a fusion approach for managing multi granularity linguistic term sets in decision making the aim of this paper is to present a fusion approach of multi granularity linguistic information for managing information assessed in different linguistic term sets multi granularity linguistic term sets together with its application in a decision making problem with multiple information sources assuming that the linguistic performance values given to the alternatives by the different sources are represented in linguistic term sets with different granularity and or semantic in this context a decision process based on two steps is proposed with a view to obtaining the solution set of alternatives first the fusion of the multi granularity linguistic performance values is carried out in order to obtain collective performance evaluations in this step on the one hand the multi granularity linguistic information is made uniform using a linguistic term set as the uniform representation base the basic linguistic term set on the other hand the collective performance evaluations of the alternatives are obtained by means of an aggregation operator being fuzzy sets on the basic linguistic term set second the choice of the best alternative s from the collective performance evaluations is performed to do that a fuzzy preference relation is computed from the collective performance evaluations using a ranking method of pairs of fuzzy sets in the setting of possibility theory applied to fuzzy sets on the basic linguistic term set then a choice degree may be applied on the preference relation in order to rank the alternatives

a fuzzy simple additive weighting system under group decision making for facility location selection with objective subjective attributes this work presents a new fuzzy multiple attributes decision making fmadm approach i e fuzzy simple additive weighting system fsaws for solving facility location selection problems by using objective subjective attributes under group decision making gdm conditions the proposed system integrates fuzzy set theory fst the factor rating system frs and simple additive weighting saw to evaluate facility locations alternatives the fsaws is applied to deal with both qualitative and quantitative dimensions the fsaws process considers the importance of each decision maker and the total scores for alternative locations are then derived by homo heterogeneous group of decision makers finally a numerical example illustrates the procedure of the proposed fsaws

abstract minimality and circumscription abstract in this paper we present an alternative approach to the generalization of circumscription traditionally the generalization of circumscription involves the change of ordering among models while in the present study we only try to generalize the minimality criteria of models we define the notion of abstractly minimal or p z minimal models by isomorphism under this generalization we come up with the fact that some theories which are unsatisfiable in the original circumscription will be satisfiable now moreover we prove that this generalization is completely coincident with the original circumscription in the case of well founded theories

the suprem architecture a new intelligent paradigm abstract we investigate the model theory of the notion of circumscription and find completeness theorems that provide a partial converse to a result of mccarthy we show that the circumscriptive theorems are precisely the truths of the minimal models in the case of various classes of theories and for various versions of circumscription we also present an example of commonsense reasoning in which first order circumscription does not achieve the intuitive and desired minimization

on bounds for the effective differential nullstellensatz abstract understanding bounds for the effective differential nullstellensatz is a central problem in differential algebraic geometry recently several bounds have been obtained using dicksonian and antichains sequences with a given growth rate in the present paper we make these bounds more explicit and therefore more applicable to understanding the computational complexity of the problem which is essential to designing more efficient algorithms

a linguistic decision model for promotion mix management solved with genetic algorithms promotion activities are those marketing tools that have a fast and direct impact in the target market due to this fact the selection of such activities is an important decision this contribution attempts to devise a decision process for this problem in conditions of uncertainty supplying a linguistic decision model for evaluating the satisfaction of the objectives by the potential solutions the process uses a genetic algorithm to find a good solution in promotion selection such that it will both accomplish the communication objectives of the company and minimise the invested amount

the importance of open and recursive circumscription research note abstract circumscription is known to result in an inconsistency when applied to certain consistent theories to counter this problem closed nonrecursive circumscription a restricted form of circumscription that has been proved not to affect the consistency of the theory over which circumscription is applied has been proposed we show that closed nonrecursive circumscription involves an excessive weakening of standard circumscription by establishing that closed nonrecursive circumscription is incomplete for some crucial theories over which standard circumscription is consistent and complete first we prove that closed circumscription cannot yield the desired uniqueness formula for the simplest of existential theories second we prove that nonrecursive circumscription fails to be as strong as predicate completion for horn clause theories third we prove that the natural way to strengthen circumscription that is adding more variable predicates may weaken nonrecursive circumscription

linguistic multiperson decision making based on the use of multiple preference relations in multiperson decision making situations it is quite natural that different decision makers who may have different background and knowledge will provide their preferences by different kinds of preference relations this paper proposes a linguistic multiperson decision making model lmdmm based on linguistic preference relations integrating fuzzy preference relations different types of multiplicative preference relations and multigranular linguistic preference relations in the lmdmm several transformation functions are first obtained to relate fuzzy preference relations and different types of multiplicative preference relations with multigranular linguistic preference relations then we design the selection process of the lmdmm based on the use of the fuzzy majority and the extended ordered weighted averaging operator or the 2 tuple ordered weighted averaging operator and discuss conditions under which the proposed selection process satisfies the social choice axioms at last we analyze the internal consistency of the proposed transformation functions the results in this paper are helpful to complete chiclana et al s fuzzy decision model integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations fuzzy sets and systems 97 1998 33 48

