5 ( xij1 x + ij5 ( xij1 x ij5, x ij2 x ij5, x ij3 x ij5, x ij4 x, x ij5 ij5 x ij5 ), C j C (10) Step 8: Obtain a best value and worst value by using the following equations: f j + = max f ij (11) i f j = min i f ij (12) where f + j and f j are the best and worst values of all criterion function. Step 9: Calculate the values of S i and R i as follows: n ( f + ) S i = w f j ij j f i + fi j=1 (13) where, w j is calculated by using the ordered weighted averaging (OWA) operator function, which has been adopted from step 7 of the previous algorithm. { ( f + )} R i = max w j f ij j j f i + fi (14) 6 300
7 where w j are the ordered weighted averaging weights of the criteria. Step 10: Calculate the values of Q i as follows: ( Si S ) ( Ri R ) Q j = v + (1 v) S S R R (15) where v is the weight introduced for the strategy of maximum group utility, and 1 v is the weight of the individual regret. S = min S i i S = max i R = min i R = max i Step 11: Rank the alternatives sorting by values S, R and Q in an ascending order. In VIKOR, ascending order is used for ranking. The minimum value gets the maximum rank. The minimum value maintains the cooperative group utility in choosing a compromise solution. Step 12: Alternative which is the best ranked by the measure Q should satisfy the following two conditions: C 1. Acceptable advantage C 2. Acceptable stability in decision making S i R i R i 4 Case Study Study area includes all the 22 blocks of Villupuram district, Tamil Nadu, South India. Through interviews the opinions have been collected from 142 respondents and based on the farming experience we have chosen the following 8 decision makers. The following table (1) represents the farming experience of the farmers who are cultivating maximum number of crops in the Villupuram district
8 Table 1: Sample respondents and their farming experience Name Age Farming Experience D 1 R. Ezhumalai 46 Owns 4.5 acres of agricultural land, with 25 years of farming experience, Sadakatti village. D 2 N. Sivasakthi 47 Owns 4.5 acres, with 15 years of experience, Kandamangalam village. D 3 V. Vedagiri 56 Owns 8 acres, with 20 years of farming experience, Marakkanam. D 4 M. Gopal 71 Owns 12 acres, with 50 years of farming experience, Sennagonam village. D 5 P. Kuppusamy 62 Owns 6 acres, with 50 years of farming experience, Olakkoor village. D 6 P. Pakkiri 50 Owns 7.5 acres, with 26 years of farming experience, Kannaarampattu village. D 7 G. Narasingam 49 Owns 6.75 acres, with 25 years of farming experience, Thirumoondicharam village. D 8 S.Kudiyarasumani 60 Owns 10 acres, with 40 years of farming experience, Mettatthur village. 4.1 Adaptation of the problem The opinions are collected for the following alternatives based on the criterion which is stated as follows: Alternatives A 1 Paddy A 2 Sugarcane A 3 Urad A 4 Groundnut A 5 Tapioca 8 302
9 4.1.2 Criteria C 1 Profit and loss in the yield C 2 Seed quality C 3 Soil quality C 4 Climatic (Sunlight) condition C 5 Water availability C 6 Assistance from government agencies C 7 Assistance from private agencies C 8 Level of underground water C 9 Fixation price of grains C 10 Agriculture loan discount The aggregated pentagonal decision matrix [12] from our previous paper has been taken again to make a comparative study. The criteria are classified with the help of following linguistic variable and its fuzzy linguistic scale values [12] Then the decision matrix characterized by pentagonal fuzzy number is aggregated (12) and the criteria weights are aggregated (12). The following table (2) shows the fuzzy centre value entries of the aggregated pentagonal decision matrix. Table 2: Fuzzy center value of the decision matrix C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 w j A A A A A Then, by using step 7 of a proposed algorithm 1, the ordered weighted averaging weights has been calculated as follows: 9 303
10 Table 3: Ordered weighted averaging (OWA) weights of each alternative w 1j w 2j w 3j w 4j w 5j w 6j w 7j w 8j w 9j w 10j A A A A A Then by using the step 8 of the proposed algorithm 1, the generalized induced ordered weighted averaging weights have been obtained as follows: Table 4: Overall evaluation using generalized induced ordered weighted aeraging (GIOWA) of each alternative A 1 * w 1 (x) A 2 * w 2 (x) A 3 * w 3 (x) A 4 * w 4 (x) A 5 * w 5 (x) C C C C C C C C C C Total Experimental results based on algorithm 1 Then the rank has been obtained as follows:
