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This paper explores a multi-criteria outranking methodology that is designed to both handle uncertain and imprecise data in describing alternatives as well as treating the decision maker's preference information in a sensible way that re flects the difficulties in articulating preferences. Based on fuzzy interval degrees, representing and measuring data imprecision, this procedure obtains a set of semi-equivalence classes assigning an intransitive order on the alternatives. Relevance measures are then explored for ranking alternatives with respect to the semi-equivalence classes, and a final illustrative example is given for comparison with standard methods like PROMETHEE. The proposed methodology takes into account the risk attitudes of decision makers, organizing the alternatives and ranking them according to their relevance. The whole interactive decision support allows understanding the dependencies among the alternatives and how they can be resolved if a finer ranking is preferred., This paper explores a multi-criteria outranking methodology that is designed to both handle uncertain and imprecise data in describing alternatives as well as treating the decision maker's preference information in a sensible way that re flects the difficulties in articulating preferences. Based on fuzzy interval degrees, representing and measuring data imprecision, this procedure obtains a set of semi-equivalence classes assigning an intransitive order on the alternatives. Relevance measures are then explored for ranking alternatives with respect to the semi-equivalence classes, and a final illustrative example is given for comparison with standard methods like PROMETHEE. The proposed methodology takes into account the risk attitudes of decision makers, organizing the alternatives and ranking them according to their relevance. The whole interactive decision support allows understanding the dependencies among the alternatives and how they can be resolved if a finer ranking is preferred.

Computing with words (CWW) explores the brain’s ability to handle and evaluate perceptions through language, i.e., by means of the linguistic representation of information and knowledge. On the other hand, standard preference structures examine decision problems through the decomposition of the preference predicate into the simpler situations of strict preference, indifference and incomparability. Hence, following the distinctive cognitive/neurological features for perceiving positive and negative stimuli in separate regions of the brain, we consider two separate and opposite poles of preference and aversion, and obtain an extended preference structure named the Preference–aversion (P–A) structure. In this way, examining the meaning of words under an ordinal scale and using CWW’s methodology, we are able to formulate the P–A model under a simple and purely linguistic approach to decision making, obtaining a solution based on the preference and non-aversion order., Computing with words (CWW) explores the brain’s ability to handle and evaluate perceptions through language, i.e., by means of the linguistic representation of information and knowledge. On the other hand, standard preference structures examine decision problems through the decomposition of the preference predicate into the simpler situations of strict preference, indifference and incomparability. Hence, following the distinctive cognitive/neurological features for perceiving positive and negative stimuli in separate regions of the brain, we consider two separate and opposite poles of preference and aversion, and obtain an extended preference structure named the Preference–aversion (P–A) structure. In this way, examining the meaning of words under an ordinal scale and using CWW’s methodology, we are able to formulate the P–A model under a simple and purely linguistic approach to decision making, obtaining a solution based on the preference and non-aversion order.

This paper explores a multi-criteria outranking methodology that is designed to both handle uncertain and imprecise data in describing alternatives as well as treating the decision maker's preference information in a sensible way that re flects the difficulties in articulating preferences. Based on fuzzy interval degrees, representing and measuring data imprecision, this procedure obtains a set of semi-equivalence classes assigning an intransitive order on the alternatives. Relevance measures are then explored for ranking alternatives with respect to the semi-equivalence classes, and a final illustrative example is given for comparison with standard methods like PROMETHEE. The proposed methodology takes into account the risk attitudes of decision makers, organizing the alternatives and ranking them according to their relevance. The whole interactive decision support allows understanding the dependencies among the alternatives and how they can be resolved if a finer ranking is preferred., This paper explores a multi-criteria outranking methodology that is designed to both handle uncertain and imprecise data in describing alternatives as well as treating the decision maker's preference information in a sensible way that re flects the difficulties in articulating preferences. Based on fuzzy interval degrees, representing and measuring data imprecision, this procedure obtains a set of semi-equivalence classes assigning an intransitive order on the alternatives. Relevance measures are then explored for ranking alternatives with respect to the semi-equivalence classes, and a final illustrative example is given for comparison with standard methods like PROMETHEE. The proposed methodology takes into account the risk attitudes of decision makers, organizing the alternatives and ranking them according to their relevance. The whole interactive decision support allows understanding the dependencies among the alternatives and how they can be resolved if a finer ranking is preferred.

