Table 3 Expert decision matrix in the form of HBCFNs.

From: AI-driven energy management system based on hesitant bipolar complex fuzzy Hamacher power aggregation operators and their applications in MADM

 

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\({\Delta }_{1}\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1324} \\ { +\upiota 0.2410} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3095} \\ { +\upiota 0.3437} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1752} \\ { -\upiota 0.2617} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3708} \\ { -\upiota 0.4181} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1109} \\ { +\upiota 0.2233} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3094} \\ { +\upiota 0.4524} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.5163} \\ { +\upiota 0.6730} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1268} \\ { -\upiota 0.2098} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3956} \\ { -\upiota 0.4151} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1114} \\ { +\upiota 0.2249} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3312} \\ { +\upiota 0.3499} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1750} \\ { -\upiota 0.2063} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3078} \\ { -\upiota 0.4129} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1281} \\ { +\upiota 0.3249} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3431} \\ { +\upiota 0.5413} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1614} \\ { -\upiota 0.2839} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3771} \\ { -\upiota 0.4485} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.5569} \\ { -\upiota 0.6813} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\({\Delta }_{2}\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1231} \\ { +\upiota 0.3245} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3643} \\ { +\upiota 0.4511} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.5464} \\ { +\upiota 0.6732} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1983} \\ { -\upiota 0.2361} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3853} \\ { -\upiota 0.4401} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.5068} \\ { -\upiota 0.6034} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1219} \\ { +\upiota 0.3232} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3487} \\ { +\upiota 0.4648} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.5174} \\ { -\upiota 0.6294} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.1019} \\ { -\upiota 0.2207} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3815} \\ { -\upiota 0.5423} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1227} \\ { +\upiota 0.3225} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3647} \\ { +\upiota 0.8406} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1735} \\ { -\upiota 0.2958} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3175} \\ { -\upiota 0.4962} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1231} \\ { +\upiota 0.3215} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3490} \\ { +\upiota 0.5423} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1064} \\ { -\upiota 0.2690} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3980} \\ { -\upiota 0.4490} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\({\Delta }_{3}\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1315} \\ { +\upiota 0.5220} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3621} \\ { +\upiota 0.7499} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1832} \\ { -\upiota 0.2913} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3900} \\ { -\upiota 0.4294} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1529} \\ { +\upiota 0.2364} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3409} \\ { +\upiota 0.5402} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1064} \\ { -\upiota 0.2671} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3768} \\ { -\upiota 0.4984} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1115} \\ { +\upiota 0.2206} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3031} \\ { +\upiota 0.4408} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.5705} \\ { +\upiota 0.6766} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1547} \\ { -\upiota 0.2338} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3709} \\ { -\upiota 0.4084} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.5906} \\ { -\upiota 0.6057} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1321} \\ { +\upiota 0.4231} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3590} \\ { +\upiota 0.6405} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1702} \\ { -\upiota 0.2709} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3989} \\ { -\upiota 0.4191} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\({\Delta }_{4}\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1931} \\ { +\upiota 0.2411} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3859} \\ { +\upiota 0.4642} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1871} \\ { -\upiota 0.2089} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3099} \\ { -\upiota 0.4142} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.5065} \\ { -\upiota 0.6439} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.3119} \\ { +\upiota 0.4282} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.4398} \\ { +\upiota 0.5442} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.5121} \\ { -\upiota 0.6289} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.7391} \\ { -\upiota 0.6407} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1211} \\ { +\upiota 0.2392} \\ \end{array} } \right),} \\ { \left( {\begin{array}{*{20}c} {0.3849} \\ { +\upiota 0.4582} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1159} \\ { -\upiota 0.2968} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3937} \\ { -\upiota 0.4158} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.5668} \\ { -\upiota 0.6496} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

\(\left( {\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {0.1181} \\ { +\upiota 0.2299} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.3932} \\ { +\upiota 0.4471} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} {0.5259} \\ { +\upiota 0.6731} \\ \end{array} } \right)} \\ \end{array} } \right\},} \\ {\left\{ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} { - 0.1072} \\ { -\upiota 0.2089} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.3119} \\ { -\upiota 0.4030} \\ \end{array} } \right),} \\ {\left( {\begin{array}{*{20}c} { - 0.5920} \\ { -\upiota 0.6429} \\ \end{array} } \right)} \\ \end{array} } \right\}} \\ \end{array} } \right)\)

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