Abstract—The challenge for everyone involved in preserving the ecosystem is to find creative ways to protect and restore the remaining ecosystems while accommodating and enhancing the country social and economic well-being. Frequent fires of anthropogenic origin have been affecting the ecosystems in many countries adversely. Hence adopting ways of decision making such as Multicriteria Decision Making (MCDM) is appropriate since it will enhance the evaluation and analysis of fire risk and hazard of the ecosystem. In this paper, fire risk and hazard data from the West Gonja area of Ghana were used in some of the methods (Analytical Hierarchy Process, Compromise Programming, and Grey Relational Analysis (GRA) for MCDM evaluation and analysis to determine the optimal weight method for fire risk and hazard. Ranking of the land cover types was carried out using; Fire Hazard, Fire Fighting Capacity and Response Risk Criteria. Pairwise comparison under Analytic Hierarchy Process (AHP) was used to determine the weight of the various criteria. Weights for sub-criteria were also obtained by the pairwise comparison method. The results were optimised using GRA and Compromise Programming (CP). The results from each method, hybrid GRA and CP, were compared and it was established that all methods were satisfactory in terms of optimisation of weight. The most optimal method for spatial multicriteria evaluation was the hybrid GRA method. Thus, a hybrid AHP and GRA method is more effective method for ranking alternatives in MCDM than the hybrid AHP and CP method. Keywords—Compromise programming, grey relational analysis, spatial multi-criteria, weight optimisationç I. INTRODUCTION CDM can generally be described as a tool for deriving priorities from a set of available alternatives; based on a set of criteria with different significance. It is used for making choices in the presence of multi-conflicting criteria. Many researchers have proposed different methods based on quantitative measurement for the selection of most optimal alternative from a set of alternatives [1]. The most frequently used MCDM methods include: Methods based on quantitative initial measurements i.e. AHP and Fuzzy Theory Set [1], methods based on quantitative measurement i.e. Technique for Yakubu I. is with the Department of Geomatic Engineering, University of Mines and Technology (UMaT), Tarkwa, Ghana (corresponding author, phone: +233 242957741; e-mail: yabsgm@gmail.com/ yissaka@umat.edu.gh). Mireku-Gyimah D. is with the Department of Mining Engineering, UMaT, Tarkwa, Ghana (e-mail: dmgyimah@umat.edu.gh). Asafo-Adjei D. is with the Department of Geomatic Engineering, UMaT, Tarkwa, Ghana as a National Service Personnel (e-mail: asafoadjeidavid00@gmail.com). Ordering Preference by Similarity to Identical Solution (TOPSIS) [2], Linear Programming Technique for Multidimensional Analysis of Preference [3], Complex Proportional Assessment (COPRAS) [4], Additive Ratio Assessment methods, GRA and CP [5]; Comparative preference methods based on pair-wise comparison alternatives i.e. Preference Ranking Organization method for Enrichment Evaluations (PROMETHEE) [3]. In MCDM, usually the evaluation criteria are associated with different weights, with the weights of the criteria having large impact on the selected alternative. Technique and decision-making methods in MCDM are dynamic [6]-[9], [3]. There are two ways of determining the weight associated with each criterion based on the importance attached to it: direct explication and indirect explication [10]. The direct explication is where weights are assigned through questionnaire surveys, conventional rules and expert interviews before the data of each alternative are collected. On the contrary, indirect explication represents the importance of the alternatives being evaluated. The weights are a reflection of the data [11]. However, it must be noted that optimality is complicated whenever multiple objectives are considered in the evaluation of a solution [12]. The most widely used concept for obtaining the optimal solution of a problem which involves multiple objectives is the concept of Pareto optimality. The concept is such that the improvement in one objective leads to the detriment of the other. This concept of Pareto optimality usually serves as a processing stage for a MCDM. In this case the information necessary to support the selection of the most optimal solution from the set of possible solutions are provided [13]. This paper is aimed at making alternative decision rules in spatial multicriteria evaluation and analysis of fire risk and hazard data from the West Gonja Area of Ghana (WGA). The AHP, GRA and the CP are the MCDM methods considered in this paper. The AHP is used to determine the weight of the various criteria based on expert’s relative preferences for the various criteria. The optimal alternative will be selected based on the result obtained by the hybrid AHP-GRA or the AHP- CP. Research has been conducted in the use of GRA and/or CP for the selection of the best alternative. Reference [14] used CP for multi-objective route planning; adaptation of CP approach for multicriteria decision analysis by [15]; [16] assesses the fire safety of underground building based on GRA; [3] used grey additive ratio assessment method for multiple criteria analysis; and [17] used GRA for criteria Hybrid Methods for Optimisation of Weights in Spatial Multi-Criteria Evaluation Decision for Fire Risk and Hazard I. Yakubu, D. Mireku-Gyimah, D. Asafo-Adjei M World Academy of Science, Engineering and Technology International Journal of Geotechnical and Geological Engineering Vol:12, No:12, 2018 723 International Scholarly and Scientific Research & Innovation 12(12) 2018 Digital Open Science Index, Geotechnical and Geological Engineering Vol:12, No:12, 2018 waset.org/Publication/10009859