The Analytic Hierarchy Process (AHP) has received different fuzzy formulations, where two main lines of research can be identified in literature. The most popular one refers to the Extent Analysis Method, which has been subject of recent criticism, among other things, due to a number of missaplications that it may lead to. The other approach refers to the Logarithmic Least Squares Method (LLSM), which offers a constrained optimization approach for estimating fuzzy weights, but fails to generalize the original AHP proposal. The fact remains that the AHP uses linguistic evaluations as input data, where experts value pairs of alternatives/criteria with words, making it essentially fuzzy under the view that words can be represented by fuzzy sets for their respective computation. Hence, reasoning with fuzzy logic is justified by the analytical framework that it offers to design the meaning of words through membership functions and not assume a direct mapping between words and crisp numbers. In this paper we propose the fuzzy representation of linguistic preferences for the AHP, and examine its generalization by means of the fuzzy-linguistic AHP algorithm., The Analytic Hierarchy Process (AHP) has received different fuzzy formulations, where two main lines of research can be identified in literature. The most popular one refers to the Extent Analysis Method, which has been subject of recent criticism, among other things, due to a number of missaplications that it may lead to. The other approach refers to the Logarithmic Least Squares Method (LLSM), which offers a constrained optimization approach for estimating fuzzy weights, but fails to generalize the original AHP proposal. The fact remains that the AHP uses linguistic evaluations as input data, where experts value pairs of alternatives/criteria with words, making it essentially fuzzy under the view that words can be represented by fuzzy sets for their respective computation. Hence, reasoning with fuzzy logic is justified by the analytical framework that it offers to design the meaning of words through membership functions and not assume a direct mapping between words and crisp numbers. In this paper we propose the fuzzy representation of linguistic preferences for the AHP, and examine its generalization by means of the fuzzy-linguistic AHP algorithm.

Computing with words (CWW) explores the brain’s ability to handle and evaluate perceptions through language, i.e., by means of the linguistic representation of information and knowledge. On the other hand, standard preference structures examine decision problems through the decomposition of the preference predicate into the simpler situations of strict preference, indifference and incomparability. Hence, following the distinctive cognitive/neurological features for perceiving positive and negative stimuli in separate regions of the brain, we consider two separate and opposite poles of preference and aversion, and obtain an extended preference structure named the Preference–aversion (P–A) structure. In this way, examining the meaning of words under an ordinal scale and using CWW’s methodology, we are able to formulate the P–A model under a simple and purely linguistic approach to decision making, obtaining a solution based on the preference and non-aversion order., Computing with words (CWW) explores the brain’s ability to handle and evaluate perceptions through language, i.e., by means of the linguistic representation of information and knowledge. On the other hand, standard preference structures examine decision problems through the decomposition of the preference predicate into the simpler situations of strict preference, indifference and incomparability. Hence, following the distinctive cognitive/neurological features for perceiving positive and negative stimuli in separate regions of the brain, we consider two separate and opposite poles of preference and aversion, and obtain an extended preference structure named the Preference–aversion (P–A) structure. In this way, examining the meaning of words under an ordinal scale and using CWW’s methodology, we are able to formulate the P–A model under a simple and purely linguistic approach to decision making, obtaining a solution based on the preference and non-aversion order.

Decision support models are required to handle the various aspects of multi-criteria decision problems in order to help the individual understand its possible solutions. In this sense, such models have to be capable of aggregating and exploiting different types of measurements and evaluations in an interactive way, where input data can take the form of uniquely-graded or interval-valued information. Here we explore the Weighted Overlap Dominance (WOD) model from a fuzzy perspective and its outranking approach to decision support and multidimensional interval analysis. Firstly, imprecision measures are introduced for characterizing the type of uncertainty being expressed by intervals, examining at the same time how the WOD model handles both non-interval as well as interval data, and secondly, relevance degrees are proposed for obtaining a ranking over the alternatives. Hence, a complete methodology is presented for ordering and identifying the best alternatives under an interactive procedure that takes into account the natural imprecision and relevance of information., Decision support models are required to handle the various aspects of multi-criteria decision problems in order to help the individual understand its possible solutions. In this sense, such models have to be capable of aggregating and exploiting different types of measurements and evaluations in an interactive way, where input data can take the form of uniquely-graded or interval-valued information. Here we explore the Weighted Overlap Dominance (WOD) model from a fuzzy perspective and its outranking approach to decision support and multidimensional interval analysis. Firstly, imprecision measures are introduced for characterizing the type of uncertainty being expressed by intervals, examining at the same time how the WOD model handles both non-interval as well as interval data, and secondly, relevance degrees are proposed for obtaining a ranking over the alternatives. Hence, a complete methodology is presented for ordering and identifying the best alternatives under an interactive procedure that takes into account the natural imprecision and relevance of information.

