A Possibilistic Logic View of Sugeno Integrals

The cube of opposition is a logical structure that underlies many information representation settings. When applied to multiple criteria decision, it displays various possible aggregation attitudes. Situations are usually assessed by combinations of properties they satisfy, but also by combinations of properties they do not satisfy. The cube of opposition applies to qualitative evaluation when criteria are weighted as well as in the general case where any subset of criteria may be weighted for expressing synergies between them, as for Sugeno integrals. Sugeno integrals are well-known as a powerful qualitative aggregation tool which takes into account positive synergies between properties. When there are negative synergies between properties we can use the so-called desintegral associated to the Sugeno integral. The paper investigates the use of the cube of opposition and of the if-then rules extracted from these integrals and desintegrals in order to better describe acceptable situations.

This paper describes a logical machinery for computing decisions, where the available knowledge on the state of the world is described by a possibilistic propositional logic base (i.e., a collection of logical statements associated with qualitative certainty levels), and where the preferences of the user are also described by another possibilistic logic base whose formula weights are interpreted in terms of priorities. Two attitudes are allowed for the decision maker: a pessimistic risk-averse one and an optimistic one. The computed decisions are in agreement with a qualitative counterpart to the classical theory of expected utility, recently developed by three of the authors. A link is established between this logical view of qualitative decision making and an ATMS-based computation procedure. Efficient algorithms for computing pessimistic and optimistic optimal decisions are finally given in this logical setting (using some previous work of the fourth author).

The themes for this conference are thus focused on "Innovating and Inspiring Soft Computing and Intelligent Pattern Recognition"

The performance measurement systems (PMS) in the industry are defined in terms of various measures to be combined for global performance. The proposed approach treats with a qualitative approach for multicriteria decision with the improvement strategy of an overall industrial performance. The approach is based on a AHP and Sugeno integral aggregation operator, permits to express the global performance, according to the fuzzy set theory of appropriate Key Performance Indicators (KPI), the nonlinearity of this model, makes data ambiguous in the process of multicriteria decision-making. Hence, this manuscript is a contribution to the selection of the strategy of the improvement of the overall performance. The approach applies to the Moroccan Automotive Suppliers to evaluate three strategies alternatives by using a fuzzy Sugeno Integral technique to deal with the complex interrelationships aspects between KPI.

A new characterization of the discrete Sugeno integral

Integrals on finite spaces (e.g., sets of criteria in multicriteria decision support) based on capacities are discussed, axiomatized and examplified. We introduce first the universal integrals, covering the Choquet, Shilkret and Sugeno integrals. Based on optimization approach, we discuss decomposition and superdecomposition integrals. We introduce integrals which are universal and decomposition (superdecomposition) ones and integrals constructed by means of copulas. Several distinguished integrals are represented as particular functionals. Finally, we recall also OWA operators and some their generalizations.KeywordsCapacityChoquet integralCopulaCopula–based integralDecomposition integralSugeno integralUniversal integral

The well-known Choquet integrals are based on given fuzzy measures, providing some sound schemes for the evaluation problems in multicriteria decision making. To further generalize and diversify these interesting aggregation functions, this article proposes the concept of derived fuzzy measures, which can serve as a generalization of normally used fuzzy measures. Based on derived fuzzy measures, we present the detailed integral methods to define the corresponding derived Choquet integrals. With some specific derived fuzzy measures, we find that both Choquet and Sugeno integrals are special cases of derived Choquet integrals. In addition, some relevant properties and propositions with practical explanations are also discussed, for example, the less/more increment properties and amplifying/attenuating properties.

