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This paper presents an intelligent technology based method for analyzing and interpreting sensory data provided by multiple panels in evaluation of industrial products. In order to process the uncertainty existing in these sensory data, we first transform all sensory data on an unified optimal scale. Based on these normalized data sets, we compute the dissimilarities or distances between different panels and between different evaluation terms used by them, defined according to the degree of consistency of data variation. The obtained distances are then transformed into fuzzy numbers for physical interpretation. These fuzzy distances permit to characterize the evaluation behaviour of each panel and the quality of the evaluation terms used. Also, based on a Genetic Algorithm with punishment policy and the dissimilarity between terms, we develop a procedure for interpreting terms of one panel using those of another panel. This method has been applied to the fabric hand evaluation for a number of samples of knitted cotton in order to identify consumers' preference of different populations.

In this paper we develop a new graphical representation of fuzzy numbers, which we then employ to propose a geometrical approach to their defuzzification. The calculations involved in the proposed method and the resultant representation use Moore's semiplane for intervals and therefore are far simpler than those involved in other approaches.

We start by representing triangular and trapezoidal fuzzy numbers in Moore's semiplane. Then we extend this work to any fuzzy number. Although this extension has to be undertaken in ${ℝ}^3$, it preserves all the properties we study for trapezoidal and triangular fuzzy numbers in Moore's semiplane.

Type-2 fuzzy sets are generalizations of ordinary fuzzy sets, in which membership grades are characterized by fuzzy membership functions. Here, a problem of finding distance between two interval type-2 fuzzy sets (IT2-FSs) was considered. Based on a new definition of centroid for an IT2-FS, a formulation for calculation of the distance between two IT2-FSs was introduced, and an algorithm was explained to obtain it. The proposed distance formula was incorporated in Yang and Shih's clustering algorithm to reach a clustering method for interval type-2 fuzzy data sets. The applicability of the proposed distance formula was evaluated using two artificial and real data sets, and reasonable results were obtained.

This paper proposes a new definition of the indefinite integral of fuzzy valued function linearly generated by structural elements using a kind of fuzzy distance. Then the new definition is used to study the basic properties of the indefinite integral of fuzzy valued function linearly generated by structural elements. They are the existence of the original function, addition together with multiplication, integration by substitution and integration by parts. Subsequently, by giving the Cauchy convergence criterion for the anomalous integral of fuzzy value function linearly generated by structural elements, the integrable conditions of the anomalous integral of fuzzy value function linearly generated by structural elements are discussed. They are absolute convergence, Dirichlet test and Abel test.