Decision support models are required to handle the various aspects of multi-criteria decision problems in order to help the individual understand its possible solutions. In this sense, such models have to be capable of aggregating and exploiting different types of measurements and evaluations in an interactive way, where input data can take the form of uniquely-graded or interval-valued information. Here we explore the Weighted Overlap Dominance (WOD) model from a fuzzy perspective and its outranking approach to decision support and multidimensional interval analysis. Firstly, imprecision measures are introduced for characterizing the type of uncertainty being expressed by intervals, examining at the same time how the WOD model handles both non-interval as well as interval data, and secondly, relevance degrees are proposed for obtaining a ranking over the alternatives. Hence, a complete methodology is presented for ordering and identifying the best alternatives under an interactive procedure that takes into account the natural imprecision and relevance of information., Decision support models are required to handle the various aspects of multi-criteria decision problems in order to help the individual understand its possible solutions. In this sense, such models have to be capable of aggregating and exploiting different types of measurements and evaluations in an interactive way, where input data can take the form of uniquely-graded or interval-valued information. Here we explore the Weighted Overlap Dominance (WOD) model from a fuzzy perspective and its outranking approach to decision support and multidimensional interval analysis. Firstly, imprecision measures are introduced for characterizing the type of uncertainty being expressed by intervals, examining at the same time how the WOD model handles both non-interval as well as interval data, and secondly, relevance degrees are proposed for obtaining a ranking over the alternatives. Hence, a complete methodology is presented for ordering and identifying the best alternatives under an interactive procedure that takes into account the natural imprecision and relevance of information.

Decision support models are required to handle the various aspects of multi-criteria decision problems in order to help the individual understand its possible solutions. In this sense, such models have to be capable of aggregating and exploiting different types of measurements and evaluations in an interactive way, where input data can take the form of uniquely-graded or interval-valued information. Here we explore the Weighted Overlap Dominance (WOD) model from a fuzzy perspective and its outranking approach to decision support and multidimensional interval analysis. Firstly, imprecision measures are introduced for characterizing the type of uncertainty being expressed by intervals, examining at the same time how the WOD model handles both non-interval as well as interval data, and secondly, relevance degrees are proposed for obtaining a ranking over the alternatives. Hence, a complete methodology is presented for ordering and identifying the best alternatives under an interactive procedure that takes into account the natural imprecision and relevance of information.

The purpose of this paper is to model the multi-criteria decision problem of identifying the most suitable facility locations for biogas plants under an integrated decision support methodology. Here the Geographical Information System (GIS) is used for measuring the attributes of the alternatives according to a given set of criteria. Measurements are taken in interval form, expressing the natural imprecision of common data, and the Fuzzy Weighted Overlap Dominance (FWOD) procedure is applied for aggregating and exploiting this kind of data, obtaining suitability degrees for every alternative. The estimation of criteria weights, which is necessary for applying the FWOD procedure, is done by means of the Analytical Hierarchy Process (AHP), such that a combined AHP-FWOD methodology allows identifying the more suitable sites for building biogas plants. We show that the FWOD relevance-ranking procedure can also be successfully applied over the outcomes of different decision makers, in case a unique social solution is required to exist. The proposed methodology can be used under an integrated decision support frame for identifying the most suitable locations for biogas facilities, taking into account the most relevant criteria for the social, economic and political dimensions., The purpose of this paper is to model the multi-criteria decision problem of identifying the most suitable facility locations for biogas plants under an integrated decision support methodology. Here the Geographical Information System (GIS) is used for measuring the attributes of the alternatives according to a given set of criteria. Measurements are taken in interval form, expressing the natural imprecision of common data, and the Fuzzy Weighted Overlap Dominance (FWOD) procedure is applied for aggregating and exploiting this kind of data, obtaining suitability degrees for every alternative. The estimation of criteria weights, which is necessary for applying the FWOD procedure, is done by means of the Analytical Hierarchy Process (AHP), such that a combined AHP-FWOD methodology allows identifying the more suitable sites for building biogas plants. We show that the FWOD relevance-ranking procedure can also be successfully applied over the outcomes of different decision makers, in case a unique social solution is required to exist. The proposed methodology can be used under an integrated decision support frame for identifying the most suitable locations for biogas facilities, taking into account the most relevant criteria for the social, economic and political dimensions.

