a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

a probability based approach to comparison of fuzzy numbers and applications to target oriented decision making in this paper we introduce a new comparison relation on fuzzy numbers based on their alpha cut representation and comparison probabilities of interval values basically this comparison process combines a widely accepted interpretation of fuzzy sets together with the uncertain characteristics inherent in the representation of fuzzy numbers the proposed comparison relation is then applied to the issue of ranking fuzzy numbers using fuzzy targets in terms of target based evaluations some numerical examples are used to illuminate the proposed ranking technique as well as to compare with previous methods more interestingly according to the interpretation of the new comparison relation on fuzzy numbers we provide a fuzzy target based decision model as a solution to the problem of decision making under uncertainty with which an interesting link between the decision maker s different attitudes about target and different risk attitudes in terms of utility functions can be established moreover an application of the proposed comparison relation to the fuzzy target based decision model for the problem of fuzzy decision making with uncertainty is provided numerical examples are also given for illustration

a discussion of critical behaviour in a mixed spin ising model abstract the critical behaviour of a mixed spin 1 2 and spin 1 ising system is investigated by the use of the two site cluster effective field theory the general expressions for evaluating the transition temperature and the tricritical point are obtained particular attention is drawn to the tricritical behaviour of the square lattice and it is shown that it strongly depends on the accuracy of calculations with a tendency to disappear when the accuracy is improved

on the instantiation of possibility distributions we investigate the problem of instantiating a variable whose value is uncertain but known to be constrained by a possibility distribution using a model based upon the dempster shafer belief structure we show that this problem of instantiation is analogous to a compound experiment in which we randomly select a subset and then perform a number of repeated experiments without replacement on this set the probability distribution resulting from this compound experiment leads to a random procedure for instantiating a possibility distribution

properties of measures of information in evidence and possibility theories abstract an overview of information measures recently introduced by several authors in the settting of shafer s theory of evidence is proposed new results pertaining to additivity and monotonicity properties of these measures of information are presented the interpretation of each measure of information as opposed to others is discussed the potential usefulness of measures of specificity or imprecision is suggested and a principle of minimal specificity is stated for the purpose of reconstructing a body of evidence from incomplete knowledge

fuzzy sets probability and measurement abstract in recent years the problem of uncertainty modeling has received much attention from scholars in artificial intelligence and decision theory various formal settings including but not restricted to fuzzy sets and possibility measures have been proposed based on different intuitions and dealing with various kinds of uncertain data the two main research directions are upper and lower probabilities which convey the idea of imprecisely estimated probability measures and distorted probabilities for the descriptive assessment of partial belief possibility measures and thereby fuzzy sets stand at the crossroads of these new approaches traditional views interpretive settings and canonical experiments for the measurement of probability such as frequentist approaches betting theories comparative uncertainty relations are currently extended to the generalized uncertainty measures these works shed new light on various interpretations of fuzzy sets and clarify their links with probability theory conversely zadeh s logical point of view on fuzzy sets suggests a set theoretic perspective on uncertainty measures that brings together numerical quantification and logic

new effective field theory for the blume capel model abstract a new type of effective field theory that has recently been used with success for many applications concerning the usual two state ising model is herein extended to the blume capel model the method which can explicitly and systematically include correlation effects is illustrated in several lattice structures by employing its simplest approximate version in which spin spin correlations are neglected it is shown that this approximative procedure although analytically simple provides in particular a vanishing critical temperature for one dimensional systems and leads to results quite superior to those currently obtained within the molecular field approximation for higher dimensional systems within this framework we discuss as functions of temperature and for any values of the anisotropy parameter d the order parameter the thermal average of the square of the single site spin variable the internal energy and the specific heat as well as the ferromagnetic phase stability limit whenever comparison is possible a satisfactory qualitative and to a certain extent quantitative agreement is observed with results available in the literature in which more sophisticated treatments are used in particular our result for the tricritical point at which the system exhibits a first order phase transition is in quite good agreement with those obtained by using series expansion methods

ranking and defuzzification methods based on area compensation abstract we present some interesting properties related to the area compensation procedure to compare fuzzy numbers it has been proved that this method produces more than a fuzzy interval order it induces a ranking of fuzzy numbers some further results are given about the transitivity property and about computational aspects extensions to non normal fuzzy numbers and fuzzy quantities are also proposed

ordering fuzzy sets over the real line an approach based on decision making under uncertainty abstract the ordering of fuzzy sets over the real line is approached from the point of view of ordering intervals rather than ordering numbers first the maximax and maximin criteria which are commonly used for ordering intervals are expressed in terms of characteristic functions these criteria and the hurwicz criterion for decision making under complete ignorance are then reformulated in a manner that allows for their generalization to the fuzzy case transitivity is established for these ordering rules a criterion based on the principle of diminishing marginal utility is also presented