11 Table 5: Ranking of the alternatives by GIOWA GIOWA Rank weights Paddy st (A 1 ) Sugarcane th (A 2 ) Urad (A 3 ) nd Groundnut rd (A 4 ) Tapioca (A 5 ) th Also, the numerical decision opinions from our previous paper has been processed by the newly proposed algorithm 2 which combines VIKOR characterized by pentagonal decision entries into ordered weighted averaging (OWA) weights. The value of S i and R i is calculated by using step 8 of the proposed algorithm 2, as follows: S 1 = S 2 = S 3 = S 4 = S 5 = Then the value of R i is calculated using the equation 14 as follows: R 1 = R 2 = R 3 = R 4 = R 5 =
12 The value of each Q i by equation 15 is calculated as follows: Q 1 = (0.5) ( ) (1 0.5) ( ) + = 0 ( ) ( ) Q 2 = Q 3 = Q 4 = Q 5 = Experimental results based on algorithm 2 Table 6: The value of S i and R i S i R i Q i A A A A A Table 7: method The ranking of the alternatives by GIOWA-VIKOR Values induced by GIOWA Rank VIKOR method Paddy st (A 1 ) Sugarcane th (A 2 ) Urad (A 3 ) rd Groundnut nd (A 4 ) Tapioca (A 5 ) th
13 5 Comparison of the results obtained from both the algorithms The results obtained from the proposed algorithm 1 (Table 5) and 2 (Table 7) are compared with the result obtained through the extended VIKOR method [12]. From the table 8, we make the following observations. The alternative (A 1 ) Paddy and (A 5 ) Tapioca ranks first and fifth respectively in both the proposed algorithms and whereas Paddy ranks 2 nd in the extended VIKOR technique. The algorithm based on generalized induced ordered weighted averaging operator considers the importance of the criteria weights and evaluates the criteria based on the ordered (decreasing order) decision opinions. By the proposed algorithm GIOWA VIKOR technique, the ordered criteria weight evaluation through VIKOR technique yield a remarkable variation in the values and that leads to the ranking. The alternatives Sugarcane (A 2 ), Urad (A 3 ) and Groundnut (A 4 ) ranks fourth, second and third position by the algorithm 1 and whereas fourth, third and second position form GIOWA VIKOR technique
14 Table 8: Comparative results of extended VIKOR, GIOWA, and GIOWA-VIKOR method Alternatives Extended VIKOR Rank GIOWA weights Rank GIOWA VIKOR method Rank Paddy nd st st (A 1 ) Sugarcane th th th (A 2 ) Urad (A 3 ) rd nd rd Groundnut st rd nd (A 4 ) Tapioca (A 5 ) th th th 6 Conclusion The newly proposed VIKOR techniques shows A 1 (Paddy) is the best compromise crop by satisfying all such criterias involved in evaluating it. Whereas, Sugarcane (A 2 ), Urad (A 3 ) and Groundnut (A 4 ) are the three crops which shows sizeable differences in reaching the best optimum. References 1. R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Management Sciences, 17, 4, (1970), D. Filev and R. R. Yager, On the issue of obtaining OWA operator weights, Fuzzy Sets and Systems, Elsevier Science Publishers, 94, (1998), T. Pathinathan and S. Johnson Savarimuthu, A Historical Overview of VIKOR Model (VIseKriterijumska Optimizacija I Kompromisno Resenje), International Journal of Multidisciplinary Research and Modern Education, 3, 1, (2017),
15 4. T. Pathinathan and S. Johnson Savarimuthu, Multi-Attribute Decision Making in a Dual Hesitant Fuzzy Set using TOP- SIS, International Journal of Engineering Science Invention Research & Development, 2, 1, (2015), T. Pathinathan and S. Johnson Savarimuthu, Pentagonal Hesitant Fuzzy Multi-Attribute Decision Making based on TOP- SIS, International Journal of Technical Research, 3, 5, (2015), T. Pathinathan and S. Johnson Savarimuthu, Trapezoidal Hesitant Fuzzy Multi-Attribute Decision Making Based on TOPSIS, International Archive of Applied Sciences and Technology, 6, 3, (2015), T. Pathinathan and S. Johnson Savarimuthu, Weight based Intuitionistic Fuzzy Set (WBIFS) and it s application to farming, International Journal of Multidisciplinary Research and Modern Education, 3, 1, (2017), T. Pathinathan and Rajkumar, Sieving out the Poor using Fuzzy Tools, International Journal of computing Algorithm (IJCOA), 3, (2014), T. Pathinathan, S. Johnson Savarimuthu and E. Mike Dison, Extended VIKOR Method and its Application to Farming using Pentagonal Fuzzy Numbers, Global Journal of Pure and Applied Mathematics, 13, 9, (2017), Raj Kumar and T. Pathinathan, Analysis of Poverty: Using Fuzzy Triangular Analytical Hierarchy Process, ARPN Journal of Engineering and Applied Sciences, 10, 12, (2015), Raj Kumar and T. Pathinathan, Sieving out the Poor using Fuzzy Decision Making Tools, Indian Journal of Science and Technology, 8, 22, (2015). 12. Z. Xu, An Overview of Methods for Determining OWA Weights, International Journal of Intelligent Systems, 20, (2005),