We study the optimal allocation of heterogeneous services without using monetary transfers. Agents have private, multi-dimensional utilities over the services, and a social planner has arbitrary priors on the utilities, which may depend on the agents' observable characteristics. The social planner's goal is to maximize a public objective, which may be complex, taking into account diverse considerations such as social welfare, equity, and system costs. Potential applications include the allocation of seats to public schools, spaces in college dorms or courses, and spots in subsidized housing. We propose an engineering approach to such problems, in which we simplify the analysis by considering a large-market model with a continuum of agents, and show using real data that a mechanism defined based on this approximation still yields good results in the finite market. In the large-market model, there are finitely many types, and a continuum of agents of each type. (Here, corresponds to an agent's observable information, which is distinct from the private utilities.) The large market assumption implies that a mechanism can be decomposed into a collection of allocation rules, one for each type. We show that any allocation rule that satisfies incentive compatibility and Pareto optimality within type is representable as Competitive Equilibrium with Equal Incomes (CEEI). In other words, for each type of agents and for each service, there exists a virtual price for a unit of probability of getting that service, and the allocation is induced by giving each agent one unit of virtual money' and having them purchase their utility-maximizing probabilities to services. In addition, if the mechanism is restricted to being 'ordinal,' which means that it only uses preference rankings but not preference intensities, then an allocation rule that satisfies incentive compatibility and ordinal efficiency within type is 'lottery-plus-cutoff': each agent receives a uniformly random lottery number between zero and one, and for each service and each type, there is a 'lottery cutoff'; an agent is 'admitted' to a service if her lottery number is below the cutoff; each agent is allocated her most preferred service for which she is admitted. Such characterization results reduce the search of the optimal mechanism to a well-defined optimization over the prices and cutoffs for each type. We show how this large market approximation can be applied to an empirically relevant finite setting and yield good results. We consider the allocation of seats in public schools in Boston, which was a real problem faced by a city committee in the 2012-2013 Boston school assignment reform. Students are classified into 868 types by home location and there is a utility model for each type that comes from fitting a multinomial logit discrete choice model on previous years' data. There are 77 elementary schools with given capacities. Depending on their home location, a student is given a menu of options and can submit a preference ranking over the schools in the menu. Given preference submissions, a centralized algorithm computes the assignment using a system of priorities, possibly randomizing to break ties. The goal is to optimize the menus and priorities to maximize a weighted combination of social welfare and max-min welfare, while staying within a budget for expected amount of busing needed. Although this is a finite market problem, we can define a large market approximation. Using the characterization results, we show that the optimal mechanism can be encoded as an exponential-sized linear program, which due to the logit utility structure can be efficiently solved using duality theory. Using the cutoffs that arise from this optimization, we define a feasible finite market mechanism that is based on the Deferred Acceptance algorithm. We evaluate the resultant mechanism by simulating in the finite market setting with real data, and show that compared to the mechanism chosen by the city, this new mechanism significantly improves simultaneously in social welfare, max-min welfare and predictability, while staying within the same expected busing budget. In sum, we incorporate prior information in the allocation problem without monetary transfers, and exhibit computational results in empirically relevant special cases.

The main stages and directions of transformation of the US priority system in bilateral relations with Middle Eastern countries are determined through their retrospective and prognostic analysis in the context of regional and global international political situation. The influence of American electoral processes on the transformation of US Middle East policy strategies is clarified. The mechanisms for implementing strategies such as "reduction," "non-intervention," "distant balancing," "containment and engagement," "regime change," "engagement as integration," "engagement as bargaining," "reconciliation," "maximum pressure," "containment and involvement" in bilateral relations with Middle Eastern countries are disclosed, along with the dynamics of American-Iranian and American-Saudi relations due to the application of selected strategies. It is proven that the influence of the US as a global power capable of exercising monopolistic control over the development of events and processes both at the global and regional (Middle Eastern) levels is diminishing, reflecting a broader shift in the global balance of power. The weakening of their leadership positions is particularly evident in the Middle East region, dominance in which was one of the guarantors of US global leadership. It is substantiated that most directions of US bilateral Middle Eastern policy have experienced negative dynamics due to the influence of both global and regional factors, including the strengthening of the positions of the PRC and the RF and intra-regional changes. If during the period of bipolar confrontation, global factors were key in shaping the priority system of US bilateral relations with Middle Eastern countries, then at the present stage, the role of regional factors is increasing while maintaining the importance of global ones (the need to counteract the PRC and the RF, the Russian-Ukrainian war, the Israel-Hamas conflict, the Iran-Israel confrontation).

The article analyses the methods of forming the aircraft flight schedule based on the classical theory of schedules as a theory of multi-stage systems. It is shown that the timetable is a system without interruptions, since each specific flight at a certain point in time is carried out by only one aircraft. In accordance with the theory of schedules, the optimal distribution of a discrete finite set of requirements serviced by deterministic systems with one or more devices is analysed under various assumptions about the nature of their maintenance. It is shown that the weakest assumption regarding the abstract operator, which translates many requirements into many agreed and executed plans, is the monotonic and unimodal behaviour of the corresponding functional of the generated plans. The possibilities of applying the theory of multi-stage systems to create the optimal schedule for medium or large airlines are investigated. The basic requirements for constructing a schedule are advanced. Mathematical models of the schedule are constructed taking into account the basic data of the current movement of aircraft in the area of ​​the airport or air hub. It has been established that if the base airports change their purpose and act as terminal arrival airports, the corresponding matrix elements are inversely symmetric, and with a rarefied spatial distribution of airports, the matrix can tend to diagonally dominant. A comparative analysis of scheduling algorithms is performed (based on queuing models, based on lists with the distribution of flights over time, etc.). The most suitable indicators of the effectiveness of the formation of the optimal schedule and system of priorities were selected and justified, taking into account the advantages of the arrival and departure times of passenger flights. An expression is derived for the resulting functional schedule efficiency, with which you can get quantitative comparative assessments of the quality of the schedule.

