Shou-Hsiung Cheng

Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology

We propose a new intuitionistic fuzzy multiattribute group decision making method.The intuitionistic fuzzy sets and evidential reasoning methodology are used.It gets the aggregated intuitionistic fuzzy value of each alternative.It calculates the transformed value of each alternative.It provides us with a useful way for intuitionistic fuzzy multiattribute group decision making. In this paper, we propose a new fuzzy multiattribute group decision making method based on intuitionistic fuzzy sets and the evidential reasoning methodology. First, the proposed method uses the evidential reasoning methodology to aggregate each decision makers decision matrix and the weights of the attributes to get the aggregated decision matrix of each decision maker. Then, it uses the obtained aggregated decision matrices of the experts, the weights of the experts and the evidential reasoning methodology to get the aggregated intuitionistic fuzzy value of each alternative. Finally, it calculates the transformed value of the obtained intuitionistic fuzzy value of each alternative. The smaller the transformed value, the better the preference order of the alternative. The proposed method can overcome the drawbacks of the existing methods for fuzzy multiattribute group decision making in intuitionistic fuzzy environments.

Fuzzy time series forecasting based on fuzzy logical relationships and similarity measures

In this paper, we propose a new fuzzy time series forecasting method for forecasting the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) based on fuzzy time series, fuzzy logical relationships, particle swarm optimization techniques, the K-means clustering algorithm, and similarity measures between the subscript of the fuzzy set of the fuzzified historical testing datum on the previous trading day and the subscripts of the fuzzy sets appearing in the current states of the fuzzy logical relationships in the chosen fuzzy logical relationship group. The particle swarm optimization techniques are used to get the optimal partition of the intervals in the universe of discourse. The K-means clustering algorithm is used to cluster the subscripts of the fuzzy sets of the current states of the fuzzy logical relationships to get the cluster center of each cluster and to divide the constructed fuzzy logical relationships into fuzzy logical relationship groups. The experimental results show that the proposed fuzzy forecasting method gets higher forecasting accuracy rates than the existing methods. The advantages of the proposed fuzzy forecasting method is that it uses the particle swarm optimization techniques to get the optimal partition of the intervals in the universe of discourse and uses the K-means clustering algorithm to cluster the subscripts of the fuzzy sets of the current states of the fuzzy logical relationships to get the cluster center of each cluster and to divide the constructed fuzzy logical relationships into fuzzy logical relationship groups for increasing the forecasting accuracy rates.

Multicriteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values

Multicriteria decision making (MCDM) in intuitionistic fuzzy environments is a very important research topic. In this paper, we propose a new MCDM method based on the TOPSIS method and similarity measures between intuitionistic fuzzy values (IFVs). First, the proposed method calculates the degree of indeterminacy of each evaluating IFV given by the decision maker. Then, it gets the relative positive ideal solution and the relative negative ideal solution for the criteria, respectively. Then, it calculates the degrees of indeterminacy of the relative positive ideal value and the relative negative ideal value for each criterion, respectively. Then, it calculates the positive similarity degrees and the negative similarity degrees between the evaluating IFVs and the relative positive ideal solutions and the relative negative ideal solutions for the criteria, respectively. Finally, it calculates the weighted positive score and the weighted negative score of each alternative, respectively, to get the relative degree of closeness of each alternative. The larger the relative degree of closeness of the alternative, the better the preference order of the alternative. The experimental results show that the proposed method can overcome the drawbacks of Joshi and Kumars method (2014), Wang and Weis method (2008) and Wu and Chens method (2011) for MCDM in intuitionistic fuzzy environments.

A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition

In this paper, we propose a new similarity measure between intuitionistic fuzzy values based on the centroid points of transformed right-angled triangular fuzzy numbers. We also prove some properties of the proposed similarity measure between intuitionistic fuzzy values. Based on the proposed similarity measure between intuitionistic fuzzy values, we propose a new similarity measure between intuitionistic fuzzy sets. We also apply the proposed similarity measure between intuitionistic fuzzy sets to deal with pattern recognition problems. The experimental results show that the proposed similarity measure between intuitionistic fuzzy sets can overcome the drawbacks of the existing similarity measures. The proposed similarity measure provides us with a useful way for dealing with pattern recognition problems in intuitionistic fuzzy environments.

Group decision making systems using group recommendations based on interval fuzzy preference relations and consistency matrices

In this paper, we present a new method for group decision making using group recommendations based on interval fuzzy preference relations and consistency matrices. First, the proposed method constructs the collective consistency matrix, the weighted collective preference relation, and the group collective preference relation. Then, it constructs a consensus relation for each expert and calculates the group consensus degree of all experts. If the group consensus degree is smaller than a predefined threshold value, then it marks the consensus values in each consensus relation which are smaller than the group consensus degree and modifies the interval fuzzy preference values corresponding to the marked consensus values. The above process is performed repeatedly, until the group consensus degree is larger than or equal to the predefined threshold value. Finally, based on the group collective preference relation, it calculates the score of each alternative for ranking the preference order of the alternatives. The proposed method can overcome the drawbacks of the existing methods for group decision making. It provides us with a useful way for group decision making using group recommendations based on interval fuzzy preference relations and consistency matrices.