16 13. Z. Xu, it Linguistic Decision Making: Theory and Methods, Science Press, Beijing, (2012). 14. Z. Xu, Uncertain Multi-Attribute Decision Making: Methods and Applications, Springer-Verlag, Berlin, Heidelberg, (2015). 15. R. R. Yager, Familiees of OWA Operators, Fuzzy Sets and Systems, Elsevier Science Publishers, 59, (1993), R. R. Yager, Induced Ordered Weighted Averaging Operators, IEEE Transactions on Systems, Man and Cybernetics, 29, 2, (1999), R. R. Yager, Interpreting Linguistically Quantified Propositions, International Journal of Intelligent Systems, 9, (1994), R. R. Yager, On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decision Making, IEEE Transactions on Systems, Man and Cybernetics, 18, 1, (1988), R. R. Yager, Quantifier Guided Aggregation Using OWA Operators, International Journal of Intelligent Systems, 2, (1996), R. R. Yager, Quantifiers in the Formulation of Multiple Objective Decision Functions, Information Sciences, 31, (1983), P. L. Yu, A Class of solutions for group decision problems, Management Sciences, 19, 8, P. L. Yu, Multiple Criteria Decision Making: Concepts, Techniques and Extensions, Plenum Press, New York, U.S.A, (1985). 23. L. A. Zadeh, A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges, Journal of Cybernetics, 2, 3, (1972),
17 311
18 312
Similarity 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 informationMultiple Attributes Decision Making Approach by TOPSIS Technique
Multiple Attributes Decision Making Approach by TOPSIS Technique P.K. Parida and S.K.Sahoo Department of Mathematics, C.V.Raman College of Engineering, Bhubaneswar-752054, India. Institute of Mathematics
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 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 informationApplication of Fuzzy Based VIKOR Approach for Multi-Attribute Group Decision Making (MAGDM): A Case Study in Supplier Selection
Decision Making in Manufacturing and Services Vol. 6 2012 No. 1 pp. 25 39 Application of Fuzzy Based VIKOR Approach for Multi-Attribute Group Decision Making (MAGDM): A Case Study in Supplier Selection
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 informationSELECTION OF AGRICULTURAL AIRCRAFT USING AHP AND TOPSIS METHODS IN FUZZY ENVIRONMENT
SELECTION OF AGRICULTURAL AIRCRAFT USING AHP AND TOPSIS METHODS IN FUZZY ENVIRONMENT Gabriel Scherer Schwening*, Álvaro Martins Abdalla** *EESC - USP, **EESC - USP Abstract Considering the difficulty and
More informationDOI /HORIZONS.B P38 UDC :519.8(497.6) COMBINED FUZZY AHP AND TOPSIS METHODFOR SOLVINGLOCATION PROBLEM 1
DOI 10.20544/HORIZONS.B.03.1.16.P38 UD 656.96:519.8(497.6) OMBINED FUZZY AHP AND TOPSIS METHODFOR SOLVINGLOATION PROBLEM 1 Marko Vasiljević 1, Željko Stević University of East Sarajevo Faculty of Transport
More informationTRIANGULAR INTUITIONISTIC FUZZY AHP AND ITS APPLICATION TO SELECT BEST PRODUCT OF NOTEBOOK COMPUTER
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 10 2017, 253 261 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu TRIANGULAR
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 informationExtended TOPSIS model for solving multi-attribute decision making problems in engineering
Decision Science Letters 6 (2017) 365 376 Contents lists available at GrowingScience Decision Science Letters homepage: www.growingscience.com/dsl Extended TOPSIS model for solving multi-attribute decision
More informationA NEW MULTI-CRITERIA EVALUATION MODEL BASED ON THE COMBINATION OF NON-ADDITIVE FUZZY AHP, CHOQUET INTEGRAL AND SUGENO λ-measure
A NEW MULTI-CRITERIA EVALUATION MODEL BASED ON THE COMBINATION OF NON-ADDITIVE FUZZY AHP, CHOQUET INTEGRAL AND SUGENO λ-measure S. Nadi a *, M. Samiei b, H. R. Salari b, N. Karami b a Assistant Professor,
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 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 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 informationPackage MCDM. September 22, 2016