exact results for the spin 1 ising model on pure square husimi lattices critical temperatures and spontaneous magnetization abstract we investigate the second order phase transitions of the ferromagnetic spin 1 ising model on pure husimi lattices built up from elementary squares with arbitrary values of the coordination number it is shown that the critical temperatures of the second order phase transitions are driven by a single equation simultaneously on all such lattices it is also shown that for arbitrary given value of the coordination number this equation is equivalent to the corresponding polynomial equation the explicit form of these polynomial equations is present for the lattices with the coordination numbers z 4 6 and 8 it is proven that at least for the small values of the coordination number the positions of the critical temperatures are uniquely determined in addition it is shown that the properties of all phases of the model are also driven by the corresponding single equations simultaneously on all pure husimi lattices built up from elementary squares the spontaneous magnetization of the model is investigated in detail

ranking fuzzy numbers with index of optimism abstract fuzzy numbers are convenient for representing imprecise numerical quantities in a vague environment and their comparison or ranking is very important for application purposes despite many methods suggested in the literature there is no single measure that is universally applicable to a wide variety of situations this paper suggests a new method for comparing fuzzy numbers based on the combination of maximizing possibility and minimizing possibility using an index of optimism in 0 1 reflecting the decision maker s risk taking attitude the method is simple but has many comparative advantages

a context dependent method for ordering fuzzy numbers using probabilites in this work we suggest an approach to comparing fuzzy numbers motivated by a probabilistic view of the underlying uncertainty an important aspect of the method suggested is its context dependency the numbers being compared affect the process we discuss the effect of decision attitude and show that this approach is particularly useful for aiding decision makers having a temperate decision attitude optimism in the face of adversity and conservatism in the face plenty

a subjective approach for ranking fuzzy numbers abstract starting from a subjective assignation of weights related to the relative importance of the different level sets we define a new method of comparison of fuzzy numbers this procedure is an extension of some well known indices adamo tsumura et al yager some properties of our index are studied in this paper as well as its behaviour on several particular cases

two spin cluster theory for the blume capel model with arbitrary spin abstract a two spin cluster effective field theory for the blume capel model with arbitrary spin s is presented by making use of exact spin identities and taking advantage of the differential operator technique the dependence of the transition temperature is studied as a function of the single ion anisotropy field strength for the particular cases s 1 3 2 and 2 the results are compared to those of the single spin cluster theory recently reported in the literature as well as to other methods in particular it is shown that the present approach correctly distinguishes the geometry of the lattice structure beyond its coordination number

an approximate approach for ranking fuzzy numbers based on left and right dominance this study presents an approximate approach for ranking fuzzy numbers based on the left and right dominance the proposed approach only requires a few left and right spreads at some levels of fuzzy numbers to determine the respective dominance of one fuzzy number over the other the total dominance is then determined by combining the left and right dominance based on a decision maker s optimistic perspectives such a dominance is useful in ranking the fuzzy numbers when membership functions cannot be acquired the approach proposed herein is relatively simple in terms of computational efforts and is efficient when ranking a large quantity of fuzzy numbers by using a few left and right spreads two groups of examples demonstrate the accuracy and applicability of the proposed approach

spin 1 blume capel model with random crystal field effects abstract the random crystal field spin 1 blume capel model is investigated by the lowest approximation of the cluster variation method which is identical to the mean field approximation the crystal field is either turned on randomly with probability p or turned off with q 1 p in a bimodal distribution then the phase diagrams are constructed on the crystal field temperature k t j planes for given values of p and on the k t j p planes for given by studying the thermal variations of the order parameters in the latter we only present the second order phase transition lines because of the existence of irregular wiggly phase transitions which are not good enough to construct lines in addition to these phase transitions the model also yields tricritical points for all values of p and the reentrant behavior at lower p values

comparison of clusters from fuzzy numbers fuzzy numbers are used for representation of numerical quantities in a vague environment their comparison or ranking is important for application purposes a new index for comparing of fuzzy numbers based on their geometrical properties is suggested in this paper this geometrical index is tested on a group of selected examples and compared with the other well known indexes a method for comparison of m tuples of fuzzy numbers and an algorithm for comparison of subsets clusters of similar closed m tuples of trapezoidal fuzzy numbers are presented

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

dynamic magnetic properties in the kinetic ising ferromagnet on triangular lattice within the effective field theory and using glauber type stochastic dynamics abstract dynamic magnetic properties in the kinetic ising ferromagnet on a triangular lattice are studied within the effective field theory with correlations and using glauber type stochastic dynamics in particular we investigate the time variations of average order parameters and thermal behaviors of the dynamic total magnetizations and present the dynamic phase diagrams the tricritical point the triple point and zero critical end point as well as reentrant behaviors are found in the dynamic phase diagrams we also study the dynamic hysteresis behaviors of the system when the hysteresis behaviors of the system are examined single hysteresis loop as well as s shaped thin loops and elliptical shapes are observed for various values of the physical parameters results are compared with some other dynamic studies and quantitatively good agreement is found

approximate amenability of k x abstract we show that if a banach space x is fairly close to a hilbert space then the banach algebra k x of all compact operators on x is approximately amenable we use this to give examples of banach spaces x for which k x is approximately amenable but not amenable thus we answer a question on existence of such spaces open since 2000