MULTI-CRITERIA DECISION-MAKING BASED ON COMBINED VAGUE SETS IN ELECTRICAL OUTAGES PROBLEMS KH. BANAN, TABRIZ UNIVERSITY & AHREC, IRAN, KHBANAN@MAIL.COM S. KHANMOHAMMADI, TABRIZ UNIVERSITY, IRAN, KHAN@TABRIZU.AC.IR S. H. HOSEINI, TABRIZ UNIVERSITY, IRAN, HOSEINI@TABRIZU.AC.IR ABSTRACT The nature of electrical distribution systems is changing from simple markets towards competitive markets. The modern distribution system must simultaneously be reliable, flexible, and cost conscious. One of the main factors that affect the reliability of power systems is outages. With all efforts that have been done, the existence of outages is a reality. Management of electrical outages is a necessity and in outage times we need some appropriate decision makings. In this paper we propose an integrated, quantitative methodology based on vague sets to assist the distribution systems in making these decisions. This methodology allows information on the suppliers and customers to be expressed either qualitatively or quantitatively to use a multi- criteria decision making model and provide new functions to measure the degree of accuracy in the grades of membership of each alternative with respect to a set of criteria represented by vague values. KEYWORDS: Vague set; Multi-criteria decision making, electrical outages 1. INTRODUCTION Most of the existing approaches in multi-criteria decision making (MCDM) consist of two phases [1]: (1) The aggregation of the judgments with corresponding author and (2) the rank ordering of the decision alternatives according to the aggregated judgments. However, a few of these approaches refer to the aspect of an explicit modeling of relationships between goals [2]. In addition, achieving to real modeling of MCDM in the real world is the case with interdependent criteria [3]. Since the theory of fuzzy sets was proposed in 1965, it has been used for handling fuzzy decision-making problems [4]. However, current relationship analysis approaches (e.g. fuzzy multiple objective programs (FMOP) [3] and decision making based on relationship between goals (DMRG) [2, 5, 6]) usually result in identifying relationships. Based on fuzzy set theory introduced by Zadeh; fuzzy set approach to multi-objective decision making is illustrated by Zimmerman; some approaches to solve multi-attribute decision problems based on fuzzy set theory are compared and a fuzzy multi-attribute decision-making method, using crisp weights is presented [7]. The structure of the knowledge based of fuzzy rule based systems in a hierarchical way was extended in order to make it more flexible [8]. Also, an ordered weighted aggregation operator is introduced and investigated the properties of the operator in [9]. Roughly speaking, a fuzzy set is a class with fuzzy boundaries [10]. The fuzzy set A in the universe of discourse U, U ={u 1 ; u 2 ; : : : ; u n }, is a set of ordered pairs {(u 1 ; µ A (u 1 )); (u 2 ; µ A (u 2 )); : : : ; (u n ; µ A (u n ))}, where ] 1 ; 0 [ ∈ A µ is the membership function of the fuzzy set A; and µ A (u i ) indicates the grade of membership of u i in A. When the universe of discourse U is a finite set, then the fuzzy set A can be represented by Eq. (1). ∑ = + + + = = n i i i A n n A A A u u u u u u u u A 1 2 2 1 1 / ) ( / ) ( ... / ) ( / ) ( µ µ µ µ (1) When the universe of discourse U is an interval of real numbers between a and b, then a fuzzy set A is often written in the form Eq. (2).