Type Package Package MCDM September 22, 2016 Title Multi-Criteria Decision Making Methods for Crisp Data Version 1.2 Date 2016-09-21 Author Blanca A. Ceballos Martin Maintainer
More informationPROJECT SCHEDULING FOR NETWORK PROBLEMS USING JOB SEQUENCING TECHNIQUE
Volume 114 No. 6 2017, 153-159 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu PROJECT SCHEDULING FOR NETWORK PROBLEMS USING JOB SEQUENCING TECHNIQUE
More informationMulti Attribute Decision Making Approach for Solving Intuitionistic Fuzzy Soft Matrix
Intern. J. Fuzzy Mathematical Archive Vol. 4 No. 2 2014 104-114 ISSN: 2320 3242 (P) 2320 3250 (online) Published on 22 July 2014 www.researchmathsci.org International Journal of Multi Attribute Decision
More informationCHAPTER 4 MAINTENANCE STRATEGY SELECTION USING TOPSIS AND FUZZY TOPSIS
59 CHAPTER 4 MAINTENANCE STRATEGY SELECTION USING TOPSIS AND FUZZY TOPSIS 4.1 INTRODUCTION The development of FAHP-TOPSIS and fuzzy TOPSIS for selection of maintenance strategy is elaborated in this chapter.
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 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 informationA new approach for ranking trapezoidal vague numbers by using SAW method
Science Road Publishing Corporation Trends in Advanced Science and Engineering ISSN: 225-6557 TASE 2() 57-64, 20 Journal homepage: http://www.sciroad.com/ntase.html A new approach or ranking trapezoidal
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 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 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 informationMulti-Objective Fuzzy Fully Linear Programming Transportation Problem using Ranking Function
Volume 117 No. 13 2017, 63-68 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Multi-Objective Fuzzy Fully Linear Programming Transportation Problem
More informationCollaborative Rough Clustering
Collaborative Rough Clustering Sushmita Mitra, Haider Banka, and Witold Pedrycz Machine Intelligence Unit, Indian Statistical Institute, Kolkata, India {sushmita, hbanka r}@isical.ac.in Dept. of Electrical
More informationGOAL GEOMETRIC PROGRAMMING PROBLEM (G 2 P 2 ) WITH CRISP AND IMPRECISE TARGETS
Volume 4, No. 8, August 2013 Journal of Global Research in Computer Science REVIEW ARTICLE Available Online at www.jgrcs.info GOAL GEOMETRIC PROGRAMMING PROBLEM (G 2 P 2 ) WITH CRISP AND IMPRECISE TARGETS
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 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 informationFuzzy bi-level linear programming problem using TOPSIS approach
FUZZY OPTIMIZATION AND MODELLING (08) -0 Contents lists available at FOMJ Fuzzy Optimization and Modelling Journal homepage: http://fomj.qaemiau.ac.ir/ Fuzzy bi-level linear programming problem using TOPSIS
More informationDecision Support System Best Employee Assessments with Technique for Order of Preference by Similarity to Ideal Solution
Decision Support System Best Employee Assessments with Technique for Order of Preference by Similarity to Ideal Solution Jasri 1, Dodi Siregar 2, Robbi Rahim 3 1 Departement of Computer Engineering, Universitas
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 informationSelection of Best Web Site by Applying COPRAS-G method Bindu Madhuri.Ch #1, Anand Chandulal.J #2, Padmaja.M #3
Selection of Best Web Site by Applying COPRAS-G method Bindu Madhuri.Ch #1, Anand Chandulal.J #2, Padmaja.M #3 Department of Computer Science & Engineering, Gitam University, INDIA 1. binducheekati@gmail.com,
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 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 informationFACILITY LIFE-CYCLE COST ANALYSIS BASED ON FUZZY SETS THEORY Life-cycle cost analysis
FACILITY LIFE-CYCLE COST ANALYSIS BASED ON FUZZY SETS THEORY Life-cycle cost analysis J. O. SOBANJO FAMU-FSU College of Engineering, Tallahassee, Florida Durability of Building Materials and Components
More informationSome Properties of Interval Valued Intuitionistic Fuzzy Sets of Second Type
Some Properties of Interval Valued Intuitionistic Fuzzy Sets of Second Type K. Rajesh 1, R. Srinivasan 2 Ph. D (Full-Time) Research Scholar, Department of Mathematics, Islamiah College (Autonomous), Vaniyambadi,
More informationA Study on Fuzzy AHP method and its applications in a tie-breaking procedure
