AGGREGATION OF FUZZY OPINIONS UNDER GROUP DECISION-MAKING BASED ON SIMILARITY AND DISTANCE

In this article,a new method for aggregating fuzzy individual opinions into a group consensusopinion is proposed.To obtain the aggregation weights of each individual opinion,a consistency indexof each expert with the other experts is introduced based on similarity and distance.The importance ofeach expert is also taken into consideration in the process of aggregation.Finally.a numerical exampleis presented to illustrate the efficiency of the procedure.     

AN EXTENSION OF TOPSIS FOR FUZZY MCDM BASED ON VAGUE SET THEORY

1.Introduction The multicriteria decision-making problem(Kickert1978)is a kind of problem that all the alternatives in the choice set can be evaluated according to a number of criteria.A MCDM problem can be concisely expressed in matrix format as C1C2C n11112122122212nnm m m mnA x x xMA x x xA x x x=W={w1,w2,,wn}where A1,A2,,Am are possible alternatives among which decision-makers have to choose,C1,C2,,C n are the criteria with which alternative performance are measured,xi j is the rati…     

COMPATIBLE EXTENSIONS OF FUZZY RELATIONS

In 1930 Szpilrajn proved that any strict partial order can be embedded in a strict linear order.This theorem was later refined by Dushnik and Miller(1941),Hansson(1968), Suzumura(1976),Donaldson and Weymark(1998), Bossert(1999). Particularly Suzumura introduced the important concept of compatible extension of a(crisp)relation.These extension theorems have an important role in welfare economics. In particularSzpilrajn theorem is the main tool for proving a known theorem of Richter that establishes theequivalence between rational and congruous consumers. In 1999 Duggan proved a general extensiontheorem that contains all these results. In this paper we introduce the notion of compatible extension of a fuzzy relation and we provean extension theorem for fuzzy relations. Our result generalizes to fuzzy set theory the main part ofDuggan's theorem. As applications we obtain fuzzy versions of the theorems of Szpilrajn, Hanssonand Suzumura. We also prove that an asymmetric and transitive fuzzy relation has a com     

MARKOV FUZZY CRITERION DECISION MODELS

1.IlltroductionMarkovdecisionmodels(MDMforshort)havebeenextensivelystudiedandagreatmanyresu1tshavebeenobtainedsincel95O's(e.g.,see[1-6]).Alltheseworks,asfarasweknow,arebasedonthefactthattheoptimalityindexesareab1etobemeaJsuredaccurately.However,inthepracticalproblem,thereasonableandaccurateindexesdonotalwaysexist,andevenso5theirvaluesarenoteasytoacquiresometimes.ThisfactlimitstheapplicationofMDMtosomeextent.FuIthermore,forcomplicatedmodelswithmultipleindexesitmaybedifficulttofindanoptimals…     

FUZZY ORDER EQUIVALENT CLASS WITH UNCERTAINTY

1. Introduction The AHP (Analytic Hierarchy Process), an analyzing method of multi-attribute and multi-criterion decision making, was first put forward by the American scientist Saaty. It decomposes a complicated problem into several levels in order to make the analysis of the original problem much simpler and quantifying the decision maker's subjective comparison (Saaty 1980, Saaty & Vargas 1987, Saaty 1990, Saaty 2003). However, there is an extensive literature which addresses the situa…     

AN EMBEDDING OPERATOR FOR FUZZY NUMBER SPACE E~1 AND ITS APPLICATION FOR FUZZY INTEGRAL

In this paper,we give an order-preserving,isometric and isomorphic embeddingoperator from the fuzzy number space E~1 to a classical Banach space and show some necessary andsufficient integrability conditions of fuzzy integrals which were defined by M.Matloka and O.Kaleva by means of such an operator.     

A TWO-PHASE APPROACH TO FUZZY SYSTEM IDENTIFICATION

A two-phase approach to fuzzy system identification is proposed. The first phase produces a baseline design to identify a prototype fuzzy system for a target system from a collection of input-output data pairs. It uses two easily implemented clustering techniques: the subtractive clustering method and the fuzzy c-means (FCM) clustering algorithm. The second phase (fine tuning) is executed to adjust the parameters identified in the baseline design. This phase uses the steepest descent and recursive least-squares estimation methods. The proposed approach is validated by applying it to both a function approximation type of problem and a classification type of problem. An analysis of the learning behavior of the proposed approach for the two test problems is conducted for further confirmation.     

MERGING FUZZY STATISTICAL DATA WITH IMPRECISE PRIOR INFORMATION

1. Introduction Solving complex decision problems can be regarded as processing of information of different kind coming from various sources. Objective information related to stochastic phenomena that describe the environment of the decision situation can be treated as statistical data. If only such information is available, then the complex decision problem may be reduced to a simpler problem of a statistical decision. However, existing statistical data are usually not sufficient enough to so…     

UNDERSTANDING OF FUZZY OPTIMIZATION： THEORIES AND METHODS

A brief summary on and comprehensive understanding of fuzzy optimizationis presented. This summary is made on aspects of fuzzy modelling and fuzzy optimization,classification and formulation for the fuzzy optimization problems, models and methods.The importance of interpretation of the problem and formulation of the optimal solutionin fuzzy sense are emphasized in the summary of the fuzzy optimization.     

