Camilo Franco

On the analytic hierarchy process and decision support based on fuzzy-linguistic preference structures

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 misapplications 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.

An ordinal approach to computing with words and the preference-aversion model

Computing with words (CWW) explores the brains 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 CWWs 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.

The value of precision for image-based decision support in weed management

Decision support methodologies in precision agriculture should integrate the different dimensions composing the added complexity of operational decision problems. Special attention has to be given to the adequate knowledge extraction techniques for making sense of the collected data, processing the information for assessing decision makers and farmers in the efficient and sustainable management of the field. Focusing on weed management, the integration of operational aspects for weed spraying is an open challenge for modeling the farmers’ decision problem, identifying satisfactory solutions for the implementation of automatic weed recognition procedures. The objective of this paper is to develop a decision support methodology for detecting the undesired weed from aerial images, building an image-based viewpoint consisting in relevant operational knowledge for applying precision spraying. In this way, it is possible to assess the potential herbicide cost reductions of increased precision at the spraying device, selecting the appropriate weed precision spraying technology. Findings from this study indicate that the potential gains and marginal cost reductions of herbicides decrease significantly with increased precision in spraying.

Handling Risk Attitudes for Preference Learning and Intelligent Decision Support

Intelligent decision support should allow integrating human knowledge with efficient algorithms for making interpretable and useful recommendations on real world decision problems. Attitudes and preferences articulate and come together under a decision process that should be explicitly modeled for understanding and solving the inherent conflict of decision making. Here, risk attitudes are represented by means of fuzzy-linguistic structures, and an interactive methodology is proposed for learning preferences from a group of decision makers (DMs). The methodology is built on a multi-criteria framework allowing imprecise observations/measurements, where DMs reveal their attitudes in linguistic form and receive from the system their associated type, characterized by a preference order of the alternatives, together with the amount of consensus and dissention existing among the group. Following on the system’s feedback, DMs can negotiate on a common attitude while searching for a satisfactory decision.

Paired Structures, Imprecision Types and Two-Level Knowledge Representation by Means of Opposites

Opposition-based models are a current hot-topic in knowledge representation. The point of this paper is to suggest that opposition can be in fact introduced at two different levels, those of the predicates of interest being represented (as short/tall) and of the logical references (true/false) used to evaluate the verification of the former. We study this issue by means of the consideration of different paired structures at each level. We also pay attention at how different types of fuzziness may be introduced in these paired structures to model imprecision and lack of knowledge. As a consequence, we obtain a unifying framework for studying the relationships between different knowledge representation models and different kinds of uncertainty.

Building the meaning of preference from logical paired structures

We propose paired structures to represent the meaning/use of preference.Preference models are logically and semantically characterized by paired structures.The semantics of reciprocal preferences reduces to strict preference.The P-A is the only preference model distinguishing between need and desire. Making decisions by learning preferences requires to consider semantical aspects dealing with the meaning and use of the preference concept. Examining recent developments on bipolarity, where concepts are measured/verified regarding a pair of opposite poles, we focus on the dialectic process by which the meaning of concepts emerges. Our proposal is based on the neutrality in between the opposite poles, such that a basic type of structure is used to characterize in logical terms the concepts and the knowledge that they generate. In this paper we model the meaning of concepts by paired structures, and apply these structures for learning and building the different meanings of preference for decision making.

Clustering Alternatives and Learning Preferences Based on Decision Attitudes and Weighted Overlap Dominance

An initial assessment on a given set of alternatives is necessary for understanding complex decision problems and their possible solutions. Attitudes and preferences articulate and come together under a decision process that should be explicitly modeled for understanding and solving the inherent conflict of decision making. This paper revises multi-criteria modeling of imprecise data, inferring outranking and indifference binary relations and classifying alternatives according to their similarity or dependency. After the initial assessment on the set of alternatives, preference orders are built according to the attitudes of decision makers, aiding the decision process by identifying solutions with minimal dissention.

The Fuzzy WOD Model with Application to Biogas Plant Location

The decision of choosing a facility location among possible alternatives can be understood as a multi-criteria problem where the solution depends on the available knowledge and the means of exploiting it. In this sense, knowledge can take various forms, where the imprecise nature of information can be expressed by degrees of intensity in which the alternatives satisfy the given criteria. Hence, such degrees can be gradually expressed either by unique values or by intervals, in order to fully represent the characteristics of each alternative. This paper examines the selection of biogas plant location based on a decision support model capable of handling and exploiting both interval and non-interval forms of knowledge. Such model is built on a fuzzy approach to weighted overlap dominance, where an interactive procedure is developed allowing the individuals to explore and put into perspective how their different attitudes affect the final ranking of alternatives.

Neutrality in Bipolar Structures

In this paper, we want to stress that bipolar knowledge representation naturally allows a family of middle states which define as a consequence different kinds of bipolar structures. These bipolar structures are deeply related to the three types of bipolarity introduced by Dubois and Prade, but our approach offers a systematic explanation of how such bipolar structures appear and can be identified.

Relevance in preference structures

Fuzzy preference and aversion relations allow measuring in a gradual manner the attitude of the individual regarding some pair of alternatives. Following the Preference-Aversion (P-A) model, previously introduced for identifying the subjective cognitive state for some decision situation; here, we explore a methodology for learning relevance degrees over the complete system of alternatives. In this way it is possible to identify in a quick way, the pieces of information that are more important for solving a given decision problem.