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 6 (2017), pp. 1619-1630 Research India Publications http://www.ripublication.com A Study on Fuzzy AHP method and its applications
More informationTRIANGULAR FUZZY MULTINOMIAL CONTROL CHART WITH VARIABLE SAMPLE SIZE USING α CUTS
TRIANGULAR FUZZY MULTINOMIAL CONTROL CHART WITH VARIABLE SAMPLE SIZE USING α CUTS S.Selva Arul Pandian Assistant Professor (Sr.) in Statistics, Department of Mathematics, K.S.R College of Engineering,
More informationApplication of the Fuzzy AHP Technique for Prioritization of Requirements in Goal Oriented Requirements Elicitation Process
Application of the Fuzzy AHP Technique for Prioritization of Requirements in Goal Oriented Requirements Elicitation Process Rajesh Avasthi PG Scholar, Rajasthan India P. S. Sharma Research Scholar, Rajasthan
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 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 informationA Comparative Study on Optimization Techniques for Solving Multi-objective Geometric Programming Problems
Applied Mathematical Sciences, Vol. 9, 205, no. 22, 077-085 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/ams.205.42029 A Comparative Study on Optimization Techniques for Solving Multi-objective
More informationA Triangular Fuzzy Model for Decision Making
American Journal of Computational and Applied Mathematics 04, 4(6): 9-0 DOI: 0.93/j.ajcam.040406.03 A Triangular uzzy Model for Decision Making Michael Gr. Voskoglou School of Technological Applications,
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 informationOptimization with linguistic variables
Optimization with linguistic variables Christer Carlsson christer.carlsson@abo.fi Robert Fullér rfuller@abo.fi Abstract We consider fuzzy mathematical programming problems (FMP) in which the functional
More informationMODELING PERFORMANCE OF LOGISTICS SUBSYSTEMS USING FUZZY APPROACH
TRANSPORT & LOGISTICS: the International Journal Article history: Received 02 February 2017 Accepted 18 March 2017 Available online 07 April 2017 ISSN 2406-1069 Article citation info: Stević, Ž., Modeling
More informationShortest Path Problem in Network with Type-2 Triangular Fuzzy Arc Length
J. Appl. Res. Ind. Eng. Vol. 4, o. (207) 7 Journal of Applied Research on Industrial Engineering www.journal-aprie.com Shortest Path Problem in etwork with Type-2 Triangular Fuzzy Arc Length Ranjan Kumar
More informationRank Similarity based MADM Method Selection
Rank Similarity based MADM Method Selection Subrata Chakraborty School of Electrical Engineering and Computer Science CRC for Infrastructure and Engineering Asset Management Queensland University of Technology
More informationCHAPTER 4 FUZZY LOGIC, K-MEANS, FUZZY C-MEANS AND BAYESIAN METHODS
CHAPTER 4 FUZZY LOGIC, K-MEANS, FUZZY C-MEANS AND BAYESIAN METHODS 4.1. INTRODUCTION This chapter includes implementation and testing of the student s academic performance evaluation to achieve the objective(s)
More informationCHAPTER IX MULTI STAGE DECISION MAKING APPROACH TO OPTIMIZE THE PRODUCT MIX IN ASSIGNMENT LEVEL UNDER FUZZY GROUP PARAMETERS
CHAPTER IX MULTI STAGE DECISION MAKING APPROACH TO OPTIMIZE THE PRODUCT MIX IN ASSIGNMENT LEVEL UNDER FUZZY GROUP PARAMETERS Introduction: Aryanezhad, M.B [2004] showed that one of the most important decisions
More informationSolving a Decision Making Problem Using Weighted Fuzzy Soft Matrix
12 Solving a Decision Making Problem Using Weighted Fuzzy Soft Matrix S. Senthilkumar Department of Mathematics,.V.C. College (utonomous), Mayiladuthurai-609305 BSTRCT The purpose of this paper is to use
More informationA framework for fuzzy models of multiple-criteria evaluation
INTERNATIONAL CONFERENCE ON FUZZY SET THEORY AND APPLICATIONS Liptovský Ján, Slovak Republic, January 30 - February 3, 2012 A framework for fuzzy models of multiple-criteria evaluation Jana Talašová, Ondřej
More informationON SOLVING A MULTI-CRITERIA DECISION MAKING PROBLEM USING FUZZY SOFT SETS IN SPORTS
ISSN Print): 2320-5504 ISSN Online): 2347-4793 ON SOLVING A MULTI-CRITERIA DECISION MAKING PROBLEM USING FUZZY SOFT SETS IN SPORTS R. Sophia Porchelvi 1 and B. Snekaa 2* 1 Associate Professor, 2* Research
More informationA NEW METHOD FOR SOLVING TWO VEHICLE COST VARYING FUZZY TRANSPORTATION PROBLEM
ISSN: 0975-766X CDEN: IJPTFI Available nline through esearch Article www.ptonline.com A NEW METHD F SLVING TW VEHICLE CST VAYING FUZZY TANSPTATIN PBLEM D.Kalpanapriya* and D.Anuradha Department of Mathematics