FUZZY MODELS FOR ESTIMATION OF SURFACE GROUND SUBSIDENCE

In this paper,the mathematical theory of fuzzy probability is used for theproblems of rock mass mechanics due to excavation,especially mining.A mathematicalmodel is developed for the movement and deformation of rock mass on the basis of theassumption that the displacement and deformation of rock mass is a fuzzy event,and fromthis model theoretical formulas are derived for calculating the displacement of rock massdue to excavationThe theories of both the two-and three-dimensional problems are developed and appliedto the analysis of engineering problems in excavation.The agreement of the theoreticalresults with the field measurements shows that our model is satisfactory and the formulaeobtained are valid and thus can be effectively used for predicting the displacements anddeformations and the safety evaluation of the buildings on the ground surface.     

ON ALGEBRICO-DIFFERENTIAL EQUATIONS-SOLVING

The char-set method of polynomial equations-solving is naturally extended to the differential case which gives rise to an algorithmic method of solving arbitrary systems of algebrico-differential equations. As an illustration of the method, the Devil's Problem of Pommaret is solved in details.     

FUZZY MULTI-LEVEL WAREHOUSE LAYOUT PROBLEM： NEW MODEL AND ALGORITHM

1. Introduction As we know, in most manufactory, above all in large-scale manufactory, warehouse operation is an important part of a manufacturer's material handling operation. Effective warehouse planning can not only reduce material handling cost but also increase productivity. Hence, it is very important for the manufacturer to make the best plan to manage the warehouse. The warehouse layout problem concerns how to place different items into the warehouse so that people resources, equipment…     

FUZZY SATISFYING INTERACTIVE MULTIOBJECTIVE THERMAL POWER DISPATCH： SWT APPROACH

In multiobjective optimization, trade-off analysis plays an important role in determining most preferred solution. This paper presents an explicit interactive trade-off analysis based on the surrogate worth trade-off function to determine the best compromised solution. In the multiobjective framework thermal power dispatch problem is undertaken in which four objectives viz. cost, NOx emission, SOx emission and COx emission are minimized simultaneously. The interactive process is implemented using a weighting method by regulating the relative weights of objectives in systematic manner. Hence the weighting method facilitates to simulate the trade-offrelation between the conflicting objectives in non-inferior domain. Exploiting fuzzy decision making theory to access the indifference band, interaction with the decision maker is obtained via surrogate worth trade-off （SWT） functions of the objectives. The surrogate worth trade-off functions are constructed in the functional space and then transformed into the decision space, so the surrogate worth trade-off functions of objectives relate the decision maker＇s preferences to non-inferior solutions through optimal weight patterns. The optimal solution of thermal power dispatch problem is obtained by considering real and reactive power losses. Decoupled load flow analysis is performed to find the transmission losses. The validity of the proposed method is demonstrated on 11-bus, 17-lines IEEE system, comprising of three generators.     

LOWER BOUND ON K-SEQUENCE

1.IntroductionK-sequenceswereilltroducedbyKl0vein[1]-Itisaclassofsequencesthatinparticularcoatainsthesonarsequences[2]andBh-sequences.Resultsthatwerepreviouslyconsideredforeach0fthesesubclassescaninmanycasesbegeneralizedtoK-sequencesandbegivenaunifiedtreatment.Thesesequenceshaveanumber0fapplicati0ns.F0rinstance,Bh-sequenceswereappliedininterm0dulation-freefrequenciesassignment(see[3,4]).AclassofK-sequencesnotpreviouslyconsideredwereimportaninaconstructionofilltermodulationfreefrequenciesass…     

ON APPROXIMATION BY SPHERICAL ZONAL TRANSLATION NETWORKS BASED ON BOCHNER-RIESZ MEANS

A sequence of spherical zonal translation networks based on the Bochner-Riesz means of spherical harmonics and the Riesz means of Jacobi polynomials is introduced, and its degree of approximation is achieved. The results obtained in the present paper actually imply that the approximation of zonal translation networks is convergent if the action functions have certain smoothness.     

ON SERVICES RESEARCH AND EDUCATION

1. Pertinent Background The importance of the services sector can not be overstated (Tien, 2006); it employs a large and growing proportion of workers in the industrialized nations. As reflected in Table 1, the services sector includes a number of large industries; indeed, services employment in the U.S. is at 82.1 percent, while the remaining four economic sectors (i.e., manufacturing, agriculture, construction, and mining), which together can be considered to be the “goods” sector, emplo…     

A NOTE ON THE PAPER "ON THE CONNECTIVITY OF CAYLEY COLOR GRAPHS

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