arXiv subjects

Mohammad Sedigh Chopannavaz

Publications and source records attributed to Mohammad Sedigh Chopannavaz.

4 recordsLinked to original sources

arXiv2026

Bipolar Fuzzy Minimum-Weight Satisfiability under Continuous t-Norms: A Clause-Witness Branch-and-Bound Framework

Minimum-weight satisfiability asks for a satisfying Boolean assignment of minimum cost, while many fuzzy decision and knowledge systems operate with graded positive and negative relations rather than crisp literals. This paper introduces a bipolar fuzzy minimum-weight satisfiability problem in which positive and negative clause--variable relations, target clause levels, and variable states are represented in the unit interval. The clause requirements are expressed by bipolar fuzzy relational equalities defined with an arbitrary continuous t-norm. Classical minimum-weight CNF satisfiability is recovered as a crisp special case, independently of the selected t-norm, and an optimal Boolean solution is shown to exist in that specialization even though the proposed formulation uses continuous variables. For the graded problem, clause satisfaction is characterized through admissible variable domains and effective clause-witness sets. This structure leads to an exact clause-witness branch-and-bound method with preprocessing, propagation, lower-point closure, and a disjoint-witness packing bound. Computational experiments verify the solver against explicit witness enumeration, mixed-integer baselines, and external SATLIB formulas; on a focused graded ablation set, the packing bound reduces the median number of explored nodes by about 45 percent relative to the single-row witness bound.

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arXiv2026

A bipolar fuzzy relation equation framework for clinical decision support systems

Clinical decision support frequently involves heterogeneous measurements, expert assessments, and guideline-based knowledge whose relationships to clinical decisions are gradual rather than purely binary. This paper develops a clinical decision-support framework based on bipolar fuzzy relational optimization, in which favorable and unfavorable clinical relationships are represented jointly through positive and negative fuzzy relational matrices together with a fuzzy requirement vector. The simultaneous participation of each decision variable and its complement in the relational constraints enables bipolar clinical information to be incorporated within a unified optimization model. The minimum \(t\)-norm is adopted to provide a noncompensatory, bottleneck-type interpretation of the interaction between fuzzy relational grades and decision levels. We characterize the feasible recommendation set by deriving clinical admissibility intervals and effective evidence activation sets, which provide the basis for feasibility analysis and systematic reduction of the relational system. The complete feasible set is then represented as a finite union of clinical recommendation regions associated with admissible Clinical Evidence-Assignment Functions. A region-wise optimal candidate is constructed for each admissible evidence assignment, and comparison of the resulting finite collection of candidates yields a globally optimal recommendation. An algorithm integrating feasibility analysis, system reduction, region-wise optimization, and global selection is developed and illustrated through a numerical CDSS example. The results show that bipolar fuzzy relational optimization provides a structured and mathematically rigorous mechanism for transforming fuzzy clinical relational information into feasible and optimized decision-support recommendations.

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arXiv2025

On the resolution and linear optimization problems subject to a system of bipolar fuzzy relational equalities defined with continuous Archimedean t-norms

This paper considers the linear objective function optimization with respect to a more general class of bipolar fuzzy relational equations, where the fuzzy compositions are defined by an arbitrary continuous Archimedean t-norm. In addition, a faster method for finding a global optimum is proposed. Analytical concepts and properties of the Archimedean bipolar fuzzy equations are investigated and two necessary conditions are presented to conceptualize the feasibility of the problem. It is shown that the feasible solution set can be resulted by a union of the finite number of compact sets, where each compact set is obtained by a function (called admissible function in this paper). Moreover, to accelerate identification of the mentioned compact sets (and therefore, to speed up solution finding), four simplification techniques are presented, which are based on either omitting redundant constraints and/or eliminating unknowns by assigning them a fixed value. Also, three additional simplification techniques are given to reduce the search domain by removing some parts of the feasible region that do not contain optimal solutions. Subsequently, a method is proposed to find an optimal solution for the current linear optimization problems. The proposed method consists of two accelerative strategies that are used during the problem solving process. By the first strategy, the method neglects some candidate solutions that are not optimal, by considering only a subset of admissible functions (called modified functions in this paper). As for the second strategy, a branch-and-bound method is used to delete non-optimal branches. Then, the method is summarized in an algorithm that represents all essential steps of the solution and finally, the whole method is applied in an example that has been chosen in such a way that the various situations are illustrated.

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arXiv2025

On the nonlinear programming problems subject to a system of generalized bipolar fuzzy relational equalities defined with continuous t-norms

As a starting point, this paper develops the system of bipolar fuzzy relational equations (FRE) to the most general case, where bipolar FREs are defined by an arbitrary continuous t-norm. Due to the fact that fuzzy relational equations are special cases of bipolar FREs, the proposed system can also be viewed as a generalization of traditional FREs, in which the fuzzy composition can be defined by a continuous t-norm. In order to determine the feasibility of the proposed system, some necessary and sufficient conditions are presented for studying continuous bipolar FREs. This is followed by a complete analysis of the set of feasible solutions to the problem. Contrary to FREs and bipolar FREs defined by continuous Archimedean t-norms, the feasible solutions set of generalized bipolar FREs consists of a finite number of compact sets that are not necessarily connected. Further, five techniques have been outlined in an attempt to simplify the current problem, and then an algorithm has been presented to find the feasible region of the problem. Next, we present a class of optimization models subject to continuous bipolar FRE constraints, in which the objective function incorporates a wide range of (non)linear functions, such as maximum functions, geometric mean functions, log-sum-exp functions, maximum eigenvalues of symmetric matrices, support functions for sets, etc. Considering that the problem has a finite number of local optimal solutions, the global optimal solution can always be obtained by choosing the point with the minimum objective value among these local optimal solutions. Lastly, as a means to illustrate the definitions, theorems, and algorithms presented in the paper, a step-by-step example is presented in several sections, in which the constraints are a system of bipolar FREs defined by the Dubois-Prade t-norm, which is a continuous non-Archimedean t-norm.

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