More informationFuzzy Reasoning. Linguistic Variables
Fuzzy Reasoning Linguistic Variables Linguistic variable is an important concept in fuzzy logic and plays a key role in its applications, especially in the fuzzy expert system Linguistic variable is a
More informationA TOPSIS Method-based Approach to Machine Tool Selection
Proceedings of the 2010 International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh, January 9 10, 2010 A TOPSIS Method-based Approach to Machine Tool Selection Vijay
More informationA TOPSIS Method-based Approach to Machine Tool Selection
Proceedings of the 200 International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh, January 9 0, 200 A TOPSIS Method-based Approach to Machine Tool Selection Viay Manikrao
More informationA New pivotal operation on Triangular Fuzzy number for Solving Fully Fuzzy Linear Programming Problems
International Journal of Applied Mathematical Sciences ISSN 0973-0176 Volume 9, Number 1 (2016), pp. 41-46 Research India Publications http://www.ripublication.com A New pivotal operation on Triangular
More informationMultiple-Criteria Fuzzy Evaluation: The FuzzME Software Package
Multiple-Criteria Fuzzy Evaluation: The FuzzME Software Package Jana Talašová 1 Pavel Holeček 2 1., 2. Faculty of Science, Palacký University Olomouc tř. Svobody 26, 771 46 Olomouc, Czech Republic Email:
More informationSolution of m 3 or 3 n Rectangular Interval Games using Graphical Method
Australian Journal of Basic and Applied Sciences, 5(): 1-10, 2011 ISSN 1991-8178 Solution of m or n Rectangular Interval Games using Graphical Method Pradeep, M. and Renukadevi, S. Research Scholar in
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 informationSELECTION OF CREATIVE INDUSTRY SECTOR ICT SUITABLE DEVELOPED IN PESANTREN USING FUZZY - AHP
SELECTION OF CREATIVE INDUSTRY SECTOR ICT SUITABLE DEVELOPED IN PESANTREN USING FUZZY - AHP 1 HOZAIRI, 2 AHMAD 1 Islamic University Of Madura, Faculty Of Engineering, Informatics Engineering Study Program
More information[Rao* et al., 5(9): September, 2016] ISSN: IC Value: 3.00 Impact Factor: 4.116
IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY MULTI-OBJECTIVE OPTIMIZATION OF MRR, Ra AND Rz USING TOPSIS Ch. Maheswara Rao*, K. Jagadeeswara Rao, K. Laxmana Rao Department
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 informationFuzzy rule-based decision making model for classification of aquaculture farms
Chapter 6 Fuzzy rule-based decision making model for classification of aquaculture farms This chapter presents the fundamentals of fuzzy logic, and development, implementation and validation of a fuzzy
More informationComputation of Fuzzy Analytic Hierarchy Process (FAHP) using MATLAB Programming in Sustainable Supply Chain
Computation of Fuzzy Analytic Hierarchy Process (FAHP) using MATLAB Programming in Sustainable Supply Chain 1a Ahamad Zaki Mohamed Noor, 1b Muhammad Hafidz Fazli Md Fauadi, 1c Nur Zul Hafiq Zulkifli, 1d
More informationIZAR THE CONCEPT OF UNIVERSAL MULTICRITERIA DECISION SUPPORT SYSTEM
Jana Kalčevová Petr Fiala IZAR THE CONCEPT OF UNIVERSAL MULTICRITERIA DECISION SUPPORT SYSTEM Abstract Many real decision making problems are evaluated by multiple criteria. To apply appropriate multicriteria
More informationResearch Article QOS Based Web Service Ranking Using Fuzzy C-means Clusters
Research Journal of Applied Sciences, Engineering and Technology 10(9): 1045-1050, 2015 DOI: 10.19026/rjaset.10.1873 ISSN: 2040-7459; e-issn: 2040-7467 2015 Maxwell Scientific Publication Corp. Submitted:
More informationApplication of Intuitionist Fuzzy Soft Matrices in Decision Making Problem by Using Medical Diagnosis
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn:2319-765x. Volume 10, Issue 3 Ver. VI (May-Jun. 2014), PP 37-43 Application of Intuitionist Fuzzy Soft Matrices in Decision Making Problem
More informationQUALITATIVE MODELING FOR MAGNETIZATION CURVE
Journal of Marine Science and Technology, Vol. 8, No. 2, pp. 65-70 (2000) 65 QUALITATIVE MODELING FOR MAGNETIZATION CURVE Pei-Hwa Huang and Yu-Shuo Chang Keywords: Magnetization curve, Qualitative modeling,
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 informationMulti-Criteria Decision Making 1-AHP
