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A multi‐objective mathematical programming problem with fuzzy relation constraints
Author(s) -
Wang HsiaoFan
Publication year - 1995
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.4020040103
Subject(s) - mathematical optimization , relation (database) , decision maker , mathematics , regular polygon , interval (graph theory) , fuzzy logic , space (punctuation) , decision problem , constant (computer programming) , computer science , algorithm , artificial intelligence , operations research , data mining , geometry , combinatorics , programming language , operating system
Abstract In this study we discuss the problem of multi‐objective mathematical programming with constraints defined by ‘max‐min’ composite fuzzy relation equations. Since the feasible region is normally non‐convex, the properties of the efficient points of a non‐convex feasible region under multi‐objectives are investigated and illustrated by examples. The necessary and sufficient conditions are proposed and proved. To facilitate decisions, a procedure that transforms these efficient points of an interval‐valued decision space into a constant‐valued decision space is proposed when the level of confidence is given by a decision maker. Then the transformed problem becomes a multi‐attribute decision problem that can be evaluated by Yager's method to find the optimal alternative.