Decision Making and Analysis

Binary extended theta operation of binary soft sets

Aslıhan Sezgin — 2026-04-27

Binary soft set theory, first introduced by Açıkgöz and Taş in 2016, has become widely accepted as a technique for addressing and modeling uncertainty. Numerous theoretical and practical problems have been solved using this approach. Scholars have shown sustained interest in the theory's core concepts and operations since its inception. In this study, we propose the binary extended theta operation, a special binary soft set operation, and provide a thorough analysis of its basic algebraic features. We also study the distribution of this operation over certain types of binary soft set operations. By considering its algebraic properties and distribution rules, we show that, when combined with specific binary soft set operations, the binary extended theta operation forms many important algebraic structures within the collection of binary soft sets over the universe under certain conditions. The fundamental conceptual difference between the proposed binary extended theta operation and existing binary extended operations in the literature is that unlike approaches based on positive information aggregation, the theta operation systematically extracts negative information through common parameters and offers a unique and complementary tool, particularly for decision problems requiring reliable elimination, risk exclusion, and error detection. Further applications, including cryptology and decision-making, rely on operations of binary soft sets, making this theoretical subject essential from both theoretical and practical perspectives.

Proper edge coloring of direct product of path and star fuzzy graphs

Bacha Khan — 2026-05-15

This research explored adjacent vertex distinguishing proper edge coloring (AVDPEC) in the context of the direct product of fuzzy graphs, with particular emphasis on combinations of fuzzy path and fuzzy star graph. In this study, the classical coloring theory of crisp graphs were applied to fuzzy graphs, as membership values introduce an additional layer of intricacy to them. The main contribution of this research is an algorithm for the direct product of fuzzy path and fuzzy star networks, which acquires appropriate edge coloring that distinguishes adjacent vertices utilizing fuzzy membership values. In applications where recognizing between entities or tasks is crucial, this algorithm ensures that each adjacent vertex pair in the fuzzy graph product is identified by the specific colors of their incident edges. By using fuzzy membership values, we provided a versatile structure for managing complicated systems with incomplete or probabilistic interactions between nodes. We also introduced two significant applications of this edge coloring technique: load balancing in data networks and task parallelism in parallel computing. All things considered, our work strengthens the concept of AVDPEC in uncertain graphs, which benefits graph theory both hypothetically and essentially.

Stakeholder bias and group decision dynamics: mitigating cognitive biases with an integrated consensus-building process‎

Omid Hossein Zadeh — 2026-06-17

This study examines how stakeholder-driven preferential amplification affects outcomes in participatory group decision-making (DM) when allocation consequences have material significance. We structured development priorities for local value chains using the Analytic Network Process (ANP) and directly compared the pairwise judgments of value-chain representatives with those of other panel members to assess incentive alignment effects. Pre-consensus analysis revealed substantial divergence between stakeholder and non-stakeholder evaluations, indicating strong preferential positioning within the ANP structure under high-stakes conditions. We then implemented a structured Delphi-based iterative consensus refinement process and returned aggregated judgments (geometric means) to participants across two rounds to enable controlled reconsideration and revision. Post-iteration analysis shows a marked reduction in between-group divergence. Effect size assessment confirms moderation of extreme preferential positions rather than their complete elimination, consistent with the limited statistical power of small stakeholder subgroups. These findings demonstrate that participatory group DM frameworks remain essential for inclusive governance. However, when incentives are directly linked to allocation outcomes, decision architects should design balanced panel structures and incorporate structured consensus-feedback mechanisms to enhance robustness, transparency, and stability in ANP-based policy applications.

Fuzzy approach to analyzing a three-factor experiment with binary levels

Rahul Thakur — 2026-06-04

A factorial experiment is a widely used statistical analysis technique in experimental studies in agricultural and engineering sciences. The classical factorial experiment design considers several factors at different crisp levels, which are quantitatively measurable. However, factor levels are often imprecise, vague, incomplete, or described linguistically. In such cases, fuzzy statistics are used instead of classical statistics when analyzing data with uncertain observations. In this paper, we propose an extension of the classical factorial design for analyzing experiments with fuzzy observations. The experimental data are represented using triangular fuzzy numbers and transformed using the α-cut interval approach, resulting in lower-level and upper-level factorial models. These models are analyzed separately to evaluate the effects of factors and their interactions under uncertainty. The results are also compared with classical ANOVA applied to defuzzified data to highlight the advantages of incorporating uncertainty through fuzzy representations. Furthermore, the robustness of the proposed approach is examined through sensitivity analysis across different α levels. The findings demonstrate that the proposed fuzzy factorial approach provides a more flexible framework for analyzing experimental data in the presence of imprecision and uncertainty.

Novel Russell's approximation method for transportation problem under hesitant bifuzzy environment

Ismat Beg — 2025-12-30

Transportation problem is one of the significant linear programming problems that emerges in several conditions and gains attention of many researchers. Reducing a commodity's transportation expense to meet demand at destination is the goal of the transportation problem. However, uncertainty plays a vital role in real life, making it challenging for decision-makers to provide precise values for the coefficients related to the transportation problem. Hesitant bifuzzy sets are a notable advancement of fuzzy set theory, as they allow decision-makers to deal with every hesitancy without any restriction. This study aims to introduce a formulation of transportation problem under a hesitant bifuzzy environment. In this study, we have introduced a novel Russel approximation method (RAM) for the hesitant bifuzzy transportation problem, where every parameter is represented by hesitant bifuzzy elements. To show the applicability of the proposed method, a real-life illustration has been taken in this article. Additionally, to demonstrate the superiority of the proposed method, a comparative study has also been conducted with other existing methods, which results in the minimum transportation cost.