sharp effective nullstellensatz the usual proofs of this result however give no information about the g1 s for instance they give no bound on their degrees this question was first considered by g hermann h she used elimination theory to get a bound on the degree of the gi s which was doubly exponential in the number of variables her results were later improved in mw and in th all these produce bounds that are doubly exponential in the number of variables a major breakthrough was achieved by brownawell b1 who proved the following result

the maximizing deviation method for group multiple attribute decision making under linguistic environment the aim of this paper is to put forward a method for multi attribute decision making problems with linguistic information in which the preference values take the form of linguistic variables an aggregating operator named linguistic weighted arithmetic averaging lwaa operator is introduced to aggregate the given decision information to get the overall preference value of each alternative some properties of the lwaa operator are also investigated based on the idea that the attribute with a larger deviation value among alternatives should be evaluated a larger weight a method to determine the optimal weighting vector of lwaa operator is developed under the assumption that attribute weights are completely unknown the based approach is extended to the situation where partially weight information can be obtained by solving a constrained non linear optimization problem then a procedure to group multiple attribute decision making is provided under linguistic environment finally an example of risk investment problem is given to verify the proposed approach a comparative study to fuzzy ordered weighted averaging f owa operator methods is also demonstrated

risk decision making method using interval numbers and its application based on the prospect value with multiple reference points a risk decision making method with multiple reference points is proposed two reference points and three reference points are set in the prospect theory two weighting optimization models are established two cases are applied to illustrate the importance of multiple reference points a multi attribute risk decision making problem using interval numbers is studied based on the prospect theory a decision making process often involves various reference standards resulting from different decision making mentalities and contexts to solve these kinds of decision making problems we propose a risk decision making method with multiple reference points for both static and dynamic situations first the guidelines for setting reference points under both static and dynamic conditions are provided based on the nature of the decision making problem second both expected values and positive ideal points for alternatives are set for the static decision making strategy and three reference points are provided for the dynamic strategy including expected values positive ideal points and the development status of alternatives according to the guidelines third characterization techniques used to solve prospect values of decision making alternatives are proposed for both static and dynamic decision making problems then a detailed analysis is provided in terms of weighting functions and prospect values in addition two optimization models using the attribute weight and multi stage weight are established by considering the sensitivity of these two weights to the decision making problem with the aim of maximizing the differentiation degree of alternatives on that basis a ranking analysis is provided for the alternatives finally the proposed method is applied to two cases including supplier selection of key components for large aircraft and an emergency event to illustrate the application and feasibility of the method

on the satisfiability of circumscription abstract etherington mercer and reiter showed on the basis of ideas of bossu and siegel that circumscription cannot lead to inconsistency for universal formulas we extend this result in three directions to formulas of a more general syntactic form to circumscription with some predicate symbols allowed to vary and to prioritized circumscription

applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy ahp the lack of consistency in decision making can lead to inconsistent conclusions in fuzzy analytic hierarchy process fuzzy ahp method it is difficult to ensure a consistent pairwise comparison furthermore establishing a pairwise comparison matrix requires nx n 1 2 judgments for a level with n criteria alternatives the number of comparisons increases as the number of criteria increases therefore the decision makers judgments will most likely be inconsistent to alleviate inconsistencies this study applies fuzzy linguistic preference relations fuzzy linprera to construct a pairwise comparison matrix with additive reciprocal property and consistency in this study the fuzzy ahp method is reviewed and then the fuzzy linprera method is proposed finally the presented method is applied to the example addressed by kahraman et al c kahraman d ruan i dogan fuzzy group decision making for facility location selection information sciences 157 2003 135 153 this study reveals that the proposed method yields consistent decision rankings from only n 1 pairwise comparisons which is the same result as in kahraman et al research the presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy ahp method

induced 2 tuple linguistic generalized aggregation operators and their application in decision making the induced 2 tuple linguistic generalized ordered weighted averaging 2 tilgowa operator is presented this new aggregation operator extends previous approaches by using generalized means order inducing variables in the reordering of the arguments and linguistic information represented with the 2 tuple linguistic approach its main advantage is that it includes a wide range of linguistic aggregation operators thus its analyses can be seen from different perspectives and we obtain a much more complete picture of the situation considered and are able to select the alternative that best fits with our interests or beliefs we further generalize the 2 tilgowa by using quasi arithmetic means and choquet integrals the result is the quasi 2 tilowa operator and the 2 tuple linguistic induced quasi arithmetic choquet integral aggregation we conclude this paper by analysing the applicability of this new approach in a multi person linguistic decision making problem concerning product management

multiple stages grey target decision making method with incomplete weight based on multi granularity linguistic label the method of grey target decision making based on a multiple stages linguistic label is extended in this research firstly the multi granularity linguistic term sets are transformed into the same linguistic set next the choice rule of a target is put forward and the calculation of a target distance is developed furthermore weight models of criteria and of stages which are based on the requirement of maximum difference of alternatives and restriction of stage harmony are suggested in addition a model of lower and upper value of a target distance is put forward moreover the method is extended to the group decision making environment this model can help to avoid faulty decision making due to uncertainty the suggested method is applied to vendor evaluation of a commercial airplane in china

