An experimental methodology for a fuzzy set preference model

A flexible fuzzy set preference model first requires approximate methodologies for implementation. Fuzzy sets must be defined for each individual consumer using computer software, requiring a minimum of time and expertise on the part of the consumer. The amount of information needed in defining sets must also be established. The model itself must adapt fully to the subject's choice of attributes (vague or precise), attribute levels, and importance weights. The resulting individual-level model should be fully adapted to each consumer. The methodologies needed to develop this model will be equally useful in a new generation of intelligent systems which interact with ordinary consumers, controlling electronic devices through fuzzy expert systems or making recommendations based on a variety of inputs. The power of personal computers and their acceptance by consumers has yet to be fully utilized to create interactive knowledge systems that fully adapt their function to the user. Understanding individual consumer preferences is critical to the design of new products and the estimation of demand (market share) for existing products, which in turn is an input to management systems concerned with production and distribution. The question of what to make, for whom to make it and how much to make requires an understanding of the customer's preferences and the trade-offs that exist between alternatives. Conjoint analysis is a widely used methodology which de-composes an overall preference for an object into a combination of preferences for its constituent parts (attributes such as taste and price), which are combined using an appropriate combination function. Preferences are often expressed using linguistic terms which cannot be represented in conjoint models. Current models are also not implemented an individual level, making it difficult to reach meaningful conclusions about the cause of an individual's behavior from an aggregate model. The combination of complex aggregate models and vague linguistic preferences has greatly limited the usefulness and predictive validity of existing preference models. A fuzzy set preference model that uses linguistic variables and a fully interactive implementation should be able to simultaneously address these issues and substantially improve the accuracy of demand estimates. The parallel implementation of crisp and fuzzy conjoint models using identical data not only validates the fuzzy set model but also provides an opportunity to assess the impact of fuzzy set definitions and individual attribute choices implemented in the interactive methodology developed in this research. The generalized experimental tools needed for conjoint models can also be applied to many other types of intelligent systems

A neural implementation of multi-adjoint logic programs via sf-homogenization

A generalization of the homogenization process needed for the neural im- plementation of multi-adjoint logic programming (a unifying theory to deal with uncertainty, imprecise data or incomplete information) is presented here. The idea is to allow to represent a more general family of adjoint pairs, but maintaining the advantage of the existing implementation recently introduced in [6]. The soundness of the transformation is proved and its complexity is analysed. In addition, the corresponding generalization of the neural-like implementation of the fixed point semantics of multi-adjoint is presented

Fuzzy implication functions based on powers of continuous t-norms

The modification (relaxation or intensification) of the antecedent or the consequent in a fuzzy “If, Then” conditional is an important asset for an expert in order to agree with it. The usual method to modify fuzzy propositions is the use of Zadeh's quantifiers based on powers of t-norms. However, the invariance of the truth value of the fuzzy conditional would be a desirable property when both the antecedent and the consequent are modified using the same quantifier. In this paper, a novel family of fuzzy implication functions based on powers of continuous t-norms which ensure the aforementioned property is presented. Other important additional properties are analyzed and from this study, it is proved that they do not intersect the most well-known classes of fuzzy implication functions.Peer ReviewedPostprint (author's final draft

Multidimensional Poverty in Pakistan: Case of Punjab Province

This paper applies Alkire & Foster (2007) approach for measuring the multidimensional poverty. The data set used in the study is Multiple Indicator Cluster Survey 2003-04 of Punjab, Pakistan. Eight dimensions used in the study are Housing, Water, Sanitation, Electricity, Assets, Education, Expenditure, and Land. Results shows that at cut off K=2; Rajanpur, Muzaffargarh, Rahimyar Khan, Kasur, Okara and Lodhran respectively are the most multidimensionally poor districts of Punjab whereas, Gunj Buksh Town Lahore, Ravi Town Lahore, Cantt Town Lahore, Sialkot, Rawalpindi, Allama Iqbal Town Lahore, Gujranwala and Jhelum are the least deprived Towns/Districts of Punjab province. Dimension wise breakdown shows that Land deprivation, expenditure, sanitation, housing and education are respectively the major contributors among overall multidimensional poverty.Multidimensional Poverty, Pakistan, MDGs