Multiple attribute group decision making based on interval-valued intuitionistic fuzzy aggregation operators and transformation techniques of interval-valued intuitionistic fuzzy values

In this paper, we propose a new method for multiple attribute group decision making (MAGDM) based on the proposed interval-valued intuitionistic fuzzy aggregation (IVIFA) operators (including the interval-valued intuitionistic fuzzy weighted averaging (IVIFWA) operator, the interval-valued intuitionistic fuzzy ordered weighted averaging (IVIFOWA) operator and the interval-valued intuitionistic fuzzy hybrid weighted averaging (IVIFHWA) operator) of interval-valued intuitionistic fuzzy values (IVIFVs). First, we propose transformation techniques between IVIFVs and right-angled triangular fuzzy numbers based on the proposed addition operator of IVIFVs. We also prove some properties of the proposed addition operator of IVIFVs. Then, we propose the IVIFWA operator, the IVIFOWA operator and the IVIFHWA operator for aggregating IVIFVs. Finally, we propose a new MAGDM method based on the proposed IVIFA operators. The experimental results show that the proposed MAGDM method can overcome the drawbacks of the existing methods. It provides us with a useful way for MAGDM in interval-valued intuitionistic fuzzy environments.

Autocratic decision making using group recommendations based on ranking interval type-2 fuzzy sets

In this paper, we propose a new autocratic decision making method using group recommendations based on ranking interval type-2 fuzzy sets. First, the proposed method calculates the ranking values of interval type-2 fuzzy sets appearing in the weighting vectors and the evaluating matrices given by decision makers, respectively, to construct the ranking weighting vectors and the ranking evaluating matrices of the decision makers, respectively. Then, it constructs the weighted evaluating matrix of each decision maker and calculates the aggregated evaluating value of each alternative with respect to each decision maker for constructing the aggregated evaluating matrix of all decision makers. Then, it gets the numerical preference order of the alternatives with respect to each decision maker represented by a preference vector. Then, it calculates the aggregated group evaluating value of each alternative with respect to all decision makers to get the numerical preference order of the alternatives with respect to all decision makers represented by a group preference vector. Then, it calculates the similarity degree between the obtained preference vector of each decision maker and the obtained group preference vector of all decision makers. Then, it gets the normalized aggregated evaluating value of each alternative with respect to each decision maker to construct the normalized aggregated evaluating vector of each decision maker. Then, it gets the normalized aggregated group evaluating value of each alternative with respect to all decision makers to construct the normalized aggregated group evaluating vector of all decision makers. Finally, it calculates the similarity degree between the obtained normalized aggregated evaluating vector of each decision maker and the obtained normalized aggregated group evaluating vector of all decision makers for changing the weights of the decision makers until the group consensus degree is larger than or equal to a predefined consensus threshold value. We apply the proposed method to deal with the system analysis engineers selection problem, the cars selection problem and the table tennis players selection problem. The proposed method can overcome the drawbacks of the existing group decision making methods in interval type-2 fuzzy sets environments.

Autocratic multiattribute group decision making for hotel location selection based on interval-valued intuitionistic fuzzy sets

Abstract In this paper, we propose a new autocratic multiattribute group decision making (AMAGDM) method for hotel location selection based on interval-valued intuitionistic fuzzy sets (IVIFSs), where the evaluating values of the attributes for alternatives and the weights of the attributes given by decision makers are represented by interval-valued intuitionistic fuzzy values (IVIFVs). The proposed method calculates the changing of the weights of the decision makers until the group consensus degree (GCD) of the decision makers is larger than or equal to a predefined threshold value. We also apply the proposed AMAGDM method to deal with the hotel location selection problem. The main contribution of this paper is that we propose a new AMAGDM method which is simpler than Wibowos method (2013), where the drawback of Wibowos method is that it is too complicated due to the fact that it adopts the concept of ideal solutions for determining the overall performance of each hotel location alternative with respect to all the selection criteria. The proposed AMAGDM method provides us with a very useful way for AMAGDM in interval-valued intuitionistic fuzzy environments.

Adaptive fuzzy interpolation based on ranking values of polygonal fuzzy sets and similarity measures between polygonal fuzzy sets

After the fuzzy interpolative reasoning processes, if two unequal fuzzy interpolative reasoning results are derived (or one derived and another observed) for a consequence variable of a fuzzy rule, then it is called a contradiction in the fuzzy interpolative reasoning process. In recent years, some adaptive fuzzy interpolation methods for sparse fuzzy rule-based systems have been presented to solve contradictions after fuzzy interpolative reasoning processes. In this paper, a new adaptive fuzzy interpolation method is proposed for sparse fuzzy rule-based systems based on ranking values and similarity measures of polygonal fuzzy sets, which can solve contradictions occurred in fuzzy interpolative reasoning processes. We also apply the proposed adaptive fuzzy interpolation method to predict the diarrheal disease rates in roadless villages. The diarrheal disease prediction problem focuses on the issue to measure how the construction of a new road or railway in a previously roadless area may affect the epidemiology of infectious diseases in northern coastal Ecuador. The experimental results show that the proposed adaptive fuzzy interpolation method can overcome the drawbacks of the existing methods.

Fuzzy interpolative reasoning based on the ratio of fuzziness of rough-fuzzy sets

In this paper, we propose a method to construct a polygonal rough-fuzzy set from a set of polygonal fuzzy sets representing the aggregation of multiple experts opinions and propose a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on the ratio of fuzziness of the constructed polygonal rough-fuzzy sets, where the values of the antecedent variables and the consequence variable appearing in the fuzzy rules are represented by the constructed polygonal rough-fuzzy sets. The proposed fuzzy interpolative reasoning method can overcome the drawbacks of the existing method due to the fact that it can deal with fuzzy interpolative reasoning using polygonal rough-fuzzy sets and it gets more reasonable fuzzy interpolative reasoning results than the existing method.