direct approach processes in group decision making using linguistic owa operators abstract in a linguistic framework several group decision making processes by direct approach are presented these processes are designed using the linguistic ordered weighted averaging lowa operator to do so first a study is made of the properties and the axiomatic of lowa operator showing the rationality of its aggregation way and secondly we present the use of lowa operator to solve group decision making problems from individuals linguistic preference relations

a method for group decision making with multi granularity linguistic assessment information this paper proposes a method to solve the group decision making gdm problems with multi granularity linguistic assessment information in the method the multi granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers in order to make the collective opinion close to each expert s opinion a linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation then a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives is constructed using the dominance possibility degree of the comparison between the fuzzy numbers by applying a non dominance choice degree to this fuzzy preference relation the ranking of alternatives is determined and the most desirable alternative s is selected an example is used to illustrate the applicability of the proposed method and its advantages

a two stage logarithmic goal programming method for generating weights from interval comparison matrices a two stage logarithmic goal programming tlgp method is proposed to generate weights from interval comparison matrices which can be either consistent or inconsistent the first stage is devised to minimize the inconsistency of interval comparison matrices and the second stage is developed to generate priorities under the condition of minimal inconsistency the weights are assumed to be multiplicative rather than additive in the case of hierarchical structures a nonlinear programming method is used to aggregate local interval weights into global interval weights a simple yet practical preference ranking method is investigated to compare the interval weights of criteria or rank alternatives in a multiplicative aggregation process the proposed tlgp is also applicable to fuzzy comparison matrices when they are transformed into interval comparison matrices using a level sets and the extension principle six numerical examples including a group decision analysis problem with a group of comparison matrices a hierarchical decision problem and a fuzzy decision problem using fuzzy comparison matrix are examined to show the applications of the proposed methods comparisons with other existing procedures are made whenever possible

comparison of design concepts in multi criteria decision making using level diagrams in this work we address the evaluation of design concepts and the analysis of multiple pareto fronts in multi criteria decision making using level diagrams such analysis is relevant when two or more design concepts with different design alternatives lie in the same objective space but describe different pareto fronts therefore the problem can be stated as a pareto front comparison between two or more design concepts that only differ in their relative complexity implementation issues or the theory applied to solve the problem at hand such analysis will help the decision maker obtain a better insight of a conceptual solution and be able to decide if the use of a complex concept is justified instead of a simple concept the approach is validated in a set of multi criteria decision making benchmark problems

method of multi criteria group decision making based on cloud aggregation operators with linguistic information abstract the cloud model which can synthetically describe the randomness and fuzziness of qualitative concepts and implement uncertain transformations between a qualitative concept and its quantitative instantiations has attracted considerable attention from researchers studying multi criteria group decision making problems involving linguistic information in this paper some operations of clouds and several new aggregation operators are proposed these include the cloud weighted arithmetic averaging cwaa operator cloud ordered weighted arithmetic averaging cowa operator and cloud hybrid arithmetic cha operator the conversion between linguistic variables and clouds is introduced based on this conversion a linguistic multi criteria group decision making method is developed in this method linguistic variables are first converted into clouds and then aggregated using cloud aggregation operators the proposed method is then compared to the existing methods to confirm its feasibility and rationality

a sequential selection process in group decision making with a linguistic assessment approach in this paper a sequential selection process in group decision making under linguistic assessments is presented where a set of linguistic preference relations represents individuals preferences a collective linguistic preference is obtained by means of a defined linguistic ordered weighted averaging operator whose weights are chosen according to the concept of fuzzy majority specified by a fuzzy linguistic quantifier then we define the concepts of linguistic non dominance linguistic dominance and strict dominance degrees as parts of the sequential selection process the solution alternative s is obtained by applying these concepts

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

saturation nonmonotonic reasoning and the closed world assumption abstract to deal with the problem of implicit negative information in databases it is necessary to use a nonmonotonic form of reasoning the form of reasoning described in this paper uses an ordering relation on interpretations of the type i is inferior to j if every elementary fact true in i is true in j in simple cases this rule may be defined by a set p of formulas implies a formula q if every minimal model of p satisfies q in more general cases this definition leads to paradox if p is consistent and has no minimal model p must not imply q and its negation we have 1 1 carefully formulated the definition of a special type of implication called sub implication to avoid this type of paradox 2 2 proved that if p is a set of clauses then p has a minimal model and more generally that every model of a set of clauses is minored by one of its minimal models 3 3 developed in this last case subject to certain conditions such as the use of a particular set of clauses called groundable clauses or g clauses a decidable algorithm to compute whether p implies q q being practically any formula

a theorem on the consistency of circumscription abstract this paper gives more general conditions under which mccarthy s circumscription is consistent allowing application of the method outside the domain of universal sentences it is shown that circumscription as presented here continues to correspond to the semantic model of minimization some applications are detailed