This paper extends the Weighted Overlap Dominance (WOD) model (initially presented in J.L. Hougaard, K. Nielsen. Weighted Overlap Dominance - A procedure for interactive selection on multidimensional interval data. Applied Mathematical Modelling 35, 2011, 3958 - 3969), as an outranking approach for decision support and multidimensional interval analysis. First, the original approach is extended using fuzzy set theory which makes it possible to handle both non-interval and interval data. Second, we re-examine the ranking procedure based on semi-equivalence classes and suggest a new complementary ranking procedure. The new ranking procedure introduces relevance degrees for ranking the given set of alternatives. In this way, a complete methodology is presented for identifying recommended solutions that aid the decision-maker when facing a specific problem, by ranking alternatives according to their relevance under imprecise measurements., This paper extends the Weighted Overlap Dominance (WOD) model (initially presented in J.L. Hougaard, K. Nielsen. Weighted Overlap Dominance - A procedure for interactive selection on multidimensional interval data. Applied Mathematical Modelling 35, 2011, 3958 - 3969), as an outranking approach for decision support and multidimensional interval analysis. First, the original approach is extended using fuzzy set theory which makes it possible to handle both non-interval and interval data. Second, we re-examine the ranking procedure based on semi-equivalence classes and suggest a new complementary ranking procedure. The new ranking procedure introduces relevance degrees for ranking the given set of alternatives. In this way, a complete methodology is presented for identifying recommended solutions that aid the decision-maker when facing a specific problem, by ranking alternatives according to their relevance under imprecise measurements.

The purpose of this paper is to model the multi-criteria decision problem of identifying the most suitable facility locations for biogas plants under an integrated decision support methodology. Here the Geographical Information System (GIS) is used for measuring the attributes of the alternatives according to a given set of criteria. Measurements are taken in interval form, expressing the natural imprecision of common data, and the Fuzzy Weighted Overlap Dominance (FWOD) procedure is applied for aggregating and exploiting this kind of data, obtaining suitability degrees for every alternative. The estimation of criteria weights, which is necessary for applying the FWOD procedure, is done by means of the Analytical Hierarchy Process (AHP), such that a combined AHP-FWOD methodology allows identifying the more suitable sites for building biogas plants. We show that the FWOD relevance-ranking procedure can also be successfully applied over the outcomes of different decision makers, in case a unique social solution is required to exist. The proposed methodology can be used under an integrated decision support frame for identifying the most suitable locations for biogas facilities, taking into account the most relevant criteria for the social, economic and political dimensions., The purpose of this paper is to model the multi-criteria decision problem of identifying the most suitable facility locations for biogas plants under an integrated decision support methodology. Here the Geographical Information System (GIS) is used for measuring the attributes of the alternatives according to a given set of criteria. Measurements are taken in interval form, expressing the natural imprecision of common data, and the Fuzzy Weighted Overlap Dominance (FWOD) procedure is applied for aggregating and exploiting this kind of data, obtaining suitability degrees for every alternative. The estimation of criteria weights, which is necessary for applying the FWOD procedure, is done by means of the Analytical Hierarchy Process (AHP), such that a combined AHP-FWOD methodology allows identifying the more suitable sites for building biogas plants. We show that the FWOD relevance-ranking procedure can also be successfully applied over the outcomes of different decision makers, in case a unique social solution is required to exist. The proposed methodology can be used under an integrated decision support frame for identifying the most suitable locations for biogas facilities, taking into account the most relevant criteria for the social, economic and political dimensions.

This paper extends the Weighted Overlap Dominance (WOD) model (initially presented in J.L. Hougaard, K. Nielsen. Weighted Overlap Dominance - A procedure for interactive selection on multidimensional interval data. Applied Mathematical Modelling 35, 2011, 3958 - 3969), as an outranking approach for decision support and multidimensional interval analysis. First, the original approach is extended using fuzzy set theory which makes it possible to handle both non-interval and interval data. Second, we re-examine the ranking procedure based on semi-equivalence classes and suggest a new complementary ranking procedure. The new ranking procedure introduces relevance degrees for ranking the given set of alternatives. In this way, a complete methodology is presented for identifying recommended solutions that aid the decision-maker when facing a specific problem, by ranking alternatives according to their relevance under imprecise measurements., This paper extends the Weighted Overlap Dominance (WOD) model (initially presented in J.L. Hougaard, K. Nielsen. Weighted Overlap Dominance - A procedure for interactive selection on multidimensional interval data. Applied Mathematical Modelling 35, 2011, 3958 - 3969), as an outranking approach for decision support and multidimensional interval analysis. First, the original approach is extended using fuzzy set theory which makes it possible to handle both non-interval and interval data. Second, we re-examine the ranking procedure based on semi-equivalence classes and suggest a new complementary ranking procedure. The new ranking procedure introduces relevance degrees for ranking the given set of alternatives. In this way, a complete methodology is presented for identifying recommended solutions that aid the decision-maker when facing a specific problem, by ranking alternatives according to their relevance under imprecise measurements.

Although consistency in information and actions is a major argument in any decision making problem, most available tools are crisp, while observation strongly suggests to consider different degrees of consistency, i.e.,consistency is fuzzy in nature. In this paper we propose to put together some of the works in the field, focusing on information consistency rather than on action consistency, showing in this way key classification features.