(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 4292, 116] NotebookOptionsPosition[ 3771, 99] NotebookOutlinePosition[ 4115, 114] CellTagsIndexPosition[ 4072, 111] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Mahalanobis fuzzy hypervolume index", "Subsection", CellChangeTimes->{ 3.5854097085807176`*^9, 3.585637218737363*^9, {3.7255165931679688`*^9, 3.725516594386836*^9}, {3.8078509217486286`*^9, 3.8078509235303373`*^9}, 3.822225222190958*^9, 3.8222263491864443`*^9, 3.8222269369146223`*^9, 3.8222271612780204`*^9, 3.8222276850838566`*^9, 3.822227789407708*^9, 3.822227911348709*^9},ExpressionUUID->"a64cb8e3-4b5a-458a-81b2-\ 359028b304d5"], Cell[BoxData[ RowBox[{"(*", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"Input", ":", " ", RowBox[{"membership", " ", "matrix", " ", "U"}]}], ",", " ", RowBox[{ RowBox[{"covariance", " ", "matrices", " ", UnderscriptBox["\[Sum]", "j"]}], "\[Element]", SuperscriptBox["\[DoubleStruckCapitalR]", RowBox[{"n", "\[Cross]", "n"}]]}], ",", " ", RowBox[{ RowBox[{"j", "=", RowBox[{"1", "\[TripleDot]k"}]}], ";", "\[IndentingNewLine]", RowBox[{"Output", ":", " ", RowBox[{"MFHV", " ", "index"}]}], ";", "\[IndentingNewLine]", RowBox[{"Submodules", ":", " ", RowBox[{"dM", "[", "]"}]}]}]}], "\[IndentingNewLine]", "*)"}]], "Input", CellChangeTimes->{{3.8208938752340946`*^9, 3.8208939165097227`*^9}, 3.8208939777537127`*^9, {3.82089402908541*^9, 3.8208940654953437`*^9}, { 3.820894178610306*^9, 3.8208942451936073`*^9}, {3.820894336841039*^9, 3.8208943606992674`*^9}, {3.8222252468201857`*^9, 3.8222252579121275`*^9}, {3.8222263768275585`*^9, 3.8222264735149126`*^9}, {3.8222267120062532`*^9, 3.8222267137917337`*^9}, 3.8222268123848886`*^9, {3.8222269734939747`*^9, 3.8222270468006*^9}, { 3.822227188241254*^9, 3.8222272187064533`*^9}, {3.822227276564354*^9, 3.822227297837488*^9}, 3.8222277085849485`*^9, {3.8222278404812093`*^9, 3.822227840804907*^9}, {3.822227929202545*^9, 3.8222279385971785`*^9}, { 3.830087256085755*^9, 3.8300872613625126`*^9}},ExpressionUUID->"46567b81-f70d-49a0-a082-\ b32f5d905c2d"], Cell[BoxData[{ RowBox[{"Clear", "[", "MFHV", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"MFHV", "[", RowBox[{"U_", ",", "cov_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"k", "=", RowBox[{"Length", "[", "cov", "]"}]}], ",", "VV", ",", "max", ",", RowBox[{"sum", "=", "0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"Det", "[", RowBox[{"cov", "[", RowBox[{"[", "j", "]"}], "]"}], "]"}], "]"}], "/", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"U", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "^", "q"}], ",", RowBox[{"{", RowBox[{"i", ",", "m"}], "}"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"j", ",", "k"}], "}"}]}], "]"}], "]"}]}], "\[IndentingNewLine]", "]"}]}]}], "Input", CellChangeTimes->{ 3.830086114459934*^9, {3.8300872192888904`*^9, 3.830087233047333*^9}},ExpressionUUID->"3936e5d4-805b-4608-a336-\ 8ad3ff5085e5"] }, Open ]] }, WindowSize->{702, 268}, WindowMargins->{{-1926, Automatic}, {Automatic, 1}}, FrontEndVersion->"12.0 for Microsoft Windows (64-bit) (April 8, 2019)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 461, 7, 53, "Subsection",ExpressionUUID->"a64cb8e3-4b5a-458a-81b2-359028b304d5"], Cell[1044, 31, 1516, 29, 110, "Input",ExpressionUUID->"46567b81-f70d-49a0-a082-b32f5d905c2d"], Cell[2563, 62, 1192, 34, 86, "Input",ExpressionUUID->"3936e5d4-805b-4608-a336-8ad3ff5085e5"] }, Open ]] } ] *)