Multi-Criteria Decision Making 1-AHP Introduction In our complex world system, we are forced to cope with more problems than we have the resources to handle We a framework that enable us to think of complex
More informationOperations on Intuitionistic Trapezoidal Fuzzy Numbers using Interval Arithmetic
Intern. J. Fuzzy Mathematical Archive Vol. 9, No. 1, 2015, 125-133 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 8 October 2015 www.researchmathsci.org International Journal of Operations on Intuitionistic
More informationPRODUCT DESIGN AND PROCESS SELECTION - ECONOMIC ANALYSIS
PRODUCT DESIGN AND PROCESS SELECTION - ECONOMIC ANALYSIS M.Tech Second Stage Project Report by Nitin R. Dhane (Roll No : 98310021) Under the guidance of Prof. B. RAVI Department of Mechanical Engineering
More informationBackground. Advanced Remote Sensing. Background contd. Land is a scarce resource. Lecture-5
Advanced Remote Sensing Lecture-5 Multi Criteria Evaluation contd. Background Multicriteria analysis appeared in the 1960s as a decisionmaking tool. It is used to make a comparative assessment of alternative
More informationA compromise method for solving fuzzy multi objective fixed charge transportation problem
Lecture Notes in Management Science (2016) Vol. 8, 8 15 ISSN 2008-0050 (Print), ISSN 1927-0097 (Online) A compromise method for solving fuzzy multi objective fixed charge transportation problem Ratnesh
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 informationHARD, SOFT AND FUZZY C-MEANS CLUSTERING TECHNIQUES FOR TEXT CLASSIFICATION
HARD, SOFT AND FUZZY C-MEANS CLUSTERING TECHNIQUES FOR TEXT CLASSIFICATION 1 M.S.Rekha, 2 S.G.Nawaz 1 PG SCALOR, CSE, SRI KRISHNADEVARAYA ENGINEERING COLLEGE, GOOTY 2 ASSOCIATE PROFESSOR, SRI KRISHNADEVARAYA
More informationFUZZY LOGIC TECHNIQUES. on random processes. In such situations, fuzzy logic exhibits immense potential for
FUZZY LOGIC TECHNIQUES 4.1: BASIC CONCEPT Problems in the real world are quite often very complex due to the element of uncertainty. Although probability theory has been an age old and effective tool to
More informationChapter 6 Multicriteria Decision Making
Chapter 6 Multicriteria Decision Making Chapter Topics Goal Programming Graphical Interpretation of Goal Programming Computer Solution of Goal Programming Problems with QM for Windows and Excel The Analytical
More informationFuzzy time series forecasting of wheat production
Fuzzy time series forecasting of wheat production Narendra kumar Sr. lecturer: Computer Science, Galgotia college of engineering & Technology Sachin Ahuja Lecturer : IT Dept. Krishna Institute of Engineering
More informationComparison of Multi Criteria Decision Making Algorithms for Ranking Cloud Renderfarm Services
Indian Journal of Science and Technology, Vol 9(31), DOI: 10.17485/ijst/2016/v9i31/93467, August 2016 ISSN (Print) : 0974-6846 ISSN (Online) : 0974-5645 Comparison of Multi Criteria Decision Making Algorithms
More informationUsing Index Matrices for Handling Multiple Scenarios in Decision Making
Using Index Matrices for Handling Multiple Scenarios in Decision Making Guy de Tré 1, S lawomir Zadrożny 2, Sotir Sotirov 3 and Krassimir Atanassov 4 1 Ghent University Department of Telecommunications
More informationMULTI-OBJECTIVE PROGRAMMING FOR TRANSPORTATION PLANNING DECISION
MULTI-OBJECTIVE PROGRAMMING FOR TRANSPORTATION PLANNING DECISION Piyush Kumar Gupta, Ashish Kumar Khandelwal, Jogendra Jangre Mr. Piyush Kumar Gupta,Department of Mechanical, College-CEC/CSVTU University,Chhattisgarh,
More informationOptimal Solution of a Mixed type Fuzzy Transportation Problem
Intern. J. Fuzzy Mathematical Archive Vol. 15, No. 1, 2018, 83-89 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 20 March 2018 www.researchmathsci.org DOI: http://dx.doi.org/10.22457/ijfma.v15n1a8
More informationTHE VARIABILITY OF FUZZY AGGREGATION METHODS FOR PARTIAL INDICATORS OF QUALITY AND THE OPTIMAL METHOD CHOICE
THE VARIABILITY OF FUZZY AGGREGATION METHODS FOR PARTIAL INDICATORS OF QUALITY AND THE OPTIMAL METHOD CHOICE Mikhail V. Koroteev 1, Pavel V. Tereliansky 1, Oleg I. Vasilyev 2, Abduvap M. Zulpuyev 3, Kadanbay
More informationSome Properties of Soft -Open Sets in Soft Topological Space
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn:2319-765x. Volume 9, Issue 6 (Jan. 2014), PP 20-24 Some Properties of Soft -Open Sets in Soft Topological Space a Gnanambal Ilango, b B.