At present, problems related to data mining are aris-ing in various poorly formalizable areas of research(genetics, archaeology, medicine, etc.). Such problemsare characterized by insufficient knowledge about theobjects under study, which hampers the development ofmathematical models for them; by a large number ofmultitype (quantitative and qualitative) factors and arelatively small amount of data; and by the requirementthat analysis results be represented in a form clear toexperts in applied areas.A promising approach to solving such problems isbased on the class of logical decision functions. Theyare frequently represented in the form of a decisiontree. A detailed description of this class and referencescan be found in [1].The construction of decision functions with a mini-mal risk of erroneous predictions is an important task inmethods based on logical decision functions and inother data analysis techniques. It is well known that thecomplexity of the class of decision functions (thecapacity characteristic of the class [2]) is a importantfactor affecting the quality of decisions. To achieve thebest quality, we need a certain tradeoff between thecomplexity of the class and the accuracy of decisionsobtained on the training sample. Thus, the problemarises of choosing an optimal complexity of the class.In numerous applications, empirical data (trainingsample) are supplemented with expert knowledge,which is not tightly related to a distribution model(expert knowledge can be specified as upper bounds forthe risk; they can express constraints on the class of dis-tributions or the class of decision functions, specifypreference rules used in decision making, etc.). Whenan optimal complexity of the class is chosen, availableempirical data and expert knowledge have to be jointlytaken into account.This problem can be solved within the framework ofthe Bayesian learning theory. The idea behind thisapproach is to use a priori knowledge about the prob-lem in question so that each possible distribution (strat-egy, the state of nature) is assigned a certain weight.This weight reflects the expert’s intuitive confidence inwhether the unknown true distribution coincides withthat under consideration.In this paper, we propose a Bayesian recognitionmodel based on a finite set of events. The model is usedto develop and analyze methods for constructing logi-cal decision functions. While choosing an optimal com-plexity of the class, the model takes into account empir-ical data and expert knowledge.In pattern recognition, the task is to predict the pat-tern’s index for an arbitrary object of the populationdescribed by a set of variables. The prediction is madeby analyzing a training sample consisting of the valuesof these variables, together with the index of the corre-sponding pattern for each object. The variables can beof different types; i.e., some of them can be quantita-tive, while the others can be qualitative. As a rule, theproblem is solved in a class of decision functions inwhich an optimal function is sought according to agiven criterion. The class of logical decision functionsis defined on a set of partitions of the feature space intoa finite number of subdomains described by conjunc-tions of simple predicates. The number of subdomainsdetermines the degree of complexity of a logical func-tion.A Bayesian pattern recognition model on a finite setof events is defined by formulating certain statementsthat avoid the local metric properties of the featurespace (the transition from points of the space to events,where an event is understood as that of the original vari-ables taking values from a certain subdomain of thepartition). Moreover, the pattern recognition problem isconsidered on the values of a discrete unordered vari-able, the concept of a learning method (a mapping from

This cross-sectional observational study examined urologic morbidity and its effects on Japanese patients' global satisfaction with their treatment outcome. A questionnaire was mailed to 44 men who had undergone radical prostatectomy for prostate cancer at a mean age of 65.5 years and were free from recurrent symptoms at a mean follow-up of 3.3 years. Most (70%) had pathologic stage C or D1 disease and many (86%) had received adjuvant endocrine therapy. After reporting urinary symptoms, the patients estimated their overall urinary, sexual, physical, psychological, and social functioning, and global satisfaction level with their treatment outcome. Regression analysis was performed to detect significant factors in predicting overall urinary conditions or satisfaction. Daily urinary leakage and forceless urinary stream was noted in 30% and 23% of patients, respectively. Overall urinary conditions were evaluated as good or very good in 61 % of patients, and were most significantly associated with the patient's satisfaction with their force of urinary flow (P < 0.001). Global satisfaction with treatment outcome was estimated as good or very good in 80% of patients, and it was predicted by physical functions (P= 0.013) and psychological distress (P= 0.036), and to a lesser extent by urinary conditions (P= 0.195). A forceless urinary stream was the most significant determinant for overall urinary conditions in patients who had a radical prostatectomy. Global satisfaction with treatment outcome was only marginally affected by urinary conditions. Physical function and psychological distress were major factors affecting the satisfaction level in this population.

This note corrects a claim made in the above-mentioned paper about the exact representation of a conditional preference network by means of a possibilistic logic base with partially ordered symbolic weights. We provide a counter-example that shows that the possibilistic logic representation is indeed not always exact. This is the basis of a short discussion on the difficulty of obtaining an exact representation.

On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decisionmaking

This paper proposes a sensor-based navigation which utilizes multicriteria decision making method in uncertain environments. The multicriteria decision-maker using fuzzy sets is used to select one of avoidance and goal-seeking behaviors according to global mission from higher level planner and situation around the mobile robot. Two behaviors are designed to produce the prescribed responses to currently perceived sensory information using fuzzy logic and reinforcement learning. A decision function to appropriately select one of two behaviors is formulated by use of a fuzzy set. The optimal alternative of two behaviors is defined as that achieving the highest degree of membership in fuzzy decision function. The effectiveness of the proposed method is verified by a series of simulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>