Fundamenta Informaticae - Volume 144, issue 3-4

Authors: Hou, Fujun

Article Type: Research Article

Abstract: Pairwise comparisons (PC) method is an efficient technique and hierarchical analysis is a popular means coping with complex decision problems. Based on two proposed theorems, this paper shows that the PC-based hierarchical decision models stem from the weighted average methods (including the arithmetic form and the geometric form). Some issues (including the rank reversal, the criterion for acceptable consistency and the method for deriving priorities, etc) associated with the current PC-based hierarchical models (including the AHP, the multiplicative AHP and the FPR-AHP) are investigated. Another PC-based hierarchical decision model, which is different from the Saaty’s AHP, is introduced for applications …by virtue of its desirable traits (such as the rank preservation, the isomorphic correspondence, etc). Show more

Keywords: hierarchical decision model, weighted average method, pairwise comparisons matrix (PCM), fuzzy preference relations (FPR), isomorphic correspondence

DOI: 10.3233/FI-2016-1339

Citation: Fundamenta Informaticae, vol. 144, no. 3-4, pp. 333-348, 2016

Authors: Huang, Han-Chen | Yang, Xiaojun

Article Type: Research Article

Abstract: The analytic hierarchy process (AHP) is the most popular extension to the pairwise comparisons method which is based on the observation that it is much easier to rank several objects when restricted to two objects at one time. As the pairwise comparisons are subjective, the use of linguistic expressions rather than numerical values is straightforward and friendlier due to the uncertainties that are inherent in human judgments. In this paper, to handle the uncertainty and hesitancy in practical decisionmaking situations, we represent pairwise comparisons in AHP using hesitant cloud linguistic term sets (HCLTSs) which are proposed based on hesitant fuzzy …linguistic term sets (HFLTSs) and normal cloud models. Then, the synthetic cloud model aggregation algorithm is proposed to transform the HCLTS pairwise comparison matrix into the positive reciprocal synthetic cloud matrix. A prioritization method using the geometric mean technique is adopted, and the ranking method based on comparing of the parameters of normal cloud models is proposed. Thus, we extend the traditional AHP method in hesitant and uncertain environment, and we call it HCLTS-AHP method. The comparative linguistic expressions of preferences become more flexible and richer and are more similar to human beings’ cognitive models. Furthermore, the synthetic cloud model is consistent with objectivity and the calculations are easy to implement. An illustrated example is applied to the ranking of four alternatives to show the usefulness of the proposed HCLTS-AHP method. Show more

Keywords: Pairwise comparison, Analytic hierarchy process (AHP), Normal cloud model, Hesitant cloud linguistic term set, Synthetic cloud model aggregation algorithm

DOI: 10.3233/FI-2016-1340

Citation: Fundamenta Informaticae, vol. 144, no. 3-4, pp. 349-362, 2016

Authors: Park, Jin Han | Kim, Ji Yu | Kwun, Young Chel

Article Type: Research Article

Abstract: The geometric Bonferroni mean (GBM) is an important aggregation technique which reflects the correlations of aggregated arguments. Based on the GBM, in this paper, we develop the optimized weighted geometric Bonferroni mean (OWGBM) and the generalized optimized weighted geometric Bonferroni mean (GOWGBM), whose characteristics are to reflect the preference and interrelationship of the aggregated arguments. Furthermore, we develop the intuitionistic fuzzy optimized weighted geometric Bonferroni mean (IFOWGBM) and the generalized intuitionistic fuzzy optimized weighted geometric Bonferroni mean (GIFOWGBM), and study their desirable properties such as idempotency, commutativity, monotonicity and boundedness. Finally, based on the IFOWGBM and GIFOWGBM, we present an …approach to multi-criteria decision making and illustrate it with a practical example. Show more

Keywords: Intuitionistic fuzzy optimized weighted geometric Bonferroni mean (IFOWGBM), generalized intuitionistic fuzzy optimized weighted geometric Bonferroni mean (GIFOWGBM), multi-criteria decision making

DOI: 10.3233/FI-2016-1341

Citation: Fundamenta Informaticae, vol. 144, no. 3-4, pp. 363-381, 2016

Authors: Blagojevic, Bosko | Srdjevic, Bojan | Srdjevic, Zorica | Zoranovic, Tihomir

Article Type: Research Article

Abstract: In AHP group decision making it is desirable that decision makers achieve the highest degree of consensus concerning the group priority vector at both levels, local and the final. Based on this philosophy, we have developed a method to derive local group priority vector respecting the three group consistency measures: geometric cardinal consensus index (GCCI ), group minimum violation coefficient (GMV ) and ordinal consensus measure (OCM ). Consistency of individual decisions against the group decision serves as an input to determine the weights of decision makers participating in the group and generate the group local priority vector. Proposed method …rewards cooperation between members of the group and raises chances for their consensus. Show more

Keywords: AHP group decision making, weights of decision makers, group consistency measures

DOI: 10.3233/FI-2016-1342

Citation: Fundamenta Informaticae, vol. 144, no. 3-4, pp. 383-395, 2016

Authors: Farkas, András

Article Type: Research Article

Abstract: We discuss the development and use of a recursive rank-one residue iteration (triple R-I) to balancing pairwise comparison matrices (PCMs). This class of positive matrices is in the center of interest of a widely used multi-criteria decision making method called analytic hierarchy process (AHP). To find a series of the ‘best’ transitive matrix approximations to the original PCM the Newton-Kantorovich (N-K) method is employed for the solution to the formulated nonlinear problem. Applying a useful choice for the update in the iteration, we show that the matrix balancing problem can be transformed to minimizing the Frobenius norm. Convergence proofs for …this scaling algorithm are given. A comprehensive numerical example is included to illustrate the useful features to measuring and reducing perturbation errors and inconsistency of a PCM as a result of the respondents’ judgments on the pairwise comparisons. Show more

Keywords: numerical mathematics, matrix balancing, diagonal similarity scaling, pairwise comparison matrix

DOI: 10.3233/FI-2016-1343

Citation: Fundamenta Informaticae, vol. 144, no. 3-4, pp. 397-417, 2016

Article Type: Other

Citation: Fundamenta Informaticae, vol. 144, no. 3-4, pp. 419-420, 2016