More informationFUZZY DIAGONAL OPTIMAL ALGORITHM TO SOLVE INTUITIONISTIC FUZZY ASSIGNMENT PROBLEMS
International Journal of Civil Engineering and Technology IJCIET Volume 9, Issue 11, November 2018, pp. 378 383, Article ID: IJCIET_09_11_037 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=9&itype=10
More informationSimultaneous Perturbation Stochastic Approximation Algorithm Combined with Neural Network and Fuzzy Simulation
.--- Simultaneous Perturbation Stochastic Approximation Algorithm Combined with Neural Networ and Fuzzy Simulation Abstract - - - - Keywords: Many optimization problems contain fuzzy information. Possibility
More informationAn expert module to improve the consistency of AHP matrices
Intl. Trans. in Op. Res. (2004) 97 05 INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH An epert module to improve the consistency of AHP matrices A. Ishizaka and M. Lusti WWZ/Information Systems, University
More informationMethod and Algorithm for solving the Bicriterion Network Problem
Proceedings of the 00 International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh, anuary 9 0, 00 Method and Algorithm for solving the Bicriterion Network Problem Hossain
More informationRanking Efficient Units in DEA. by Using TOPSIS Method
Applied Mathematical Sciences, Vol. 5, 0, no., 805-85 Ranking Efficient Units in DEA by Using TOPSIS Method F. Hosseinzadeh Lotfi, *, R. Fallahnead and N. Navidi 3 Department of Mathematics, Science and
More informationINFORMATION RETRIEVAL SYSTEM USING FUZZY SET THEORY - THE BASIC CONCEPT
ABSTRACT INFORMATION RETRIEVAL SYSTEM USING FUZZY SET THEORY - THE BASIC CONCEPT BHASKAR KARN Assistant Professor Department of MIS Birla Institute of Technology Mesra, Ranchi The paper presents the basic
More informationDESIGNING A MODEL OF INTUITIONISTIC FUZZY VIKOR IN MULTI-ATTRIBUTE GROUP DECISION-MAKING PROBLEMS
Iranian Journal of Fuzzy Systems Vol. 13, No. 1, (2016) pp. 45-65 45 DESIGNING A MODEL OF INTUITIONISTIC FUZZY VIKOR IN MULTI-ATTRIBUTE GROUP DECISION-MAKING PROBLEMS S. M. MOUSAVI, B. VAHDANI AND S. SADIGH
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 informationWEB STRUCTURE MINING USING PAGERANK, IMPROVED PAGERANK AN OVERVIEW
ISSN: 9 694 (ONLINE) ICTACT JOURNAL ON COMMUNICATION TECHNOLOGY, MARCH, VOL:, ISSUE: WEB STRUCTURE MINING USING PAGERANK, IMPROVED PAGERANK AN OVERVIEW V Lakshmi Praba and T Vasantha Department of Computer
More informationGenetic Tuning for Improving Wang and Mendel s Fuzzy Database
Proceedings of the 2009 IEEE International Conference on Systems, Man, and Cybernetics San Antonio, TX, USA - October 2009 Genetic Tuning for Improving Wang and Mendel s Fuzzy Database E. R. R. Kato, O.
More informationMulti objective linear programming problem (MOLPP) is one of the popular
CHAPTER 5 FUZZY MULTI OBJECTIVE LINEAR PROGRAMMING PROBLEM 5.1 INTRODUCTION Multi objective linear programming problem (MOLPP) is one of the popular methods to deal with complex and ill - structured decision
More information