The Analytic Hierarchy Process (AHP) proposed by T. L. Saaty has been widely used in decision making. Inner dependence method AHP is used for cases in which criteria or alternatives are not independent enough and using the original AHP or inner dependence AHP may cause results to lose reliability because the comparison matrix is not necessarily sufficiently consistent. In such cases, fuzzy repr...

This paper considers dissimilarity measures and clustering techniques for two special cases of set-defined objects: fuzzy granules and subsequence time series. To deal with clustering of such kind of objects, we propose two implementations that generalize the Fuzzy C-Means algorithm to granular feature spaces. Granular computing is a paradigm oriented towards capturing and processing meaningful...

This paper presents a fuzzy CBR (case-based reasoning) technique for generating new product ideas from a product database for enhancing the functions of a given product (called the baseline product). In the database, a product is modeled by a 100-attribute vector, 87 of which are used to model the use-scenario and 13 are used to describe the manufacturing/recycling features. Based on the usesce...

The aim of this work is to introduce and study the nondegenerate inner product $<\cdot , \cdot >_{det}$ induced by determinant map on space $Sym(2)$ symmetric $2\times 2$ real matrices. This bilinear form index $2$ defines a rational function pairs rays in plane an associated $2$-torus can be expressed with usual Hopf bundle projection $S^3\rightarrow S^2(\frac{1}{2})$. Also, trea...