Some Aggregation Operators for Bipolar-Valued Hesitant Fuzzy Information based on Einstein Operational Laws

  • murad ullah khan Islamia College Peshawar, kpk, pakistan
  • Tahir Mahmood . International Islamic University, Islamabad.
  • Kifayat Ullah . Department of Mathematics & Statistics, International Islamic University, Islamabad.
  • Naeem Jan . Department of Mathematics & Statistics, International Islamic University, Islamabad.
  • Irfan Deli . Muallim Rıfat Faculty of Education, Kilis 7 Aralık University, Kilis, Turkey.
  • Qaisar Khan . Department of Mathematics & Statistics, International Islamic University, Islamabad.
Keywords: Bipolar-valued hesitant fuzzy sets. Einstein operations. Aggregation operators. Decision making.

Abstract

This article is based on Einstein operations for bipolar-valued hesitant fuzzy sets (BVHFSs). We extend the concept of Einstein operators for BVHFSs by defining bipolar-valued hesitant fuzzy Einstein weighted averaging (BPVHFEWA) operators and weighted geometric (BPVHFEWG) operators. Similarly, we define ordered weighted averaging operators and hybrid operators i.e. BVHFEOWA operators, BVHFEOWG operators, BVHFEHA operator and BVHFEHG operator. Further, these operators are applied in decision making DM) problems.

Author Biographies

murad ullah khan, Islamia College Peshawar, kpk, pakistan

Assisstant Professor, Deptt of Mathematics, ICP

Tahir Mahmood ., International Islamic University, Islamabad.

Assistant Professor, Department of Mathematics & Statistics, International Islamic University, Islamabad

Kifayat Ullah ., Department of Mathematics & Statistics, International Islamic University, Islamabad.

Ph.D. Scholar.

Naeem Jan ., Department of Mathematics & Statistics, International Islamic University, Islamabad.

Ph.D. Scholar.

Irfan Deli ., Muallim Rıfat Faculty of Education, Kilis 7 Aralık University, Kilis, Turkey.

Assistant Professor, Muallim Rıfat Faculty of Education, Kilis 7 Aralık University, Kilis, Turkey.

Qaisar Khan ., Department of Mathematics & Statistics, International Islamic University, Islamabad.

Ph.D. Scholar.

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Published
2017-12-29
How to Cite
khan, murad, ., T., ., K., ., N., ., I., & ., Q. (2017, December 29). Some Aggregation Operators for Bipolar-Valued Hesitant Fuzzy Information based on Einstein Operational Laws. JOURNAL OF ENGINEERING AND APPLIED SCIENCES, 36(2). Retrieved from https://journals.uetjournals.com/index.php/JEAS/article/view/2071