the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

Phasor measurement units (PMUs) are becoming a vital device in wide-area monitoring, operation, and control. The allocation of PMU at each bus will make that directly observable. However, considering the high installation costs, it is not feasible to place bus. Thus, placing PMUs optimal locations extremely important. In this study, Preference Ranking Organization Method for Enrichment Evaluati...

<abstract><p>Many real-world decision-making issues frequently involve competing sets of criteria, uncertainty, and inaccurate information. Some these require the involvement a group decision-makers, where it is necessary to reduce various available individual preferences single collective preference. To enhance effectiveness multi-criteria decisions, popular technique that makes pr...

Methods of multi-criteria decision making (MCDM) from operations research have been applied to provide information for long-term decisions in the energy sector, and policy. For example, sustainability evaluations, multiple conflicting criteria can be considered. While most MCDM approaches evaluate systems a single period, evaluation system evolution over time has received less attention. To suc...

This paper proposes the application of multi-criteria analysis to the problem of allocating public funds to competing programs, projects, or policies, with a subjective approach applied to define the concept of highest portfolio social return. This portfolio corresponds to an attainable non-strictly outranked state of the social object under consideration. Its existence requires a decision-make...

Several interactive methods exist to identify nondominated solutions in a Multiple Objective Mixed Integer Linear Program. But what if the Decision Maker is also interested in sorting those solutions (assigning them to pre-established ordinal categories)? We propose an interactive ‘‘branch-and-bound like’’ technique to progressively build the nondominated set, combined with ELECTRE TRI method (...